The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated. The plate exchanges heat with an external fluid. ...The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique. The velocity, temperature, skin friction, and Nusselt num- bers at the plates are discussed numerically and presented through graphs.展开更多
Several new techniques in the field of heat transfer in fluids have opened new avenues for studying the heat transfer effects in nanofluids and thermodynamic flow parameters, leading to novel applications. There have ...Several new techniques in the field of heat transfer in fluids have opened new avenues for studying the heat transfer effects in nanofluids and thermodynamic flow parameters, leading to novel applications. There have been studies on nanofluids, including metal, ceramic and magnetic nanoparticles mixed with base fluids such as Water, Kerosene, and Ethylene glycol. However, research on fluids employing semiconductor nanoparticles as supplements to base fluids to generate nanofluids and hybrid nanofluids is limited. For the investigation, Gallium nitrite, a binary semiconductor with excellent heat convection, is together with Cu metal nanoparticles and Al<sub>2</sub>O<sub>3</sub> ceramic nanoparticles separately in the base fluid Ethylene glycol (EG) to form hybrid nanofluids. The effects of convective boundary conditions, thermal radiation, heat source/sink, suction/injection, and activation energy on three-dimensional Williamson MHD hybrid nanofluid flow of Cu + GaN + EG, Al<sub>2</sub>O<sub>3</sub> + GaN + EG, and Cu + Al<sub>2</sub>O<sub>3</sub> + EG are investigated on a stretched sheet with porosity. A similarity transformation is performed on the governing equations to transform them into dimensionless ordinary differential equations ODEs. Numerical analysis is carried out in MATLAB utilizing bvp5c and the shooting technique. The variations of velocity, temperature, and concentration profiles as a function of different physical effects are presented graphically with dimensionless parameters and explained the variations scientifically. As varied with different parameters, the values of the Skin-friction coefficient, Nusselt number, and Sherwood number are mentioned in the table.展开更多
The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary laye...The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into coupled nonlinear ordinary differential equations. The ordinary differential equations are solved numerically by the Bvp4c with MATLAB, which is a collocation method equivalent to the fourth-order mono-implicit Runge-Kutta method. Furthermore, more attention is paid to the effects of the physical parameters, especially the parameters related to nanoparticles, on the temperature and concentration distributions with consideration of permeability and the heat source/sink.展开更多
The present study deals with the flow over a nonlinearly stretching sheet of Casson fluid with the effects of radiation and heat source/sink. The Casson fluid model is used to characterize the non-Newtonian fluid beha...The present study deals with the flow over a nonlinearly stretching sheet of Casson fluid with the effects of radiation and heat source/sink. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of justified similarity transformations the governing equations were reduced to couple nonlinear ordinary differential equations. The effective numerical technique Keller Box method is used to solve these equations. The variations in velocity, temperature profiles were presented with the various values of nonlinear stretching parameter n and Casson parameter β. The nature of Skinfriction and Local nusselt number has presented. Effects of radiation and heat source/sink on temperature profiles have been discussed.展开更多
An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. ...An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. Heat transfer characteristics are examined for two different kinds of boundary conditions, namely 1) variable wall temperature and 2) variable heat flux. The governing partial differential equations are transformed to system of ordinary differential equations. These equations are solved numerically by applying RKF-45 method. The effects of various physical parameters such as magnetic parameter, dust interaction parameter, number density, Prandtl number, Eckert number, heat source/sink parameter and unsteadiness parameter on velocity and temperature profiles are studied.展开更多
This work is focused on the effects of heat source/sink, viscous dissipation, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a nonlinear stretching sheet. The similarity ...This work is focused on the effects of heat source/sink, viscous dissipation, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a nonlinear stretching sheet. The similarity transformations have been used to convert the governing partial differential equations into a set of nonlinear ordinary differential equations. These equations are then solved numerically using a very efficient implicit finite difference method. Favorable comparison with previously published work is performed and it is found to be in excellent agreement. The results of this parametric study are shown in several plots and tables and the physical aspects of the problem are highlighted and discussed.展开更多
The purpose of this paper is to find the effect of heat source/sink parameter on free convective flow of a polar fluid in open-ended vertical concentric annuli. Exact solutions of the non-dimensional differential equa...The purpose of this paper is to find the effect of heat source/sink parameter on free convective flow of a polar fluid in open-ended vertical concentric annuli. Exact solutions of the non-dimensional differential equations describing the flow model have been obtained one by one for two different cases of source and sink. To observe the effect of the physical parameters such as source/sink and vertex viscosity, the numerical results of the velocity and microrotational velocity are finally shown on the graphs.展开更多
Using the 1961–1995 monthly averaged meteorological data from 148 surface stations in the Qinghai-Xizang Plateau (QXP) and its surrounding areas, calculation of the 35-year atmospheric heat source/sink (<Qi>) a...Using the 1961–1995 monthly averaged meteorological data from 148 surface stations in the Qinghai-Xizang Plateau (QXP) and its surrounding areas, calculation of the 35-year atmospheric heat source/sink (<Qi>) and an analysis on its climatic features and relation to rainfall in China have been made. It is found that on the average, the atmospheric heat source over the QXP is the strongest in June (78 W / m2) and cold source is the strongest in December (?72 W/m2). The sensible heat of the surface increases remarkably over the southwest of the QXP, causing the obvious increase of <Qi> there in February and March, which makes a center of the atmospheric heat source appear over the north slope of the Himalayas. Afterwards, this center continues to intensify and experiences noticeable migration westwards twice, separately occurring in April and June. The time when the atmosphere over the east of the QXP becomes heat source and reaches strongest is one month later than that over the southwest of the QXP. In summer, the latent heat of condensation becomes a heating factor as important as the sensible heat and is also a main factor that makes the atmospheric heat source over the east of the QXP continue growing. On the interdecadal time scale, (Q1) of the QXP shows an abrupt change in 1977 and a remarkable increase after 1977. The atmospheric heat source of the spring over the QXP is a good indicator for the subsequent summer rainfall over the valleys of the Changjiang and Huaihe rivers and South China and North China. There is remarkable positive correlation between the QXP heat source of summer and the summer rainfall in the valleys of the Changjiang River.展开更多
