This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The m...This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The motion of the fluid is taken as two-dimensional with the impact of a magnetic field in the normal direction. The variable, permeable, and stretching nature of sheet's surface sets the fluid into motion. Thermal and mass diffusions are controlled through the use of the Cattaneo–Christov flux model. A dataset is generated using MATLAB bvp4c package solver and employed to train an artificial neural network(ANN) based on the Levenberg–Marquardt back-propagation(LMBP) algorithm. It has been observed as an outcome of this study that the modeled problem achieves peak performance at epochs 637, 112, 4848, and 344 using ANN-LMBP. The linear velocity of the fluid weakens with progression in variable porous and magnetic factors.With an augmentation in magnetic factor, the micro-rotational velocity profiles are augmented on the domain 0 ≤ η < 1.5 due to the support of micro-rotations by Lorentz forces close to the sheet's surface, while they are suppressed on the domain 1.5 ≤ η < 6.0 due to opposing micro-rotations away from the sheet's surface. Thermal distributions are augmented with an upsurge in thermophoresis, Brownian motion, magnetic, and radiation factors, while they are suppressed with an upsurge in thermal relaxation parameter. Concentration profiles increase with an expansion in thermophoresis factor and are suppressed with an intensification of Brownian motion factor and solute relaxation factor. The absolute errors(AEs) are evaluated for all the four scenarios that fall within the range 10^(-3)–10^(-8) and are associated with the corresponding ANN configuration that demonstrates a fine degree of accuracy.展开更多
A fractional Cattaneo model is derived for studying the heat transfer in a finite slab irradiated by a short pulse laser. The analytical solutions for the fractional Cattaneo model, the classical Cattaneo-Vernotte mod...A fractional Cattaneo model is derived for studying the heat transfer in a finite slab irradiated by a short pulse laser. The analytical solutions for the fractional Cattaneo model, the classical Cattaneo-Vernotte model, and the Fourier model are obtained with finite Fourier and Laplace transforms. The effects of the fractional order parameter and the relaxation time on the temperature fields in the finite slab are investigated.The results show that the larger the fractional order parameter, the slower the thermal wave. Moreover, the higher the relaxation time, the slower the heat flux propagates. By comparing the fractional order Cattaneo model with the classical Cattaneo-Vernotte and Fourier models, it can be found that the heat flux predicted using the fractional Cattaneo model always transports from the high temperature to the low one, which is in accord with the second law of thermodynamics. However, the classical Cattaneo-Vernotte model shows that the unphysical heat flux sometimes transports from the low temperature to the high one.展开更多
The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a por...The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.展开更多
Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction areinvestigated analytically and numerically. The corresponding dispersion relation is a sixth-orderalgebraic equation, governed b...Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction areinvestigated analytically and numerically. The corresponding dispersion relation is a sixth-orderalgebraic equation, governed by six non-dimensional parameters: two thermoelastic couplingconstants, one chirality parameter, the ratio between extensional and torsional moduli, the Fouriernumber, and the dimensionless thermal relaxation. The behavior of the solutions is discussedfrom two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxationon the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wavecelerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered.However, with large wavenumbers, the solutions behave differently depending on the thermalrelaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from theclassical result of the speed of second sound.展开更多
To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomal...To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.展开更多
A numerical study is reported for two-dimensional flow of an incompressible Powell-Eyring fluid by stretching the surface with the Cattaneo-Christov model of heat diffusion. Impacts of heat generation/absorption and d...A numerical study is reported for two-dimensional flow of an incompressible Powell-Eyring fluid by stretching the surface with the Cattaneo-Christov model of heat diffusion. Impacts of heat generation/absorption and destructive/generative chemical reactions are considered. Use of proper variables leads to a system of non-linear dimensionless expressions. Velocity, temperature and concentration profiles are achieved through a finite difference based algorithm with a successive over-relaxation(SOR) method. Emerging dimensionless quantities are described with graphs and tables. The temperature and concentration profiles decay due to enhancement in fluid parameters and Deborah numbers.展开更多
