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

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.

Mechanical Work at a Boundary and its Associated Exergy Transfer

This paper is a didactic discussion of mechanical work at a boundary from the standpoint of exergy analysis. It is shown that the use of the material velocity vector and the mechanical stress tensor of continuum mechanics allows the magnitude and direction of the energy flux vector at a point to be determined unambiguously. Hence, the amount and direction of the energy transfer at a boundary can be established. This methodology is then extended to the calculation of the associated exergy flux vector and the exergy transfer at the boundary. It is noted that the exergy transfer is not always equal to the energy transfer as mechanical work. In general, the exergy transfer also involves a term consisting of the product of the environmental pressure and a volume displacement or transfer.