Numerical Analysis of Natural Convection of Thermoelectrically Conducting Fluids in a Cubic Cavity under a Constant Magnetic Field. 3rd Report. Heat Transfer Enhancement Effect, Discrete Del Operator Method.

Abstract

Generally speaking, the finite-element method in computational fluid dynamics is universally accepted, however computation by the CPU is time-consuming and requires large memory capacity for data storage. Therefore development of an analytical formulation to reduce the time and storage required for calculation is desired. In this paper, we propose a novel discrete del operator method in order to overcome these defects. This method is formulated using the discrete del operator as the element coefficient matrices in finite-element analysis, and low-memory and high-speed calculations are carried out. In particular, we examine whether this method is effective for the numerical analysis of natural convection of thermoelectrically conducting fluids in a cubic cavity. Moreover, we estimate the effect of heat transfer enhancement under a weak magnetic field on the Hartmann number.