In this paper,Newtonian nanofluid flow is observed under the effects of the magnetic field,activation energy and motile microorganisms over an inclined stretchable cylinder.The magnificent aspects of nanoliquid are de...In this paper,Newtonian nanofluid flow is observed under the effects of the magnetic field,activation energy and motile microorganisms over an inclined stretchable cylinder.The magnificent aspects of nanoliquid are demonstrated by enduring the Brownian motion and thermophoresis diffusion features.Nonlinear higher order partial differential equations are transformed into first-order ordinary differential equations with suitable similarity variables.The attained sets of governing equations are then cracked by bvp4 c procedure in MATLAB mathematical software.The numerical and graphical outcomes of controlling parameters such as Prandtl number,mixed convection,activation energy,thermophoresis,Brownian parameter,Biot number,Lewis number,Peclet number and motile concentration parameter against the velocity,temperature,volumetric concentration and motile concentration of nanoparticles of the fluid are discussed.The velocity is enhanced with the growth valuation in mixed convection and decay by rising variation of buoyancy ratio parameter,magnetic parameter and bio-convective Rayleigh parameter.The evolution in motile microorganisms is due to the increasing values of microorganisms Biot number.The presented data can be helpful in enhancement of manufacturing processes,biomolecules,extrusion systems applications and energy production improvement.展开更多
The nonlinear thermoelastic responses of an elastic medium exposed to laser generated shortpulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the imp...The nonlinear thermoelastic responses of an elastic medium exposed to laser generated shortpulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the impact of thermal loading with energy dissipation is the focus of this research. To model the thermal boundary condition(in the form of thermal conduction),generalized Cattaneo model(GCM) is employed. In the reference configuration, a nonlinear coupled Lord-Shulman-type generalized thermoelasticity formulation using finite strain theory(FST) is developed and the temperature dependency of the thermal conductivity is considered to derive the equations. In order to solve the time-dependent and nonlinear equations, Newmark’s numerical time integration technique and an updated finite element algorithm is applied and to ensure achieving accurate continuity of the results, the Hermitian elements are used instead of Lagrangian’s. The numerical responses for different factors such as input heat flux and nonlinear terms are expressed graphically and their impacts on the system’s reaction are discussed in detail.The results of the study are presented for Green–Lindsay model and the findings are compared with Lord-Shulman model especially with regards to heat wave propagation. It is shown that the nature of the laser’s thermal shock and its geometry are particularly determinative in the final stage of deformation. The research also concluded that employing FST leads to achieving more accuracy in terms of elastic deformations;however, the thermally nonlinear analysis does not change the results markedly. For this reason, the nonlinear theory of deformation is required in laser related reviews, while it is reasonable to ignore the temperature changes compared to the reference temperature in deriving governing equations.展开更多
This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is conside...This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is considered. The flow generation is due to the bidirectional stretching of sheet. The combined phenomenon of heat and mass transport is accounted. The Cattaneo-Christov model of heat and mass diffusion is used to develop the expressions of energy and mass species. The first-order chemical reaction term in the mass species equation is considered. The boundary layer assumptions lead to the governing mathematical model. The homotopic simulation is adopted to visualize the results of the dimensionless flow equations. The graphs of velocities, temperature, and concentration show the effects of different arising parameters. A numerical benchmark is presented to visualize the convergent values of the computed results. The results show that the concentration and temperature fields are decayed for the Cattaneo^Christov theory of heat and mass diffusion.展开更多
The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the imple...The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier＇s law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.展开更多
We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary la...We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformatioris. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method （OHAM）. The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo-Christov heat flux model than those in the Fourier＇s law of heat conduction.展开更多
