On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part I: Description of the method

Abstract

ABSTRACTThe purpose of this paper is to introduce a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method. The approach has already been presented in the context of two-dimensional incompressible flow problems without heat transfer. It has been shown that the pressure–velocity coupling on co-located grids can be correctly modeled via the so-called method of proper closure equations (MPCE). Here, MPCE is extended to the numerical simulation of natural, forced, and mixed convection heat transfer problems. It is shown that the couplings between pressure, velocity, and temperature can be conveniently handled on co-located grids by resorting again to the modified forms of the governing equations, i.e., the proper closure equations. The set of discrete equations is solved in a fully coupled manner in this study. Here, in part I of the paper, only the basic methodology is described; in part II, the results of application of the method to some test problems are presented.