Based on the 1961-1995 atmospheric apparent heat source/sink and the 1961-1990 snow-cover days and depth over the Qinghai-Xizang Plateau (QXP) and the 1961-1995 reanalysis data of NCEP/NCAR and the 1975-1994 OLR data,...Based on the 1961-1995 atmospheric apparent heat source/sink and the 1961-1990 snow-cover days and depth over the Qinghai-Xizang Plateau (QXP) and the 1961-1995 reanalysis data of NCEP/NCAR and the 1975-1994 OLR data, this paper discusses the interannual variability of the heat regime and its relation to atmospheric circulation It is shown that the interannual variability is pronounced, with maximal variability in spring and autumn, and the variability is heterogeneous horizontally. In the years with the weak (or strong) winter cold source, the deep trough over East Asia is to the east (or west) of its normal, which corresponds to strong (or weak) winter monsoon in East Asia. In the years with the strong (or weak) sum mer heat source, there exists an anomalous cyclone (or anticyclone) in the middle and lower troposphere over the QXP and ifs neighborhood and anomalous southwest (or northeast) winds over the Yangtze River valley of China, corresponding to strong (or weak) summer monsoon in East Asia. The summer heat source of the QXP is related to the intensity and position of the South Asia high. The QXP snow cover condition of April has a close relation to the heating intensity of summer. There is a remarkable negative correlation between the summer heat source of the QXP and the convection over the southeastern QXP, the Bay of Bengal, the Indo-China Peninsula, the southeastern Asia, the southwest part of China and the lower reaches of the Yangtze River and in the area from the Yellow Sea of China to the Sea of Japan.展开更多
The Tibetan Plateau(TP),acting as a large elevated land surface and atmospheric heat source during spring and summer,has a substantial impact on regional and global weather and climate.To explore the multi-scale tempo...The Tibetan Plateau(TP),acting as a large elevated land surface and atmospheric heat source during spring and summer,has a substantial impact on regional and global weather and climate.To explore the multi-scale temporal variation in the thermal forcing effect of the TP,here we calculated the surface sensible heat and latent heat release based on 6-h routine observations at 80(32)meteorological stations during the period 1979–2016(1960–2016).Meanwhile,in situ air-column net radiation cooling during the period 1984–2015 was derived from satellite data.This new data-set provides continuous,robust,and the longest observational atmospheric heat source/sink data over the third pole,which will be helpful to better understand the spatial-temporal structure and multi-scale variation in TP diabatic heating and its influence on the earth’s climatic system.展开更多
Micropolar theories present an excellent mechanism for exploring new non-Newtonian materials processing provides a stimulating area for process engineering simulation.Motivated by area for process engineering applicat...Micropolar theories present an excellent mechanism for exploring new non-Newtonian materials processing provides a stimulating area for process engineering simulation.Motivated by area for process engineering applications,the present article presents the scope offinite element method in solving a mathematical model for magnetohydrodynamic,incom-pressible,dissipative and chemically reacting micropolar fluid flow and heat and mass transferthrough a porous medium from an inclined plate with heat sourcelsink has been investigated.For this purpose,the set of governing equations have been reframed and put into adimensionless form under the assumption of low Reynolds number with appropriatedimensionless quantities that can fit into the finite element fommulation.In addition tohighlighting the operational aspects of weighted residual scheme,a detailed investigation hasbeen camied out on the associated flow stnucture,heat and mass transfer.The evolution ofmany multi-physical parameters in these variables is illustrated graphically.Finite elementcode is benchmarked with the results reported in the literature to check the validity andaccuracy under some limiting cases and excellent agreement is seen with published solutionsand results of skin friction coefficient,couple stress coefficient,Nusselt number and Sherwoodnumber for invoked parameter are tabulated which shows that increasing heat sourcelsinkparameter elevates temperature.Chemical reaction parameter reduces velocity and concentra-tion gradients.Sherwood number enhances as chemical reaction parameter increases but reverse phenomena is observed in case of inclination of angle.Furthermore,a gridindependency test has been caried out for different grid sizes which has proven this methodis adequate.展开更多
This study focuses on the combined impact of heat source/sink and chemical reaction on slip flow of micropolar fluid through a permeable wedge in the existence of Hall and ion-slip currents.The governing highly non-li...This study focuses on the combined impact of heat source/sink and chemical reaction on slip flow of micropolar fluid through a permeable wedge in the existence of Hall and ion-slip currents.The governing highly non-lincar PDEs were altered into a set of non-linear coupled ODEs by using similarity transformations.Differential transformation method(DTM)has been implemented in transformed ODEs equations.The comparison with previous literatures was performed and the data of this study was found to be in accordance with each other.The analytical solutions for skin-friction coefficients(surface drag forces),Nussclt and Sherwood numbers are depicted through graphs and tables.The study of boundary layer flow over a wedge surface plays an imperative role in the field of aerodynamics,heat exchanger,ground water pollution and geothermal system etc.展开更多
In this paper,an investigation is made to study the effects of radiation and heat source/sink on the unsteady boundary layerflow and heat transfer past a shrinking sheet with suction/injection.Theflow is permeated by an...In this paper,an investigation is made to study the effects of radiation and heat source/sink on the unsteady boundary layerflow and heat transfer past a shrinking sheet with suction/injection.Theflow is permeated by an externally applied magneticfield normal to the plane offlow.The self-similar equations correspond-ing to the velocity and temperaturefields are obtained,and then solved numerically byfinite difference method using quasilinearization technique.The study reveals that the momentum boundary layer thickness increases with increasing unsteadiness and decreases with magneticfield.The thermal boundary layer thickness decreases with Prandtl number,radiation parameter and heat sink parameter,but it increases with heat source parameter.Moreover,increasing unsteadiness,magneticfield strength,radiation and heat sink strength boost the heat transfer.展开更多
