The heat transfer rate of the thermal Marangoni convective flow of a hybrid nanomaterial is optimized by using the response surface methodology(RSM).The thermal phenomenon is modeled in the presence of a variable incl...The heat transfer rate of the thermal Marangoni convective flow of a hybrid nanomaterial is optimized by using the response surface methodology(RSM).The thermal phenomenon is modeled in the presence of a variable inclined magnetic field,thermal radiation,and an exponential heat source.Experimentally estimated values of the thermal conductivity and viscosity of the hybrid nanomaterial are utilized in the calculation.The governing intricate nonlinear problem is treated numerically,and a parametric analysis is carried out by using graphical visualizations.A finite difference-based numerical scheme is utilized in conjunction with the 4-stage Lobatto IIIa formula to solve the nonlinear governing problem.The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM.The mono and hybrid nanomaterial flow fields are compared.The hybrid nanomaterial possesses enhanced thermal fields for nanoparticle volume fractions less than 2%.The irregular heat source and the thermal radiation enhance the temperature profiles.The high level of the thermal radiation and the low levels of the exponential heat source and the angle of inclination(of the magnetic field)lead to the optimized heat transfer rate(Nux=7.46275).展开更多
The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study.The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon.The conventio...The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study.The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon.The conventional models for heat and mass flux,i.e.,Fourier and Fick models,are modified using the Cattaneo-Christov(CC)model for the more accurate modeling of the process.The boundary layer equations that govern this problem are solved using the apt similarity variables.The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg(RKF)scheme.The graphical visualizations of the results are discussed with the physical significance.The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters.The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid.The external magnetism is observed to decrease the velocity field.Also,more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles.The heat transport is enhanced by the stretching of the rotating disk.展开更多
The thermodynamic features of the Reiner-Rivlin nanoliquid flow induced by a spinning disk are analyzed numerically.The non-homogeneous two-phase nanofluid model is considered to analyze the effect of nanoparticles on...The thermodynamic features of the Reiner-Rivlin nanoliquid flow induced by a spinning disk are analyzed numerically.The non-homogeneous two-phase nanofluid model is considered to analyze the effect of nanoparticles on the thermodynamics of the Reiner-Rivlin nanomaterial,which also includes a temperature-dependent heat source(THS)and an exponential space-dependent heat source(ESHS).Further,the transfer of heat and mass is analyzed with velocity slip,volume fraction jump,and temperature jump boundary conditions.The finite difference method-based routine is used to solve the complicated differential equations formed after using the von-Karman similarity technique.Limiting cases of the present problem are found to be in good agreement with benchmarking studies.The relationship of the pertinent parameters with the heat and mass transport is scrutinized using correlation,which is further evaluated based on the probable error estimates.Multivariable models are fitted for the friction factor at the disk and heat transport,which accurately predict the dependent variables.The Reiner-Rivlin nanoliquid temperature is influenced comparatively more by the ESHS than by THS.The Nusselt number is decreased by the ESHS and THS,whereas the friction factor at the disk is predominantly decremented by the wall roughness aspect.The increment in the non-Newtonian characteristic of the liquid leads more fluid to drain away in the radial direction far from the disk compared with the fluid nearby the disk in the presence of the centrifugal force during rotation.The increased thermal and volume fraction slip lowers the nanoliquid temperature and nanoparticle volume fraction profiles.展开更多
文摘The heat transfer rate of the thermal Marangoni convective flow of a hybrid nanomaterial is optimized by using the response surface methodology(RSM).The thermal phenomenon is modeled in the presence of a variable inclined magnetic field,thermal radiation,and an exponential heat source.Experimentally estimated values of the thermal conductivity and viscosity of the hybrid nanomaterial are utilized in the calculation.The governing intricate nonlinear problem is treated numerically,and a parametric analysis is carried out by using graphical visualizations.A finite difference-based numerical scheme is utilized in conjunction with the 4-stage Lobatto IIIa formula to solve the nonlinear governing problem.The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM.The mono and hybrid nanomaterial flow fields are compared.The hybrid nanomaterial possesses enhanced thermal fields for nanoparticle volume fractions less than 2%.The irregular heat source and the thermal radiation enhance the temperature profiles.The high level of the thermal radiation and the low levels of the exponential heat source and the angle of inclination(of the magnetic field)lead to the optimized heat transfer rate(Nux=7.46275).
文摘The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study.The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon.The conventional models for heat and mass flux,i.e.,Fourier and Fick models,are modified using the Cattaneo-Christov(CC)model for the more accurate modeling of the process.The boundary layer equations that govern this problem are solved using the apt similarity variables.The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg(RKF)scheme.The graphical visualizations of the results are discussed with the physical significance.The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters.The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid.The external magnetism is observed to decrease the velocity field.Also,more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles.The heat transport is enhanced by the stretching of the rotating disk.
文摘The thermodynamic features of the Reiner-Rivlin nanoliquid flow induced by a spinning disk are analyzed numerically.The non-homogeneous two-phase nanofluid model is considered to analyze the effect of nanoparticles on the thermodynamics of the Reiner-Rivlin nanomaterial,which also includes a temperature-dependent heat source(THS)and an exponential space-dependent heat source(ESHS).Further,the transfer of heat and mass is analyzed with velocity slip,volume fraction jump,and temperature jump boundary conditions.The finite difference method-based routine is used to solve the complicated differential equations formed after using the von-Karman similarity technique.Limiting cases of the present problem are found to be in good agreement with benchmarking studies.The relationship of the pertinent parameters with the heat and mass transport is scrutinized using correlation,which is further evaluated based on the probable error estimates.Multivariable models are fitted for the friction factor at the disk and heat transport,which accurately predict the dependent variables.The Reiner-Rivlin nanoliquid temperature is influenced comparatively more by the ESHS than by THS.The Nusselt number is decreased by the ESHS and THS,whereas the friction factor at the disk is predominantly decremented by the wall roughness aspect.The increment in the non-Newtonian characteristic of the liquid leads more fluid to drain away in the radial direction far from the disk compared with the fluid nearby the disk in the presence of the centrifugal force during rotation.The increased thermal and volume fraction slip lowers the nanoliquid temperature and nanoparticle volume fraction profiles.
