Role of finite element based grids and simulations on evaluation of Nusselt numbers for heatfunctions within square and triangular cavities involving multiple discrete heaters

Abstract

Nusselt number is an important non-dimensional parameter which quantifies the heat transfer rate. Local Nusselt number is useful in predicting the heat transfer rate along the various hot and cold sections of the side walls in a discretely heated enclosed cavity. In addition, the overall heat balance in an enclosed cavity (total heat delivered by the hot isothermal walls should be equal to the total heat gained by the cold isothermal walls) can be validated via the average Nusselt numbers. Current finite element based simulations and post-processing have been carried out in order to analyze the influence of the multiple heaters on the Nusselt number along various sections (hot and cold) of the side walls in discretely heated square and triangular (design 1 and design 2) cavities. The working fluid is considered to be air (Pr=0.7) and the numerical studies have been carried out for a large range of Rayleigh number (Ra=103–105) for four different biquadratic elements (24×24, 28×28, 32×32 and 34×34). The current work also estimates the fractional error in the heat balance (ϵ) and it is clearly inferred that ϵ is comparatively lower for 34×34 biquadratic elements. Current work also reveals that the fractional error (ϵ) is mainly induced due to the sharp variations in the Nusselt number at the cold-hot junctions along the side walls. The present study also involves the detailed evaluation of the heatfunction (Π) expressions along the cold-hot junctions of the side walls. The computations of the heatfunctions are intrinsically related to the Nusselt numbers of the hot-cold junctions.