A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic （MHD） Casson fluid across a slendering sheet in the presence of microorg...A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic （MHD） Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips （diffusion, thermal, and momentum slips） are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that th~ velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.展开更多
The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow(EOF)of an incompressible fractional secondgrade fluid with low-dense mixtures of two spherical na...The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow(EOF)of an incompressible fractional secondgrade fluid with low-dense mixtures of two spherical nanoparticles,copper,and titanium.The flow of the hybrid nanofluid takes place through a vertical micro-channel.A fractional Cattaneo model with heat conduction is considered.For the DC-operated micropump,the Lorentz force is responsible for the pressure difference through the microchannel.The Debye-H¨ukel approximation is utilized to linearize the charge density.The semianalytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses.In addition to the analytical procedures,a numerical algorithm based on the finite difference method is introduced for the given domain.A comparison between the two solutions is presented.The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically.It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields.The present work has theoretical implications for biofluid-based microfluidic transport systems.展开更多
Cattaneo-Christov heat and mass flux models are considered rather than Fourier and Fick laws due to the presence of thermal and concentration transport hyperbolic phenomena. The generalized form of the Navier-Stokes m...Cattaneo-Christov heat and mass flux models are considered rather than Fourier and Fick laws due to the presence of thermal and concentration transport hyperbolic phenomena. The generalized form of the Navier-Stokes model is considered in hydromagnetic flow. Three-dimensional (3D) unsteady fluid motion is generated by the periodic oscillations of a rotating disk. Similarity transformations are used to obtain the normalized fluid flow model. The successive over relaxation (SOR) method with finite difference schemes are accomplished for the numerical solution of the obtained partial differential non-linear system. The flow features of the velocity, microrotation, temperature, and concentration fields are discussed in pictorial forms for various physical flow parameters. The couple stresses and heat and mass transfer rates for different physical quantities are explained via tabular forms. For better insight of the physical fluid model, 3D fluid phenomena and two-dimensional (2D) contours are also plotted. The results show that the micropolar fluids contain microstructure having non-symmetric stress tensor and are useful in lubrication theory. Moreover, the thermal and concentration waves in Cattaneo-Christov models have a significance role in the laser heating and enhancement in thermal conductivity.展开更多
The Cattaneo-Christov heat flux in the two-dimensional （2D） flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Simil...The Cattaneo-Christov heat flux in the two-dimensional （2D） flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temper- ature gradient while reduces the temperature profile.展开更多
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through large Research Group Project (Grant No. RGP2/198/45)Project supported by Prince Sattam bin Abdulaziz University (Grant No. PSAU/2025/R/1446)。
文摘This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The motion of the fluid is taken as two-dimensional with the impact of a magnetic field in the normal direction. The variable, permeable, and stretching nature of sheet's surface sets the fluid into motion. Thermal and mass diffusions are controlled through the use of the Cattaneo–Christov flux model. A dataset is generated using MATLAB bvp4c package solver and employed to train an artificial neural network(ANN) based on the Levenberg–Marquardt back-propagation(LMBP) algorithm. It has been observed as an outcome of this study that the modeled problem achieves peak performance at epochs 637, 112, 4848, and 344 using ANN-LMBP. The linear velocity of the fluid weakens with progression in variable porous and magnetic factors.With an augmentation in magnetic factor, the micro-rotational velocity profiles are augmented on the domain 0 ≤ η < 1.5 due to the support of micro-rotations by Lorentz forces close to the sheet's surface, while they are suppressed on the domain 1.5 ≤ η < 6.0 due to opposing micro-rotations away from the sheet's surface. Thermal distributions are augmented with an upsurge in thermophoresis, Brownian motion, magnetic, and radiation factors, while they are suppressed with an upsurge in thermal relaxation parameter. Concentration profiles increase with an expansion in thermophoresis factor and are suppressed with an intensification of Brownian motion factor and solute relaxation factor. The absolute errors(AEs) are evaluated for all the four scenarios that fall within the range 10^(-3)–10^(-8) and are associated with the corresponding ANN configuration that demonstrates a fine degree of accuracy.