Ground source heat pump systems demonstrate significant potential for northern rural heating applications;however,the effectiveness of these systems is often limited by challenging geological conditions.For instance,i...Ground source heat pump systems demonstrate significant potential for northern rural heating applications;however,the effectiveness of these systems is often limited by challenging geological conditions.For instance,in certain regions,the installation of buried pipes for heat exchangers may be complicated,and these pipes may not always serve as efficient low-temperature heat sources for the heat pumps of the system.To address this issue,the current study explored the use of solar-energy-collecting equipment to supplement buried pipes.In this design,both solar energy and geothermal energy provide low-temperature heat to the heat pump.First,a simulation model of a solar‒ground source heat pump coupling system was established using TRNSYS.The accuracy of this model was validated through experiments and simulations on various system configurations,including varying numbers of buried pipes,different areas of solar collectors,and varying volumes of water tanks.The simulations examined the coupling characteristics of these components and their influence on system performance.The results revealed that the operating parameters of the system remained consistent across the following configurations:three buried pipes,burial depth of 20 m,collector area of 6 m^(2),and water tank volume of 0.5 m^(3);four buried pipes,burial depth of 20 m,collector area of 3 m^(2),and water tank volume of 0.5 m^(3);and five buried pipes with a burial depth of 20 m.Furthermore,the heat collection capacity of the solar collectors spanning an area of 3 m^(2)was found to be equivalent to that of one buried pipe.Moreover,the findings revealed that the solar‒ground source heat pump coupling system demonstrated a lower annual cumulative energy consumption compared to the ground source heat pump system,presenting a reduction of 5.31%compared to the energy consumption of the latter.展开更多
The arsenic(As)release from sediments in great lakes is affected by various factors.In this study,the characteristics of As release fromsediments was investigated,and the As sources and sinks with the strengths in sed...The arsenic(As)release from sediments in great lakes is affected by various factors.In this study,the characteristics of As release fromsediments was investigated,and the As sources and sinks with the strengths in sediments from different areas(grass-type,algae-type,and grass-algae alternation areas)in great shallow lakes(Taihu Lake,China)were analyzed,and the influence of P competition in the process of As release was also studied.The results showed that changing trend of the values of equilibrium As concentration in sediments were consistent with the regional changes(0 to 28.12μg/L),and the sediments from algaetype areas had the higher values.The sediments from western lake and northwest lake bay were a strong As and a weak P source,and the north lake bay had the opposite trend of these two regions.Intense P source competition with As from the sediments occurred in algae-type areas.The grass-type areas had strong As and P retention capacities,indicating a sink role of sediment with high As and P sorption capacities.The degree of As and P saturation had similar trend in sediments,and the grass-type areas had the higher values,18.3%-21.4%and 15.31%-20.34%,respectively.Contribution analysis results showed that most of As release contribution was from the bottom(30-50 cm)sediments,and the surface(0-10 cm)sediments from algae-type areas contributed more to the overlying water than other region.展开更多
The apparent heat sources (?Q1 ?) and moisture sinks (?Q2 ?) are calculated based on the reanalyzed data of the South China Sea Monsoon Experiment (SCSMEX) from May 1 to August 31, 1998. It is found that the formation...The apparent heat sources (?Q1 ?) and moisture sinks (?Q2 ?) are calculated based on the reanalyzed data of the South China Sea Monsoon Experiment (SCSMEX) from May 1 to August 31, 1998. It is found that the formation and distribution of the atmospheric heat sources are important for the monsoon onset. The earlier onset of the SCS monsoon is the result of enduring atmospheric heating in the Indo–China Peninsula and South China areas. The atmospheric heating firstly appears in the Indo–China Peninsula area and the sensible heat is the major one. The 30–50 day periodic oscillation of atmospheric heat sources between the SCS area and the western Pacific warm pool has a reverse phase distribution before the middle of July and the low frequency oscillation of heat sources in SCS area has an obvious longitudinal propagation. The 30–50 day low frequency oscillation has vital modificatory effects on the summer monsoon evolution during 1998. Key words Apparent heat sources - Apparent moisture sinks - The South China Sea monsoon - Diagnostic Study Sponsored by the National Key Project of Fundamental Research “ SCSMEX” and the Research Fund for the Doctoral Program of Higher Education: “ Study of the Air-sea Interaction in the SCS Monsoon Region”.展开更多
An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a param...An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a parameter estimation problem)and a time-varying heat source is considered in the transient heat transfer problem(a function estimation problem).Since a general irregular 2D heat conducting body is considered,a body-fitted grid generation is used to mesh the domain.Then governing equations and associated boundary and initial conditions are transformed from the physical domain to the computational domain and finite difference method is used to solve the governing equations to obtain the temperature distribution in the body.Using an efficient,accurate,and very easy to implement sensitivity analysis incorporated in a gradient based minimization method(here,steepest descentmethod),the unknown heat source is estimated accurately.In the function estimation part,it is assumed that there is no prior information on the functional form of the heat source and the estimation process can be performed with a reasonable initial guess for the heat source.The main advantage of the proposed inverse analysis is that the sensitivity matrix(and hence,the objective function gradient with respect to the unknown variables)can be computed during the direct heat transfer solution through newyet simple explicit expressions with no need to solve extra equations such as the sensitivity and adjoint problems and impose additional computational costs comparable to the direct problem solution ones.Some test cases are presented to investigate the accuracy,efficiency,and effect of measurement error on the estimated parameter and function for the line heat source.展开更多
