Numerical study on free convection flow with joule heating, heat generation and viscous dissipation along a vertical wavy surface

Abstract

A steady two-dimensional natural convection flow of viscous incompressible fluid considering viscous dissipation along a uniformly heated vertical wavy surface in presence of internal heat generation and Joule heating has been investigated. Using the appropriate transformations the basic equations are changed to non-dimensional boundary layer equations, which are solved numerically by employing the implicit finite difference method together with Keller-box scheme. The program code of this method has been developed in FORTRAN. Here I have focused my attention on the changes of surface shear stress in terms of local skin friction, rate of heat transfer in terms of local Nusselt Number, velocity profile, temperature distribution, isotherms as well as the streamlines for a selection of parameter sets consisting of heat generation parameter Q(0.30 to 1.0) the Joule heating parameter J(0.001 to 0.040), the magnetic parameter M(0.0 to 3.0), viscous dissipation parameter Ec(0.50 to 5.0), Prandtl number Pr(0.73 to 7.00) and the amplitude of waviness of the surface α(0.0 to 0.3). The results have been shown graphically by utilizing the visualizing software TECHPLOT. The results obtained from the numerical study have been discussed emphasizing the physical prospects.