基金supported by the National Natural Science Foundation of China(No.11372281)the Science and Technology Plan Project of Zhoushan(No.2016C41009)the Innovative Team Project of Zhejiang Ocean University
文摘A fractional Cattaneo model is derived for studying the heat transfer in a finite slab irradiated by a short pulse laser. The analytical solutions for the fractional Cattaneo model, the classical Cattaneo-Vernotte model, and the Fourier model are obtained with finite Fourier and Laplace transforms. The effects of the fractional order parameter and the relaxation time on the temperature fields in the finite slab are investigated.The results show that the larger the fractional order parameter, the slower the thermal wave. Moreover, the higher the relaxation time, the slower the heat flux propagates. By comparing the fractional order Cattaneo model with the classical Cattaneo-Vernotte and Fourier models, it can be found that the heat flux predicted using the fractional Cattaneo model always transports from the high temperature to the low one, which is in accord with the second law of thermodynamics. However, the classical Cattaneo-Vernotte model shows that the unphysical heat flux sometimes transports from the low temperature to the high one.
文摘The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.
基金supported by the National Science Foundation of United States (Grants IIP-1362146 and CMMI-1462749)
文摘Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction areinvestigated analytically and numerically. The corresponding dispersion relation is a sixth-orderalgebraic equation, governed by six non-dimensional parameters: two thermoelastic couplingconstants, one chirality parameter, the ratio between extensional and torsional moduli, the Fouriernumber, and the dimensionless thermal relaxation. The behavior of the solutions is discussedfrom two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxationon the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wavecelerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered.However, with large wavenumbers, the solutions behave differently depending on the thermalrelaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from theclassical result of the speed of second sound.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11072134, and 91130017)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AQ014)the Independent Innovation Foundation of Shandong University, China (Grant No. 2010ZRJQ002)
文摘To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.
文摘A numerical study is reported for two-dimensional flow of an incompressible Powell-Eyring fluid by stretching the surface with the Cattaneo-Christov model of heat diffusion. Impacts of heat generation/absorption and destructive/generative chemical reactions are considered. Use of proper variables leads to a system of non-linear dimensionless expressions. Velocity, temperature and concentration profiles are achieved through a finite difference based algorithm with a successive over-relaxation(SOR) method. Emerging dimensionless quantities are described with graphs and tables. The temperature and concentration profiles decay due to enhancement in fluid parameters and Deborah numbers.
基金funding this work through research groups program under grant number R.G.P-2/97/42。
文摘In this paper,Newtonian nanofluid flow is observed under the effects of the magnetic field,activation energy and motile microorganisms over an inclined stretchable cylinder.The magnificent aspects of nanoliquid are demonstrated by enduring the Brownian motion and thermophoresis diffusion features.Nonlinear higher order partial differential equations are transformed into first-order ordinary differential equations with suitable similarity variables.The attained sets of governing equations are then cracked by bvp4 c procedure in MATLAB mathematical software.The numerical and graphical outcomes of controlling parameters such as Prandtl number,mixed convection,activation energy,thermophoresis,Brownian parameter,Biot number,Lewis number,Peclet number and motile concentration parameter against the velocity,temperature,volumetric concentration and motile concentration of nanoparticles of the fluid are discussed.The velocity is enhanced with the growth valuation in mixed convection and decay by rising variation of buoyancy ratio parameter,magnetic parameter and bio-convective Rayleigh parameter.The evolution in motile microorganisms is due to the increasing values of microorganisms Biot number.The presented data can be helpful in enhancement of manufacturing processes,biomolecules,extrusion systems applications and energy production improvement.