Using the summer (June to August) monthly mean data of the National Centers for Environmental Predictions (NCEP) - National Center for Atmospheric Research (NCAR) reanalysis from 1980 to 1997, atmospheric heat sources...Using the summer (June to August) monthly mean data of the National Centers for Environmental Predictions (NCEP) - National Center for Atmospheric Research (NCAR) reanalysis from 1980 to 1997, atmospheric heat sources and moisture sinks are calculated. Anomalous circulation and the vertically integrated heat source with the vertical integrated moisture sink and outgoing longwave radiation (OLR) flux are examined based upon monthly composites for 16 great wet-spells and 8 great dry-spells over the middle-lower reaches of the Yangtze River. The wind anomaly exhibits prominent differences between the great wet-spell and the great dry-spell over the Yangtze River Valley. For the great wet-spell, the anomalous southerly from the Bay of Bengal and the South China Sea and the anomalous northerly over North China enhanced low-level convergence toward a narrow latitudinal belt area (the middle-lower reaches of the Yangtze River). The southerly anomaly is connected with an anticyclonic anomalous circulation system centered at 22 degreesN, 140 degreesE and the northerly anomaly is associated with a cyclonic anomalous circulation system centered at the Japan Sea. In the upper level, the anomalous northwesterly between an anticyclonic anomalous system with the center at 23 degreesN, 105 degreesE and a cyclonic anomalous system with the center at Korea diverged over the middle-lower reaches of the Yangtze River. On the contrary, for the great dry-spell, the anomalous northerly over South China and the anomalous southerly over North China diverged from the Yangtze River Valley in the low level. The former formed in the western part of a cyclonic anomalous system centered at 23 degreesN, 135 degreesE. The latter was located in the western ridge of an anticyclonic anomalous system in the northwestern Pacific. The upper troposphere showed easterly anomaly that converged over the middle-lower reaches of the Yangtze River. A cyclonic anomalous system in South China and an anticyclonic system centered in the Japan Sea enhanced the easterly. Large atmospheric heat source anomalies of opposite signs existed over the western Pacific - the South China Sea, with negative in the great wet-spell and positive in the great dry-spell. The analysis of heat source also revealed positive anomalous heat sources during the great wet-spell and negative anomalous heat sources during the great dry-spell over the Yangtze River valley. The changes of the moisture sink and OLR were correspondingly altered, implying the change of heat source anomaly is due to the latent heat releasing of convective activity. Over the southeastern Tibetan Plateau- the Bay of Bengal, the analysis of heat source shows positive anomalous heat sources during the great wet-spell and negative anomalous heat sources during the great dry-spell because of latent heating change. The change of divergent wind coexisted with the change of heat source. In the great wet-spell, southerly divergent wind anomaly in the low level and northerly divergent wind anomaly in high-level are seen over South China. These divergent wind anomalies are helpful to the low-level convergence anomaly and high-level divergence anomaly over the Yangtze River valley. The low-level northerly divergent wind anomaly and high-level southerly divergent wind anomaly over South China reduced the low-level convergence and high-level divergence over the Yangtze River valley during the great dry-spell.展开更多
An innovative and accurate method for controlling the interfacial structure of Mg-alloy/steel direct lap joints using a hybrid laser-gas tungsten arc(GTA)flexible control heat source was proposed.The study investigate...An innovative and accurate method for controlling the interfacial structure of Mg-alloy/steel direct lap joints using a hybrid laser-gas tungsten arc(GTA)flexible control heat source was proposed.The study investigated the impact of spatial regulation of a flexible hybrid heat source on the thermal gradient distribution across the joint geometry and the resulting stress states in the joints,revealing the respective bonding and strengthening mechanisms.The findings indicate that the malposition alters the thermal gradient distribution within the joint,influencing the metallurgical bonding area,interfacial structure,fracture mode,and fracture path.Furthermore,the results showed that varying the laser pulse frequency affected the frequency of the laser-induced arc and the number of keyholes generated per unit length of the joint,which effectively altered the joint geometry and interfacial stress state,and could be used to enhance the load-bearing capacity of the joints.The joint's maximum load was measured to be 325.2 N/mm,which is approximately 88%of the Mg-alloy matrix and the highest reported strength for Mg alloy-steel dissimilar lap joints.A composite interfacial layer structure was achieved,consisting of Al_(11)(Mn,Fe)_(4)and a small amount of Mg_(2)Al_(3)intermetallic compounds(IMCs)at the weld front,along with Al_(11)(Mn,Fe)_(4)and Fe3Al IMCs in the weld middle.The key factors to achieving a high bonding strength of Mg-alloy/steel lap joints have been summarized.This study provides a technical and theoretical reference for the precise collaborative control of joint geometry,interfacial structure,and mechanical properties of dissimilar material lap joints.展开更多
This paper deals with an unsteady magnetohydrodynamics(MHD)heat and masstransfer for a viscous incompressible fluid through a vertical stretching surface embedded ina Darcy-Forchheimer porous medium in the presence of...This paper deals with an unsteady magnetohydrodynamics(MHD)heat and masstransfer for a viscous incompressible fluid through a vertical stretching surface embedded ina Darcy-Forchheimer porous medium in the presence of a non-uniform heat source/sink andfirst-order chemical reaction.The porous surface is subjected to a uniform transverse magneticfield.The influence of velocity,thermal,and concentration slip is also investigated.The governing equations are coupled non-linear partial differential equations,which have been converted via similarity transformation into a set of ordinary differential equations.The resultantsystem of non-linear ordinary differential equations has been solved numerically with the helpof the“MATLAB”BVP4C Solver.Results are presented graphically to analyze the effects ofvarious physical parameters discovered in the problem such as Hartmann number(M),Forchheimer number(Fr),Grashof number(Gr),solutal Grashof number(Gc),suction parameter(S),porosity parameter(el),dimensionless velocity slip(Sv),Prandtl number(Pr),dimensionless thermal slip(St),space-dependent heat source/sink parameter(eA1),temperature-dependent heat source/sink(eB)1),Eckert number(Ec),Schmidt number(Sc),chemical reaction parameter(g),unsteadiness parameter(A),and dimensionless concentration slip(Sc)on non-dimensionalvelocity ec0ðhÞ,temperature zðhÞ,and concentration efðhÞprofiles.The influence of these parameters on skin-friction coefficient(C)f),Nusselt number(Nu)x),and Sherwood number(Sh)x)areexpressed in tabular form.It is observed that an enhancement in Fr and el results in the declination of the velocity profile.There is an enhancement in temperature with an increment in theeA)1 and eB)1.The physical representation of flow characteristics that appeared in the problem ispresented using various graphs to depict real-world applications in industrial and engineeringoperations.The results were compared to previous studies,revealing that the two are in goodagreement.The novelty of the present investigation is:To interpret the combined effects ofviscous dissipation and Joule heating on a vertical stretching surface embedded in a highlyporous medium modeled using the Darcy-Forchheimer model.The findings could be valuablein understanding the flow of oil,gas,and water through an oil or gas field reservoir,as well asgroundwater migration and filtering and purification procedures.展开更多
基金University Grant Commission in New Delhi for the financial support under UGC-Major Research Project and Maulana Azad National Fellowship for Minority Students
文摘The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique. The velocity, temperature, skin friction, and Nusselt num- bers at the plates are discussed numerically and presented through graphs.
