Natural convection of third-grade non-Newtonian fluid flow in a porous medium with heat source: Analytical solution

摘要

.Heat transfer by natural convection occurs in many physical and engineering applications. Governing equations of these problems are non-linear and need special methods for being solved. This paper aims to conduct an analytical analysis on the natural convection of a non-Newtonian fluid flow between two infinite vertical flat plates within a porous medium considering a variable heat source. The addition of porous medium and heat source marks the difference between the present work and previous researches. In the first phase of the current analysis, the governing equations including partial differential equations (PDE) are turned into ordinary differential equations (ODE) utilizing the similarity solution. Afterwards, a system of differential equations is solved using the Least Square Method (LSM), and reliable functions for the temperature and velocity distributions are presented. In order to investigate the accuracy of this method, the governing equations are also solved using numerical solutions. Proper agreement is observed between the analytical and numerical results. Regarding the very small errors observed in the results yielded by the LSM method, it can be concluded that this method is an efficient and reliable approach for solving non-linear ordinary differential equations. Finally, the effects of two main parameters, namely porosity and heat source parameters, are meticulously discussed. It is shown that as the value of the heat source parameter increases, the values of velocity and temperature decrease. Also, the results indicate that by enhancing the porosity parameter the flow velocity decreases, whereas there is no change in temperature. The results could be helpful for systems such as geothermal systems, heat exchangers, petroleum reservoirs and nuclear waste repositories in which natural convection is important.