Mixed convection and role of multiple solutions in lid-driven trapezoidal enclosures

Abstract

This paper analyzes probable steady state flow structures and temperature patterns that may evolve during mixed convection within a lid-driven trapezoidal enclosure with cold top wall and hot bottom wall as the speed of moving lid varies with respect to the intensity of imposed temperature gradients. In this regard, a Grashof (Gr)-Reynolds (Re)-Prandtl (Pr) number formulation has been used to induce varying contributions from moving lid compared to that from imposed thermal gradients, where Grashof number has been varied from 10(3) to 10(5) at Re = 1 and 100 for three different fluids of Pr = 0.015, 0.7 and 10. Simulations have been performed for two different scenarios of isothermal (case 1) and non-isothermal (case 2) bottom wall with inclination angle of the side wall being kept at 45 degrees. It has been found that non-isothermal bottom wall (case 2) leads to multiple steady states in either natural convection dominated regime (Gr/Re-2 >> 1) or mixed convection regime (Gr/Re-2 similar to O(1)) in convection dominated heat transport regime (Pr x Re greater than or similar to 1). Number of steady states are observed to be more in natural convection dominated regime at Re = 1. The flow structures of various steady states are found to be crucial to achieve higher heat transfer rates for non-isothermal bottom wall. (c) 2013 Elsevier Ltd. All rights reserved.