文摘Several new techniques in the field of heat transfer in fluids have opened new avenues for studying the heat transfer effects in nanofluids and thermodynamic flow parameters, leading to novel applications. There have been studies on nanofluids, including metal, ceramic and magnetic nanoparticles mixed with base fluids such as Water, Kerosene, and Ethylene glycol. However, research on fluids employing semiconductor nanoparticles as supplements to base fluids to generate nanofluids and hybrid nanofluids is limited. For the investigation, Gallium nitrite, a binary semiconductor with excellent heat convection, is together with Cu metal nanoparticles and Al<sub>2</sub>O<sub>3</sub> ceramic nanoparticles separately in the base fluid Ethylene glycol (EG) to form hybrid nanofluids. The effects of convective boundary conditions, thermal radiation, heat source/sink, suction/injection, and activation energy on three-dimensional Williamson MHD hybrid nanofluid flow of Cu + GaN + EG, Al<sub>2</sub>O<sub>3</sub> + GaN + EG, and Cu + Al<sub>2</sub>O<sub>3</sub> + EG are investigated on a stretched sheet with porosity. A similarity transformation is performed on the governing equations to transform them into dimensionless ordinary differential equations ODEs. Numerical analysis is carried out in MATLAB utilizing bvp5c and the shooting technique. The variations of velocity, temperature, and concentration profiles as a function of different physical effects are presented graphically with dimensionless parameters and explained the variations scientifically. As varied with different parameters, the values of the Skin-friction coefficient, Nusselt number, and Sherwood number are mentioned in the table.
基金supported by the National Natural Science Foundation of China(No.11302024)the Fundamental Research Funds for the Central Universities(No.FRF-TP-15-036A3)+1 种基金the Beijing Higher Education Young Elite Teacher Project(No.YETP0387)the Foundation of the China Scholarship Council in 2014(No.154201406465041)
文摘The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into coupled nonlinear ordinary differential equations. The ordinary differential equations are solved numerically by the Bvp4c with MATLAB, which is a collocation method equivalent to the fourth-order mono-implicit Runge-Kutta method. Furthermore, more attention is paid to the effects of the physical parameters, especially the parameters related to nanoparticles, on the temperature and concentration distributions with consideration of permeability and the heat source/sink.
文摘The present study deals with the flow over a nonlinearly stretching sheet of Casson fluid with the effects of radiation and heat source/sink. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of justified similarity transformations the governing equations were reduced to couple nonlinear ordinary differential equations. The effective numerical technique Keller Box method is used to solve these equations. The variations in velocity, temperature profiles were presented with the various values of nonlinear stretching parameter n and Casson parameter β. The nature of Skinfriction and Local nusselt number has presented. Effects of radiation and heat source/sink on temperature profiles have been discussed.
文摘An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. Heat transfer characteristics are examined for two different kinds of boundary conditions, namely 1) variable wall temperature and 2) variable heat flux. The governing partial differential equations are transformed to system of ordinary differential equations. These equations are solved numerically by applying RKF-45 method. The effects of various physical parameters such as magnetic parameter, dust interaction parameter, number density, Prandtl number, Eckert number, heat source/sink parameter and unsteadiness parameter on velocity and temperature profiles are studied.
文摘This work is focused on the effects of heat source/sink, viscous dissipation, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a nonlinear stretching sheet. The similarity transformations have been used to convert the governing partial differential equations into a set of nonlinear ordinary differential equations. These equations are then solved numerically using a very efficient implicit finite difference method. Favorable comparison with previously published work is performed and it is found to be in excellent agreement. The results of this parametric study are shown in several plots and tables and the physical aspects of the problem are highlighted and discussed.
文摘The purpose of this paper is to find the effect of heat source/sink parameter on free convective flow of a polar fluid in open-ended vertical concentric annuli. Exact solutions of the non-dimensional differential equations describing the flow model have been obtained one by one for two different cases of source and sink. To observe the effect of the physical parameters such as source/sink and vertex viscosity, the numerical results of the velocity and microrotational velocity are finally shown on the graphs.
基金the National Natural Science Foundation of China (Grant No. 40075018).
文摘Using the 1961–1995 monthly averaged meteorological data from 148 surface stations in the Qinghai-Xizang Plateau (QXP) and its surrounding areas, calculation of the 35-year atmospheric heat source/sink (<Qi>) and an analysis on its climatic features and relation to rainfall in China have been made. It is found that on the average, the atmospheric heat source over the QXP is the strongest in June (78 W / m2) and cold source is the strongest in December (?72 W/m2). The sensible heat of the surface increases remarkably over the southwest of the QXP, causing the obvious increase of <Qi> there in February and March, which makes a center of the atmospheric heat source appear over the north slope of the Himalayas. Afterwards, this center continues to intensify and experiences noticeable migration westwards twice, separately occurring in April and June. The time when the atmosphere over the east of the QXP becomes heat source and reaches strongest is one month later than that over the southwest of the QXP. In summer, the latent heat of condensation becomes a heating factor as important as the sensible heat and is also a main factor that makes the atmospheric heat source over the east of the QXP continue growing. On the interdecadal time scale, (Q1) of the QXP shows an abrupt change in 1977 and a remarkable increase after 1977. The atmospheric heat source of the spring over the QXP is a good indicator for the subsequent summer rainfall over the valleys of the Changjiang and Huaihe rivers and South China and North China. There is remarkable positive correlation between the QXP heat source of summer and the summer rainfall in the valleys of the Changjiang River.
