Discrete ordinates interpolation method incorporated into a flow and energy solver for solution of combined heat transfer problems

Abstract

Combined conduction–radiation and natural convection–radiation in two-dimensional enclosures containing gray absorbing/emitting medium are numerically investigated. The discrete ordinates interpolation method (DOIM) is used to solve the radiative transfer equation (RTE). It is incorporated into a commercial software (FLUENT ®) by using user-defined function (UDF) to be used in a finite volume-based code for fluid flow computation. Two issues are critically examined: accuracy and versatility. Cases of combined conduction–radiation are considered first and the results are compared with other benchmark solutions to validate the accuracy. Additional problems are also tested to verify the capability of handling unstructured grid system and irregular geometry. Combined natural convection–radiation problem is then examined varying the optical thickness. The radiation effect is investigated through the profiles of velocity, temperature distributions and streamlines. The results are compared with discrete ordinates (DO) solutions, Rosseland solutions and P1 solutions which are offered by FLUENT ® package. The accuracy and other numerical characteristics of DOIM are scrutinized. The DOIM shows very successful results from the viewpoint of accuracy and grid compatibility. It is proved to be a reliable future numerical tool for combined heat transfer problems in engineering applications.