The theoretical and numerical analysis is carried out on the effect of three types of configurations of Rayleigh-Bénard (RB) convection driven by the boundary combinations of Rigid-Rigid (R-R), Rigid-Free (R-F) a...The theoretical and numerical analysis is carried out on the effect of three types of configurations of Rayleigh-Bénard (RB) convection driven by the boundary combinations of Rigid-Rigid (R-R), Rigid-Free (R-F) and Free-Free (F-F). The RB convection models are distinguished by the three different temperature boundary conditions like: 1) RB1: lower and upper at fixed-temperature, 2) RB2: lower and upper with fixed-heat flux, or perfectly insulating and 3) RB3: bottom surface is fixed-temperature and top surface is fixed-heat flux. A Galerkin-type is based on the weighted residual method (WRM) which has been used to obtain the eigenvalue for gravity thermal Rayleigh number. It is noted that the porous medium of Darcy parameter <img alt="" src="Edit_ba52bac5-73fb-46dc-87b2-9ab918cb67c9.bmp" /> and spin diffusion (couple stress) parameter <em>N</em><sub>3</sub> is to hasten coupling parameter <em style="white-space:normal;">N</em><sub style="white-space:normal;">1 </sub>and micropolar heat conduction parameter <em style="white-space:normal;">N</em><sub style="white-space:normal;">5</sub> is to delay the onset of convection. Further, increase in the value of <em style="white-space:normal;">N</em><sub style="white-space:normal;">1</sub>, <em style="white-space:normal;">N</em><sub style="white-space:normal;">5</sub>, <img alt="" src="Edit_2d2de547-a7ed-4351-b3c4-8d1c36d83a20.bmp" /> and as well as decrease in <em style="white-space:normal;">N</em><sub style="white-space:normal;">3</sub> is to diminish the size of convection cells.展开更多
Convection driven by a spatially non-uniform internal heat source between two horizontal isothermal walls is studied by theoretical analysis and numerical simulation,in order to explore the bounds of the temperature a...Convection driven by a spatially non-uniform internal heat source between two horizontal isothermal walls is studied by theoretical analysis and numerical simulation,in order to explore the bounds of the temperature and the vertical heat flux.Specifically,the rigorous lower bound of the weighted average temperature<QT>is derived analytically,by decomposing the temperature field into a background profile and a fluctuation part.This bound obtained for the first time to consider non-uniform heat sources is found to be compatible with the existing bound obtained in uniform internal heat convection.Of physical importance,an analytical relationship is derived as an inequality connecting<QT>and the average vertical heat flux<wT>,by employing the average heat flux on the bottom wall(qb)as an intermediary variable.It clarifies the intrinsic relation between the lower bound of<QT>and the upper bound of<wT>,namely,these two bounds are essentially equivalent providing an easy way to obtain one from another.Furthermore,the analytical bounds are extensively demonstrated through a comprehensive series of direct numerical simulations.展开更多
The present paper is concerned with the wave propagation in a micropolar thermoelastic solid with distinct two temperatures under the effect of the magnetic field in the presence of the gravity field and an internal h...The present paper is concerned with the wave propagation in a micropolar thermoelastic solid with distinct two temperatures under the effect of the magnetic field in the presence of the gravity field and an internal heat source.The formulation of the problem is applied in the context of the three-phase-lag model and Green-Naghdi theory without dissipation.The medium is a homogeneous isotropic thermoelastic in the half-space.The exact expressions of the considered variables are obtained by using normal mode analysis.Comparisons are made with the results in the two theories in the absence and presence of the magnetic field as well as the two-temperature parameter.A comparison is also made in the two theories for different values of an internal heat source.展开更多
The objective of the present work is to analyze the flow,heat and mass transfer characteristics in a thin nanofluid film over a heated stretched sheet in the presence of a non-uniform heat source/sink and thermal radi...The objective of the present work is to analyze the flow,heat and mass transfer characteristics in a thin nanofluid film over a heated stretched sheet in the presence of a non-uniform heat source/sink and thermal radiation.Similarity variables are used to transform the partial differential equations into a system of ordinary differential equations.The resulting system of nonlinear ordinary differential equations is then solved numerically by using the Runge-Kutta-Fehlberg integration scheme with a shooting technique.The effects of the unsteadiness parameter,the thermal radiation,the non-uniform heat source/sink parameter on flow and heat transfer fields are analyzed.It is found that an increase in the unsteadiness parameter is to increase the velocity and temperature gradient profiles.However,an increase in the thermal radiation parameter affects the nanoparticle temperature gradient of the nanofluid film but the reversed is true with the concentration gradient.展开更多
