Non-Darcy Newtonian Liquid Flow with Internal Heat Generation using Boundary Conditions of the Third Kind of Fully Developed Mixed Convection in a Vertical Channel

Abstract

An analysis of the impact of internal heat generation and other heat parameters on the temperature, velocity and rate of heat transfer of the liquid moving upward in a channel is studied. A fully developed non-Darcy flow using boundary conditions of the third kind with internal heat generation in a vertical channel is selected as the mathematical model. By utilising the similarity transformation, the governing equations are reduced to non-linear ordinary differential equations (ODEs). The converted ODEs are numerically solved and analysed using the fourth-order Runge-Kutta (RK4) method, incorporating a shooting technique with Newton’s method. The generated numerical algorithms are programmed in MATLAB for velocity, temperature and the local Nusselt number analysis. The numerical results of the flow and temperature variables are presented graphically. The impact of the parameters on the Nusselt number is also graphed to determine which of the three types of boundary conditions is the best for allowing heat transmission. The severity of flow reversal is increased under the Robin and Dirichlet conditions by enhancing the Darcy and Forchheimer numbers while decreasing the Brinkman and internal heat generation values. The temperature profiles improved with the increase in Brinkman numbers. Both Nusselt numbers remained constant for the Neumann boundary condition for all parameters except internal heat generation and local heat exponent. The Robin boundary condition is found to be the best facilitates heat transmission, since it delivers more pleasing and realistic results than the Dirichlet and Neumann conditions