Radiation effect on the natural convection flow of an optically thin viscous incompressible fluid near a vertical plate with ramped wall temperature in a porous medium has been studied. The exact solution of momentum ...Radiation effect on the natural convection flow of an optically thin viscous incompressible fluid near a vertical plate with ramped wall temperature in a porous medium has been studied. The exact solution of momentum and energy equations is obtained by the use of Laplace transform technique. The variations in fluid velocity and temperature are shown graphically whereas the numerical values of shear stress and the rate of heat transfer at the wall are presented in tabular form for various values of flow parameters. The results show that the fluid velocity increases with increase in Grashof number, Darcy number and time parameters whereas the fluid velocity decreases with increase in the radiation parameter and Prandtl number for ramped temperature as well as isothermal wall temperature. It is found that an increase in radiation parameter leads to rise the temperature for both ramped wall temperature as well as isothermal wall temperature. Further, it is found that an increase in Prandtl number leads to fall the temperature for both ramped wall temperature as well as isothermal wall temperature. The shear stress at the wall decreases with increases in either Prandtl number or porosity parameter while the result shows reverse in the case of radiation parameter. Finally, the rate of heat transfer is increased with increases in the radiation parameter for both ramped wall temperature as well as isothermal wall temperature.展开更多
The combined influences of Hall currents and rotation on the MHD Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel porous plates channel in a rotating syst...The combined influences of Hall currents and rotation on the MHD Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel porous plates channel in a rotating system in the presence of a uniform transverse magnetic field have been carried out. The solutions for the velocity field as well as shear stresses have been obtained for small time as well as for large times by Laplace transform technique. It is found that for large times the Hall currents accelerates primary flow whereas it retards secondary flow while the rotation retards the primary flow whereas it accelerates the secondary flow. It is also found that the velocity components converge more rapidly for small time solution than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of magnetic parameter M2, rotation parameter K2 and Reynolds number Re. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the layer increases with increase in either Hall parameter m or Reynolds number Re while it decreases with increase in Hartmann number M. It is interesting to note that for large values of M2 , the boundary layer thickness is independent of the rotation parameter.展开更多
文摘Radiation effect on the natural convection flow of an optically thin viscous incompressible fluid near a vertical plate with ramped wall temperature in a porous medium has been studied. The exact solution of momentum and energy equations is obtained by the use of Laplace transform technique. The variations in fluid velocity and temperature are shown graphically whereas the numerical values of shear stress and the rate of heat transfer at the wall are presented in tabular form for various values of flow parameters. The results show that the fluid velocity increases with increase in Grashof number, Darcy number and time parameters whereas the fluid velocity decreases with increase in the radiation parameter and Prandtl number for ramped temperature as well as isothermal wall temperature. It is found that an increase in radiation parameter leads to rise the temperature for both ramped wall temperature as well as isothermal wall temperature. Further, it is found that an increase in Prandtl number leads to fall the temperature for both ramped wall temperature as well as isothermal wall temperature. The shear stress at the wall decreases with increases in either Prandtl number or porosity parameter while the result shows reverse in the case of radiation parameter. Finally, the rate of heat transfer is increased with increases in the radiation parameter for both ramped wall temperature as well as isothermal wall temperature.
文摘The combined influences of Hall currents and rotation on the MHD Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel porous plates channel in a rotating system in the presence of a uniform transverse magnetic field have been carried out. The solutions for the velocity field as well as shear stresses have been obtained for small time as well as for large times by Laplace transform technique. It is found that for large times the Hall currents accelerates primary flow whereas it retards secondary flow while the rotation retards the primary flow whereas it accelerates the secondary flow. It is also found that the velocity components converge more rapidly for small time solution than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of magnetic parameter M2, rotation parameter K2 and Reynolds number Re. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the layer increases with increase in either Hall parameter m or Reynolds number Re while it decreases with increase in Hartmann number M. It is interesting to note that for large values of M2 , the boundary layer thickness is independent of the rotation parameter.
