Analytical Solution for Natural Convection in an Internally Heated Inclined Cavity With Multiple Heat Source/Sink Pairs

ABSTRACT

This paper presents an analytical solution for steady‐state natural convection within an inclined rectangular cavity subject to volumetric heat generation and various configurations of discrete surface heat sources and sinks. The governing coupled partial differential equations (PDEs) are solved using a combination of Fourier series expansions and perturbation theory (PT), with the internal Rayleigh number (denoted as Ra), which characterizes the heat generated within the cavity, selected as the perturbation parameter and fixed at . The analysis considers key variables such as the number of heat source/sink pairs (), the aspect ratio of the cavity () and the inclination angle (). The temperature difference between heat sources and sinks, denoted by the amplitude (), is maintained at 0.5. The effects of these parameters are explored by examining streamlines, isotherms, and local Nusselt numbers. The analytical results are validated against numerical simulations, showing strong agreement between the two approaches, thus confirming the robustness of the analytical method employed.