文摘The theoretical and numerical analysis is carried out on the effect of three types of configurations of Rayleigh-Bénard (RB) convection driven by the boundary combinations of Rigid-Rigid (R-R), Rigid-Free (R-F) and Free-Free (F-F). The RB convection models are distinguished by the three different temperature boundary conditions like: 1) RB1: lower and upper at fixed-temperature, 2) RB2: lower and upper with fixed-heat flux, or perfectly insulating and 3) RB3: bottom surface is fixed-temperature and top surface is fixed-heat flux. A Galerkin-type is based on the weighted residual method (WRM) which has been used to obtain the eigenvalue for gravity thermal Rayleigh number. It is noted that the porous medium of Darcy parameter <img alt="" src="Edit_ba52bac5-73fb-46dc-87b2-9ab918cb67c9.bmp" /> and spin diffusion (couple stress) parameter <em>N</em><sub>3</sub> is to hasten coupling parameter <em style="white-space:normal;">N</em><sub style="white-space:normal;">1 </sub>and micropolar heat conduction parameter <em style="white-space:normal;">N</em><sub style="white-space:normal;">5</sub> is to delay the onset of convection. Further, increase in the value of <em style="white-space:normal;">N</em><sub style="white-space:normal;">1</sub>, <em style="white-space:normal;">N</em><sub style="white-space:normal;">5</sub>, <img alt="" src="Edit_2d2de547-a7ed-4351-b3c4-8d1c36d83a20.bmp" /> and as well as decrease in <em style="white-space:normal;">N</em><sub style="white-space:normal;">3</sub> is to diminish the size of convection cells.
基金supported by the National Natural Science Foundation of China(Grant Nos.92252202,92152301,12293000,12293002,12302320,and 12388101)the Fundamental Research Funds for the Central Universities.
文摘Convection driven by a spatially non-uniform internal heat source between two horizontal isothermal walls is studied by theoretical analysis and numerical simulation,in order to explore the bounds of the temperature and the vertical heat flux.Specifically,the rigorous lower bound of the weighted average temperature<QT>is derived analytically,by decomposing the temperature field into a background profile and a fluctuation part.This bound obtained for the first time to consider non-uniform heat sources is found to be compatible with the existing bound obtained in uniform internal heat convection.Of physical importance,an analytical relationship is derived as an inequality connecting<QT>and the average vertical heat flux<wT>,by employing the average heat flux on the bottom wall(qb)as an intermediary variable.It clarifies the intrinsic relation between the lower bound of<QT>and the upper bound of<wT>,namely,these two bounds are essentially equivalent providing an easy way to obtain one from another.Furthermore,the analytical bounds are extensively demonstrated through a comprehensive series of direct numerical simulations.
文摘The present paper is concerned with the wave propagation in a micropolar thermoelastic solid with distinct two temperatures under the effect of the magnetic field in the presence of the gravity field and an internal heat source.The formulation of the problem is applied in the context of the three-phase-lag model and Green-Naghdi theory without dissipation.The medium is a homogeneous isotropic thermoelastic in the half-space.The exact expressions of the considered variables are obtained by using normal mode analysis.Comparisons are made with the results in the two theories in the absence and presence of the magnetic field as well as the two-temperature parameter.A comparison is also made in the two theories for different values of an internal heat source.
文摘The objective of the present work is to analyze the flow,heat and mass transfer characteristics in a thin nanofluid film over a heated stretched sheet in the presence of a non-uniform heat source/sink and thermal radiation.Similarity variables are used to transform the partial differential equations into a system of ordinary differential equations.The resulting system of nonlinear ordinary differential equations is then solved numerically by using the Runge-Kutta-Fehlberg integration scheme with a shooting technique.The effects of the unsteadiness parameter,the thermal radiation,the non-uniform heat source/sink parameter on flow and heat transfer fields are analyzed.It is found that an increase in the unsteadiness parameter is to increase the velocity and temperature gradient profiles.However,an increase in the thermal radiation parameter affects the nanoparticle temperature gradient of the nanofluid film but the reversed is true with the concentration gradient.