文摘The nonlinear thermoelastic responses of an elastic medium exposed to laser generated shortpulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the impact of thermal loading with energy dissipation is the focus of this research. To model the thermal boundary condition(in the form of thermal conduction),generalized Cattaneo model(GCM) is employed. In the reference configuration, a nonlinear coupled Lord-Shulman-type generalized thermoelasticity formulation using finite strain theory(FST) is developed and the temperature dependency of the thermal conductivity is considered to derive the equations. In order to solve the time-dependent and nonlinear equations, Newmark’s numerical time integration technique and an updated finite element algorithm is applied and to ensure achieving accurate continuity of the results, the Hermitian elements are used instead of Lagrangian’s. The numerical responses for different factors such as input heat flux and nonlinear terms are expressed graphically and their impacts on the system’s reaction are discussed in detail.The results of the study are presented for Green–Lindsay model and the findings are compared with Lord-Shulman model especially with regards to heat wave propagation. It is shown that the nature of the laser’s thermal shock and its geometry are particularly determinative in the final stage of deformation. The research also concluded that employing FST leads to achieving more accuracy in terms of elastic deformations;however, the thermally nonlinear analysis does not change the results markedly. For this reason, the nonlinear theory of deformation is required in laser related reviews, while it is reasonable to ignore the temperature changes compared to the reference temperature in deriving governing equations.
文摘This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is considered. The flow generation is due to the bidirectional stretching of sheet. The combined phenomenon of heat and mass transport is accounted. The Cattaneo-Christov model of heat and mass diffusion is used to develop the expressions of energy and mass species. The first-order chemical reaction term in the mass species equation is considered. The boundary layer assumptions lead to the governing mathematical model. The homotopic simulation is adopted to visualize the results of the dimensionless flow equations. The graphs of velocities, temperature, and concentration show the effects of different arising parameters. A numerical benchmark is presented to visualize the convergent values of the computed results. The results show that the concentration and temperature fields are decayed for the Cattaneo^Christov theory of heat and mass diffusion.
文摘The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier＇s law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.
基金supported by the Deanship of Scientific Research(DSR)King Abdulaziz University,Jeddah,Saudi Arabia(Grant No.32-130-36-Hi Ci)
文摘We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformatioris. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method （OHAM）. The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo-Christov heat flux model than those in the Fourier＇s law of heat conduction.
文摘A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic （MHD） Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips （diffusion, thermal, and momentum slips） are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that th~ velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.
基金the Taif University Researchers Supporting Project of Taif University of Saudi Arabia (No. TURSP-2020/96)
文摘The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow(EOF)of an incompressible fractional secondgrade fluid with low-dense mixtures of two spherical nanoparticles,copper,and titanium.The flow of the hybrid nanofluid takes place through a vertical micro-channel.A fractional Cattaneo model with heat conduction is considered.For the DC-operated micropump,the Lorentz force is responsible for the pressure difference through the microchannel.The Debye-H¨ukel approximation is utilized to linearize the charge density.The semianalytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses.In addition to the analytical procedures,a numerical algorithm based on the finite difference method is introduced for the given domain.A comparison between the two solutions is presented.The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically.It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields.The present work has theoretical implications for biofluid-based microfluidic transport systems.
文摘Cattaneo-Christov heat and mass flux models are considered rather than Fourier and Fick laws due to the presence of thermal and concentration transport hyperbolic phenomena. The generalized form of the Navier-Stokes model is considered in hydromagnetic flow. Three-dimensional (3D) unsteady fluid motion is generated by the periodic oscillations of a rotating disk. Similarity transformations are used to obtain the normalized fluid flow model. The successive over relaxation (SOR) method with finite difference schemes are accomplished for the numerical solution of the obtained partial differential non-linear system. The flow features of the velocity, microrotation, temperature, and concentration fields are discussed in pictorial forms for various physical flow parameters. The couple stresses and heat and mass transfer rates for different physical quantities are explained via tabular forms. For better insight of the physical fluid model, 3D fluid phenomena and two-dimensional (2D) contours are also plotted. The results show that the micropolar fluids contain microstructure having non-symmetric stress tensor and are useful in lubrication theory. Moreover, the thermal and concentration waves in Cattaneo-Christov models have a significance role in the laser heating and enhancement in thermal conductivity.
文摘The Cattaneo-Christov heat flux in the two-dimensional （2D） flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temper- ature gradient while reduces the temperature profile.
