Analysis of Energy Flux Vector on Natural Convection Heat Transfer in Porous Wavy-Wall Square Cavity with Partially-Heated Surface

Yan-Ting Lin,Ching-Chang Cho

doi:10.3390/en12234456

Yan-Ting Lin, Ching-Chang Cho

Open Access

https://doi.org/10.3390/en12234456

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Abstract

The study utilizes the energy-flux-vector method to analyze the heat transfer characteristics of natural convection in a wavy-wall porous square cavity with a partially-heated bottom surface. The effects of the modified Darcy number, modified Rayleigh number, modified Prandtl number, and length of the partially-heated bottom surface on the energy-flux-vector distribution and mean Nusselt number are examined. The results show that when a low modified Darcy number with any value of modified Rayleigh number is given, the recirculation regions are not formed in the energy-flux-vector distribution within the porous cavity. Therefore, a low mean Nusselt number is presented. The recirculation regions do still not form, and thus the mean Nusselt number has a low value when a low modified Darcy number with a high modified Rayleigh number is given. However, when the values of the modified Darcy number and modified Rayleigh number are high, the energy flux vectors generate recirculation regions, and thus a high mean Nusselt number is obtained. In addition, in a convection-dominated region, the mean Nusselt number increases with an increasing modified Prandtl number. Furthermore, as the length of the partially-heated bottom surface lengthens, a higher mean Nusselt number is presented.

Highlights

The plot of the heat energy flow paths is important since it can provide physical insights into the energy transport process in detail
Hooman [5, 6] has presented an energy-flux-vector method, which is basically similar to the heatline technique, for visualizing the transport process of heat energy
Comparing the two visualization methods, Hooman [5, 6] has pointed out that the energy-flux-vector method is better than the heatline visualization technique since the algebraic equations do not require to be solved

Summary

Introduction

The plot of the heat energy flow paths is important since it can provide physical insights into the energy transport process in detail To achieve this purpose, Kimura and Bejan [1] have suggested a heatline visualization technique. Biswal et al [15] have utilized the energy-flux-vector method for explaining the transport process of heat energy of natural convection within a porous cavity with curved side walls. Their results have shown that given suitable curved-sidewall forms with appropriate flow conditions, the heat transfer effect can be enhanced. Simulations focus on the effects of the modified Darcy number and modified Rayleigh number on the energy-flux-vector distribution and mean Nusselt number, respectively

Governing Equations and Boundary Conditions

Geometric Description and Numerical Method

Numerical Validation and Grid Independence Evaluation

Results and discussion

Conclusions

Methods