Radiation Effect on Natural Convection Near a Vertical Plate Embedded in Porous Medium with Ramped Wall Temperature

S Das,M Jana,R N Jana

doi:10.4236/ojfd.2011.11001

Abstract

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.

Highlights

The phenomenon of natural convection arises in fluids when temperature changes cause density variations leading to buoyancy forces acting on the fluid particles
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
We have presented the expression for the rate of heat transfer Nu and shear stress 0 at the wall 0 in the following form for both the ramped wall temperature and isothermal wall temperature

Summary

Introduction

The phenomenon of natural convection arises in fluids when temperature changes cause density variations leading to buoyancy forces acting on the fluid particles Such flows which are driven by temperature differences abound in nature and have been studied extensively because of its applications in engineering, geophysical and astrophysical environments. The unsteady fluid flow past a moving plate in the presence of free convection and radiation were studied by Mansure [3], Raptis and Perdikis [4], Das et al [5], Grief et al [6], Ganeasan and Loganathan [7], Mbeledogu et al [8], Makinde [9] and Abdus-Sattar and Hamid Kalim [10]. Israel-Cookey et al [11] have studied the influence of viscous dissipation and radiation on unsteady MHD freeconvection flow past an infinite heated vertical plate in a porous medium with time-dependent suction. It is found that an increase in Prandtl number leads to fall the temperature for ramped temperature as well as isothermal case

Formulation of the Problem and Its Solutions

Solution for Isothermal Case

Results and Discussion

MaDa erf

Conclusions