Conjugate Heat Transfer Model Based on SIMPLE and Coupled Energy and Heat Equations

Abstract

In this study, a numerical weak coupling strategy for the modeling of a conjugate heat transfer phenomenon is considered. Where the incompressible Navier-Stokes equations are solved using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) as a first step, and then the heat conduction equation for solid is solved in a second step considering the convective velocity field resulting from the first step. A finite-difference approach is used for both discretized time and spatial operators. In this paper, a two-dimensional simulation case study of a steady uniform streamwise flow around heated rectangular and triangle solids is presented. The simulation is forward in time until the steady-state regime is reached as the residuals converge and tend to zero. The spatial analysis of the temperature is obtained through the numerical resolution of the incompressible Navier-Stokes energy equation and the heat diffusion equation for the fluid and solid media, respectively. The results show the temperature, velocity, and pressure fields in the space domain. The code is written in MATLAB®, and the flow chart of the method is provided. It was noted that the convection was more dominant than the diffusion.