Analysis of heat absorption on natural convection flow along a vertical wavy surface with viscous dissipation under variable viscosity

Abstract

Viscous incompressible fluid in a steady two-dimensional natural convection flow considering viscous dissipation along a uniformly heated vertical wavy surface in presence of internal heat absorption and variable viscosity has been investigated in this thesis. Using the appropriate transformations of variables of the basic governing 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. Attention is focused on the evolution of the surface shear stress in terms of local skin friction, rate of heat transfer in terms of local Nusselt Number, velocity, temperature, isotherms as well as the streamlines for a selection of parameter sets consisting of viscosity parameter ε, heat absorption parameter Q, Eckert Number Ec, Prandtl number Pr and the amplitude of waviness of the surface α. The results obtained from the numerical study have been discussed emphasizing the physical prospects and shown graphically by utilizing the visualizing software TECHPLOT. The skin friction coefficient Cfx, the rate of heat transfer in terms of Nusselt number Nux, the velocity, the temperature, the streamlines as well as the isotherms are shown graphically in figures for different values of the viscosity variation parameter ε (= 0.0 to 60.0), heat absorption parameter Q(= -0.40 to 0.0), Eckert number Ec (= 0.0 to 8.0), the amplitude of waviness of the surface α(= 0.0 to 0.4)and Prandtl number Pr (= 0.73 , 3.0, 7.0, 15.5) which correspond to the air at 2100°K, water at20℃, 60℃ and 100℃respectively. The results of the present investigations for heat absorption parameter Q, the rate of heat transfer and velocity increases and the skin friction coefficient and temperature decreases. For increasing Eckert number Ec, the skin friction coefficient, velocity and temperature are increases, but the significant decreases over the whole boundary layer for the rate of heat transfer. The comparisons of the present numerical results with previous published works performed and the results show excellent agreement.