ANALYSIS OF MHD MIXED CONVECTION AND JOULE HEATING IN A LID-DRIVEN CAVITY HAVING A SQUARE BLOCK USING CU-WATER NANOFLUID

Abstract

A numerical study has been conducted to illustrate the effect of magnetic field and Joule heating on the flow and thermal fields in a lid-driven cavity with a centered heat-conducting horizontal square block. Both sidewalls of the cavity are kept at constant different temperatures Th and Tc (Th >Tc) to enhance the natural convection and at the same time, the top and bottom walls are kept adiabatic. The left vertical wall is moving upward at a constant speed, but the other walls remain stationary. The nanofluid considered within the cavity is electrically conducting. The number of Cu particles is mixed at a different ratio within the water to observe the effect of volume fraction on the isotherm, streamline, and other characteristics. The problem was solved by Galerkin weighted residual finite element method and the governing equation along with the boundary conditions were solved by Newton Raphson’s iterative algorithm. The computation is carried out for wide ranges of Richardson numbers, Hartman’s numbers, Joule heating parameter, Volume fraction, and the size of the inner Block. The main objective of this study is to investigate the effect of Joule heating in the presence of magnetic field in mixed convection for the case of nanofluid. A list of figures consisting of streamlines, isothermal lines, average Nusselt number at the hot wall, and average fluid temperature in the cavity for the prementioned parameters are used to present the result of the study. It has been found that the flow field and temperature distribution are strongly dependent on the magnetic Parameter, Joule heating parameter, volume fraction of nanoparticles, and the size of the inner block at the pure mixed convection region.

Keywords: Galerkin Weighted Residual Method, Lid-Driven Cavity, MHD-Mixed Convection, Nanofluids, Square Block