Thermal resistance analysis on conjugate free convective flow in a thick-walled square chamber

Abstract

A numerical analysis of the conjugate free convective flow of air in a thick-walled square chamber has been conducted in this study. The finite left thick wall is heated with any of the four heating conditions, while the finite right thick surface is kept at a fixed cold temperature, and the remaining walls are assumed to be insulated. The governing equations are simulated via the Galerkin finite element technique with a triangular discretization scheme. Thermal resistance analysis is done for an extensive range of Rayleigh numbers (103 ≤ Ra ≤ 107) under four heating conditions of the left wall: isothermal, linear, sinusoidal, and isoflux. Besides, ten different combinations of wall thickness (0 ≤ t1/L ≤ 0.2 and 0 ≤ t2/L ≤ 0.2, where L is the length of the chamber) and three wall materials, such as glass fiber (ks = 0.035 W/mK), pinewood (ks = 0.15 W/mK), and plexiglass (ks = 0.195 W/mK), are considered in this parametric study. The effects of these parameters are presented in terms of the mean Nusselt number along the left solid-fluid interacting wall and the overall thermal performance index. In addition, qualitative visualization of heatlines, streamlines, and isotherms is illustrated for the optimum condition. Numerical results suggest that wall materials with higher thermal conductivity and lower wall thickness give the highest overall thermal performance for a linear heating condition.

Keywords

• Thick-walled cavity
• Thermal resistance
• Rayleigh number
• Overall thermal performance
• Heatlines