Analysis of natural convection in tall vertical cavities heated by a linear heat flux and cooled isothermally

摘要

Purpose- This work is devoted to the numerical analysis of laminar natural convection in two-dimensional vertical cavities, filled with air and of high aspect ratios. One of the sidewalls is cooled isothermally while the other is heated by a uniform or linear heat flux whose average is located at mid-height of the wall. The paper aims to discuss these issues. Design/methodology/approach- The governing equations are discretized by the finite volume method and solved, in transient regime, by using the SIMPLE algorithm. Findings- The flow structure, air temperature field, local convective heat flux on the cold wall, variation of the temperature along the heated wall as well as its average and its maximum are analyzed for various combinations of the controlling parameters. These parameters are the linear heat flux slope γ (γ = 0, 1 and - 1, for a uniform, increasing and decreasing heat flux, respectively), the average Rayleigh number Ra_m (10~3=Ra_m = 31~4) and the aspect ratio A (10 = A = 80). It was found that for a given A and Ra_m, the highest (lowest) mean temperature of the hot wall is obtained when the linear heating is descending (ascending). While the maximum temperature increases with the three controlling parameters. Practical implications- Accurate correlations which allow calculating the average and maximum temperatures of the heated wall are developed for each type of heating. Also, an empirical relationship for the position of the maximum temperature is provided for γ = - 1. Originality/value- Despite its fundamental and practical interest, natural convection in cavities with 10=A = 80 and submitted to non-uniform heat flux was not examined before. Development of original correlations.