基金the auspices of the National!(G1998040800)CAS's Key Project for Basic Research on the Tibetan Plateau! (KZ951-A1-204, KZ95T-
文摘Based on the 1961-1995 atmospheric apparent heat source/sink and the 1961-1990 snow-cover days and depth over the Qinghai-Xizang Plateau (QXP) and the 1961-1995 reanalysis data of NCEP/NCAR and the 1975-1994 OLR data, this paper discusses the interannual variability of the heat regime and its relation to atmospheric circulation It is shown that the interannual variability is pronounced, with maximal variability in spring and autumn, and the variability is heterogeneous horizontally. In the years with the weak (or strong) winter cold source, the deep trough over East Asia is to the east (or west) of its normal, which corresponds to strong (or weak) winter monsoon in East Asia. In the years with the strong (or weak) sum mer heat source, there exists an anomalous cyclone (or anticyclone) in the middle and lower troposphere over the QXP and ifs neighborhood and anomalous southwest (or northeast) winds over the Yangtze River valley of China, corresponding to strong (or weak) summer monsoon in East Asia. The summer heat source of the QXP is related to the intensity and position of the South Asia high. The QXP snow cover condition of April has a close relation to the heating intensity of summer. There is a remarkable negative correlation between the summer heat source of the QXP and the convection over the southeastern QXP, the Bay of Bengal, the Indo-China Peninsula, the southeastern Asia, the southwest part of China and the lower reaches of the Yangtze River and in the area from the Yellow Sea of China to the Sea of Japan.
基金This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences[grant number XDA19070404]the National Natural Science Foundation of China[grant numbers 41725018 and 91637312].
文摘The Tibetan Plateau(TP),acting as a large elevated land surface and atmospheric heat source during spring and summer,has a substantial impact on regional and global weather and climate.To explore the multi-scale temporal variation in the thermal forcing effect of the TP,here we calculated the surface sensible heat and latent heat release based on 6-h routine observations at 80(32)meteorological stations during the period 1979–2016(1960–2016).Meanwhile,in situ air-column net radiation cooling during the period 1984–2015 was derived from satellite data.This new data-set provides continuous,robust,and the longest observational atmospheric heat source/sink data over the third pole,which will be helpful to better understand the spatial-temporal structure and multi-scale variation in TP diabatic heating and its influence on the earth’s climatic system.
文摘Micropolar theories present an excellent mechanism for exploring new non-Newtonian materials processing provides a stimulating area for process engineering simulation.Motivated by area for process engineering applications,the present article presents the scope offinite element method in solving a mathematical model for magnetohydrodynamic,incom-pressible,dissipative and chemically reacting micropolar fluid flow and heat and mass transferthrough a porous medium from an inclined plate with heat sourcelsink has been investigated.For this purpose,the set of governing equations have been reframed and put into adimensionless form under the assumption of low Reynolds number with appropriatedimensionless quantities that can fit into the finite element fommulation.In addition tohighlighting the operational aspects of weighted residual scheme,a detailed investigation hasbeen camied out on the associated flow stnucture,heat and mass transfer.The evolution ofmany multi-physical parameters in these variables is illustrated graphically.Finite elementcode is benchmarked with the results reported in the literature to check the validity andaccuracy under some limiting cases and excellent agreement is seen with published solutionsand results of skin friction coefficient,couple stress coefficient,Nusselt number and Sherwoodnumber for invoked parameter are tabulated which shows that increasing heat sourcelsinkparameter elevates temperature.Chemical reaction parameter reduces velocity and concentra-tion gradients.Sherwood number enhances as chemical reaction parameter increases but reverse phenomena is observed in case of inclination of angle.Furthermore,a gridindependency test has been caried out for different grid sizes which has proven this methodis adequate.
文摘This study focuses on the combined impact of heat source/sink and chemical reaction on slip flow of micropolar fluid through a permeable wedge in the existence of Hall and ion-slip currents.The governing highly non-lincar PDEs were altered into a set of non-linear coupled ODEs by using similarity transformations.Differential transformation method(DTM)has been implemented in transformed ODEs equations.The comparison with previous literatures was performed and the data of this study was found to be in accordance with each other.The analytical solutions for skin-friction coefficients(surface drag forces),Nussclt and Sherwood numbers are depicted through graphs and tables.The study of boundary layer flow over a wedge surface plays an imperative role in the field of aerodynamics,heat exchanger,ground water pollution and geothermal system etc.
基金the financial support of National Board for Higher Mathematics(NBHM),DAE,Mumbai,India for pursuing this work.
文摘In this paper,an investigation is made to study the effects of radiation and heat source/sink on the unsteady boundary layerflow and heat transfer past a shrinking sheet with suction/injection.Theflow is permeated by an externally applied magneticfield normal to the plane offlow.The self-similar equations correspond-ing to the velocity and temperaturefields are obtained,and then solved numerically byfinite difference method using quasilinearization technique.The study reveals that the momentum boundary layer thickness increases with increasing unsteadiness and decreases with magneticfield.The thermal boundary layer thickness decreases with Prandtl number,radiation parameter and heat sink parameter,but it increases with heat source parameter.Moreover,increasing unsteadiness,magneticfield strength,radiation and heat sink strength boost the heat transfer.
