Lahcen El Moutaouakil, Zaki Zrikem and Abdelhalim Abdelbaki
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…
Abstract
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 (103Ra m3×104) and the aspect ratio A (10A80). 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 10A80 and submitted to non-uniform heat flux was not examined before. Development of original correlations.
Details
Keywords
Lahcen El Moutaouakil, Zaki Zrikem and Abdelhalim Abdelbaki
A detailed numerical study is conducted on the effect of surface radiation on laminar natural convection in a tall vertical cavity filled with air. The cavity is heated and…
Abstract
Purpose
A detailed numerical study is conducted on the effect of surface radiation on laminar natural convection in a tall vertical cavity filled with air. The cavity is heated and cooled, through its two vertical walls, by a linear or uniform heat flux q(y) and by a constant cold temperature, respectively. The horizontal walls are considered adiabatic. The paper aims to discuss these issues.
Design/methodology/approach
The radiosity method is employed to calculate the net radiative heat exchanges between elementary surfaces, while the finite volume method is implemented to resolve the governing equations of the fluid flow.
Findings
For each heat flux q(y) (ascending, descending or uniform), the effect of the emissivity ε (0ε1) on the local, average and maximum temperatures of the heated wall is determined as a function of the average Rayleigh number Ram (103Ram6×104) and the cavity aspect ratio A (10A80). The effect of the coupling on the flow structures, convective and radiative heat transfers is also presented and analyzed. Overall, it is shown that surface radiation significantly reduces the local and average temperatures of the heated wall and therefore reduces the convective heat transfer between the active walls.
Practical implications
The studied configuration is of practical interest in several areas where overheating must be avoided. For this purpose, a simple design tool is developed to estimate the mean and the maximum temperatures of the hot wall in different operating conditions (Ram, A et ε).
Originality/value
The originality lies in the study of the interaction between surface radiation and natural convection in tall cavities submitted to a non-uniform heat flux and a constant cold temperature on the active walls. Also, the development of an original simplified calculation procedure for the hot wall temperatures.