Unsteady Natural Convection in a Differentially Heated Rectangular Enclosure Possessing Sinusoidal Corrugated Side Walls Loaded with Power Law Non-Newtonian Fluid

Abstract

This research is a numerical analysis exhaustively investigating two-dimensional (2D) transient convective heat transfer in a differentially heated rectangle, possessing sinusoidal corrugated side walls at constant temperatures. The quadrilateral space is filled with a power-law non-Newtonian fluid, plus the right and left walls are uniformly cooled and heated, respectively. The top and bottom walls are retained as adiabatic and the side walls are recast exploiting sinusoidal corrugated shape. The governing equations of the problem are solved using the finite volume method. The evaluation of fluid flow and heat transfer is conducted in such a manner that the power law index n varies from 0.6 to 1.4, the Rayleigh number Ra from 10³ to 10⁷, the corrugation amplitude CA from 0.1 to 0.5, and the corrugation frequency CF of the sinusoidal side walls is in the range of 1 to 5. The results are studied at different values of Ra, n, CA, and CF; they are presented in the form of streamlines, isotherms, and average Nusselt numbers (\(\overline{\rm{Nu}}\)) of the hot side wall. Further, the heat transfer characteristics are presented and the effect of sudden differential heating, as well as its consequential transient behavior, on the fluid flow, velocity, and temperature plots are demonstrated in accordance with the scope of the governing parameters.