基金supported by 2024 Central Guidance Local Science and Technology Development Fund Project"Study on the mechanism and evaluation method of thermal pollution in water bodies,as well as research on thermal carrying capacity".(Grant 246Z4506G)Key Research and Development Project in Hebei Province:"Key Technologies and Equipment Research and Demonstration of Multiple Energy Complementary(Electricity,Heat,Cold System)for Solar Energy,Geothermal Energy,Phase Change Energy"(Grant 236Z4310G)the Hebei Academy of Sciences Key Research and Development Program"Research on Heat Transfer Mechanisms and Efficient Applications of Intermediate and Deep Geothermal Energy"(22702)。
文摘Ground source heat pump systems demonstrate significant potential for northern rural heating applications;however,the effectiveness of these systems is often limited by challenging geological conditions.For instance,in certain regions,the installation of buried pipes for heat exchangers may be complicated,and these pipes may not always serve as efficient low-temperature heat sources for the heat pumps of the system.To address this issue,the current study explored the use of solar-energy-collecting equipment to supplement buried pipes.In this design,both solar energy and geothermal energy provide low-temperature heat to the heat pump.First,a simulation model of a solar‒ground source heat pump coupling system was established using TRNSYS.The accuracy of this model was validated through experiments and simulations on various system configurations,including varying numbers of buried pipes,different areas of solar collectors,and varying volumes of water tanks.The simulations examined the coupling characteristics of these components and their influence on system performance.The results revealed that the operating parameters of the system remained consistent across the following configurations:three buried pipes,burial depth of 20 m,collector area of 6 m^(2),and water tank volume of 0.5 m^(3);four buried pipes,burial depth of 20 m,collector area of 3 m^(2),and water tank volume of 0.5 m^(3);and five buried pipes with a burial depth of 20 m.Furthermore,the heat collection capacity of the solar collectors spanning an area of 3 m^(2)was found to be equivalent to that of one buried pipe.Moreover,the findings revealed that the solar‒ground source heat pump coupling system demonstrated a lower annual cumulative energy consumption compared to the ground source heat pump system,presenting a reduction of 5.31%compared to the energy consumption of the latter.
基金supported by the National Natural Science Foundation(Nos.52000024 and 41907335)the Natural Science Foundation of Shanghai(No.23ZR1400700).
文摘The arsenic(As)release from sediments in great lakes is affected by various factors.In this study,the characteristics of As release fromsediments was investigated,and the As sources and sinks with the strengths in sediments from different areas(grass-type,algae-type,and grass-algae alternation areas)in great shallow lakes(Taihu Lake,China)were analyzed,and the influence of P competition in the process of As release was also studied.The results showed that changing trend of the values of equilibrium As concentration in sediments were consistent with the regional changes(0 to 28.12μg/L),and the sediments from algaetype areas had the higher values.The sediments from western lake and northwest lake bay were a strong As and a weak P source,and the north lake bay had the opposite trend of these two regions.Intense P source competition with As from the sediments occurred in algae-type areas.The grass-type areas had strong As and P retention capacities,indicating a sink role of sediment with high As and P sorption capacities.The degree of As and P saturation had similar trend in sediments,and the grass-type areas had the higher values,18.3%-21.4%and 15.31%-20.34%,respectively.Contribution analysis results showed that most of As release contribution was from the bottom(30-50 cm)sediments,and the surface(0-10 cm)sediments from algae-type areas contributed more to the overlying water than other region.
基金National Key Project of Fundamental Research u SCSMEX" the Research Fund for the Doctoral Program of Higher Education:" Stud
文摘The apparent heat sources (?Q1 ?) and moisture sinks (?Q2 ?) are calculated based on the reanalyzed data of the South China Sea Monsoon Experiment (SCSMEX) from May 1 to August 31, 1998. It is found that the formation and distribution of the atmospheric heat sources are important for the monsoon onset. The earlier onset of the SCS monsoon is the result of enduring atmospheric heating in the Indo–China Peninsula and South China areas. The atmospheric heating firstly appears in the Indo–China Peninsula area and the sensible heat is the major one. The 30–50 day periodic oscillation of atmospheric heat sources between the SCS area and the western Pacific warm pool has a reverse phase distribution before the middle of July and the low frequency oscillation of heat sources in SCS area has an obvious longitudinal propagation. The 30–50 day low frequency oscillation has vital modificatory effects on the summer monsoon evolution during 1998. Key words Apparent heat sources - Apparent moisture sinks - The South China Sea monsoon - Diagnostic Study Sponsored by the National Key Project of Fundamental Research “ SCSMEX” and the Research Fund for the Doctoral Program of Higher Education: “ Study of the Air-sea Interaction in the SCS Monsoon Region”.
文摘An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a parameter estimation problem)and a time-varying heat source is considered in the transient heat transfer problem(a function estimation problem).Since a general irregular 2D heat conducting body is considered,a body-fitted grid generation is used to mesh the domain.Then governing equations and associated boundary and initial conditions are transformed from the physical domain to the computational domain and finite difference method is used to solve the governing equations to obtain the temperature distribution in the body.Using an efficient,accurate,and very easy to implement sensitivity analysis incorporated in a gradient based minimization method(here,steepest descentmethod),the unknown heat source is estimated accurately.In the function estimation part,it is assumed that there is no prior information on the functional form of the heat source and the estimation process can be performed with a reasonable initial guess for the heat source.The main advantage of the proposed inverse analysis is that the sensitivity matrix(and hence,the objective function gradient with respect to the unknown variables)can be computed during the direct heat transfer solution through newyet simple explicit expressions with no need to solve extra equations such as the sensitivity and adjoint problems and impose additional computational costs comparable to the direct problem solution ones.Some test cases are presented to investigate the accuracy,efficiency,and effect of measurement error on the estimated parameter and function for the line heat source.
基金Supported by National Key Programme for Developing Basic Sciences G1998040900 Part 1 and IAPInnovation Foundation 8-1308.
