On heat transport and energy partition in thermal convection with mixed boundary conditions

Abstract

A two-dimensional square enclosure thermally insulated on the vertical walls and heated nonuniformly on the horizontal walls is numerically studied in comparison with the classical Rayleigh-Bénard (RB) convection in the range of Rayleigh number 105 ≤ Ra ≤ 109. Two possible configurations, namely, (1) HCCH and (2) HCHC, are studied in which a unit step function describes the conduction wall temperature as a combination of hot (H) and cold (C) temperatures. The first two letters (of HCCH or HCHC) represent the applied thermal conditions on the bottom wall and the last two letters represent those on the top wall. In the mentioned configurations, the average temperature difference between the bottom and top walls is zero, yet the complex convection state is observed. The diagonally aligned large-scale elliptic roll observed in the RB convection for the Rayleigh number Ra = 108 is found to be replaced by a circular roll in HCCH and a square roll in HCHC. The mean and fluctuating temperature fields in cases of HCCH and HCHC are significantly high as compared to the RB case. We found that heat transport is higher for HCCH and HCHC as compared to the RB convection in a range of 105 ≤ Ra < 108. The increase in heat transport is due to (1) an increase in the background potential energy in the case of HCCH and (2) an increase in the available potential energy in the case of HCHC, which is confirmed by using the global energy budget.