文摘Using the summer (June to August) monthly mean data of the National Centers for Environmental Predictions (NCEP) - National Center for Atmospheric Research (NCAR) reanalysis from 1980 to 1997, atmospheric heat sources and moisture sinks are calculated. Anomalous circulation and the vertically integrated heat source with the vertical integrated moisture sink and outgoing longwave radiation (OLR) flux are examined based upon monthly composites for 16 great wet-spells and 8 great dry-spells over the middle-lower reaches of the Yangtze River. The wind anomaly exhibits prominent differences between the great wet-spell and the great dry-spell over the Yangtze River Valley. For the great wet-spell, the anomalous southerly from the Bay of Bengal and the South China Sea and the anomalous northerly over North China enhanced low-level convergence toward a narrow latitudinal belt area (the middle-lower reaches of the Yangtze River). The southerly anomaly is connected with an anticyclonic anomalous circulation system centered at 22 degreesN, 140 degreesE and the northerly anomaly is associated with a cyclonic anomalous circulation system centered at the Japan Sea. In the upper level, the anomalous northwesterly between an anticyclonic anomalous system with the center at 23 degreesN, 105 degreesE and a cyclonic anomalous system with the center at Korea diverged over the middle-lower reaches of the Yangtze River. On the contrary, for the great dry-spell, the anomalous northerly over South China and the anomalous southerly over North China diverged from the Yangtze River Valley in the low level. The former formed in the western part of a cyclonic anomalous system centered at 23 degreesN, 135 degreesE. The latter was located in the western ridge of an anticyclonic anomalous system in the northwestern Pacific. The upper troposphere showed easterly anomaly that converged over the middle-lower reaches of the Yangtze River. A cyclonic anomalous system in South China and an anticyclonic system centered in the Japan Sea enhanced the easterly. Large atmospheric heat source anomalies of opposite signs existed over the western Pacific - the South China Sea, with negative in the great wet-spell and positive in the great dry-spell. The analysis of heat source also revealed positive anomalous heat sources during the great wet-spell and negative anomalous heat sources during the great dry-spell over the Yangtze River valley. The changes of the moisture sink and OLR were correspondingly altered, implying the change of heat source anomaly is due to the latent heat releasing of convective activity. Over the southeastern Tibetan Plateau- the Bay of Bengal, the analysis of heat source shows positive anomalous heat sources during the great wet-spell and negative anomalous heat sources during the great dry-spell because of latent heating change. The change of divergent wind coexisted with the change of heat source. In the great wet-spell, southerly divergent wind anomaly in the low level and northerly divergent wind anomaly in high-level are seen over South China. These divergent wind anomalies are helpful to the low-level convergence anomaly and high-level divergence anomaly over the Yangtze River valley. The low-level northerly divergent wind anomaly and high-level southerly divergent wind anomaly over South China reduced the low-level convergence and high-level divergence over the Yangtze River valley during the great dry-spell.
基金financially supported by the National Key Research and Development Program of China(No.2022YFB4600900)the National Natural Science Foundation of China(Nos.U1960111 and 52375309)the Liaoning ProvinceApplied Basic Research Program Project(Nos.2023JH2 and 101300157).
文摘An innovative and accurate method for controlling the interfacial structure of Mg-alloy/steel direct lap joints using a hybrid laser-gas tungsten arc(GTA)flexible control heat source was proposed.The study investigated the impact of spatial regulation of a flexible hybrid heat source on the thermal gradient distribution across the joint geometry and the resulting stress states in the joints,revealing the respective bonding and strengthening mechanisms.The findings indicate that the malposition alters the thermal gradient distribution within the joint,influencing the metallurgical bonding area,interfacial structure,fracture mode,and fracture path.Furthermore,the results showed that varying the laser pulse frequency affected the frequency of the laser-induced arc and the number of keyholes generated per unit length of the joint,which effectively altered the joint geometry and interfacial stress state,and could be used to enhance the load-bearing capacity of the joints.The joint's maximum load was measured to be 325.2 N/mm,which is approximately 88%of the Mg-alloy matrix and the highest reported strength for Mg alloy-steel dissimilar lap joints.A composite interfacial layer structure was achieved,consisting of Al_(11)(Mn,Fe)_(4)and a small amount of Mg_(2)Al_(3)intermetallic compounds(IMCs)at the weld front,along with Al_(11)(Mn,Fe)_(4)and Fe3Al IMCs in the weld middle.The key factors to achieving a high bonding strength of Mg-alloy/steel lap joints have been summarized.This study provides a technical and theoretical reference for the precise collaborative control of joint geometry,interfacial structure,and mechanical properties of dissimilar material lap joints.
文摘This paper deals with an unsteady magnetohydrodynamics(MHD)heat and masstransfer for a viscous incompressible fluid through a vertical stretching surface embedded ina Darcy-Forchheimer porous medium in the presence of a non-uniform heat source/sink andfirst-order chemical reaction.The porous surface is subjected to a uniform transverse magneticfield.The influence of velocity,thermal,and concentration slip is also investigated.The governing equations are coupled non-linear partial differential equations,which have been converted via similarity transformation into a set of ordinary differential equations.The resultantsystem of non-linear ordinary differential equations has been solved numerically with the helpof the“MATLAB”BVP4C Solver.Results are presented graphically to analyze the effects ofvarious physical parameters discovered in the problem such as Hartmann number(M),Forchheimer number(Fr),Grashof number(Gr),solutal Grashof number(Gc),suction parameter(S),porosity parameter(el),dimensionless velocity slip(Sv),Prandtl number(Pr),dimensionless thermal slip(St),space-dependent heat source/sink parameter(eA1),temperature-dependent heat source/sink(eB)1),Eckert number(Ec),Schmidt number(Sc),chemical reaction parameter(g),unsteadiness parameter(A),and dimensionless concentration slip(Sc)on non-dimensionalvelocity ec0ðhÞ,temperature zðhÞ,and concentration efðhÞprofiles.The influence of these parameters on skin-friction coefficient(C)f),Nusselt number(Nu)x),and Sherwood number(Sh)x)areexpressed in tabular form.It is observed that an enhancement in Fr and el results in the declination of the velocity profile.There is an enhancement in temperature with an increment in theeA)1 and eB)1.The physical representation of flow characteristics that appeared in the problem ispresented using various graphs to depict real-world applications in industrial and engineeringoperations.The results were compared to previous studies,revealing that the two are in goodagreement.The novelty of the present investigation is:To interpret the combined effects ofviscous dissipation and Joule heating on a vertical stretching surface embedded in a highlyporous medium modeled using the Darcy-Forchheimer model.The findings could be valuablein understanding the flow of oil,gas,and water through an oil or gas field reservoir,as well asgroundwater migration and filtering and purification procedures.
