Visualization of heat transport using dimensionless heatfunction for natural convection and conduction in an enclosure with thick solid ceiling

Abstract

A conjugate conduction-(natural)convection problem is numerically studied in order to present the application of dimensionless heatfunction for entire computational domain including solid and fluid regions in an enclosure with thick solid ceiling. The modified dimensionless heatfunction for solid region is defined to provide continuity of dimensionless heatfunction on solid-fluid interface. The enclosure is differentially heated from vertical walls, and horizontal walls are adiabatic. Finite difference method is employed to solve the set of governing equations. The dimensionless governing parameters for computations are: Rayleigh number (from 103 to 106), dimensionless ceiling wall thickness (0.05 and 0.5) and thermal conductivity ratio (from 1 to 100). The obtained results shows that the heat and fluid flows in the enclosure are considerably influenced by Rayleigh number and thermal conductivity ratio. Dimensionless wall thickness comparatively has less effect on heat transfer rate through the cavity. © 2008 Elsevier Ltd. All rights reserved

Sensitivity of heatfunction boundary conditions on invariance of Bejan’s heatlines for natural convection in enclosures with various wall heatings

“…The reference of heatfunction (P ¼ 0) is generally considered at the adiabatic wall of the cavity or any convenient point (origin or cold-cold junction) as mentioned in previous studies [17,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. However, in this study, various possible locations of datum of heatfunction (P ¼ 0) and heatfunction boundary conditions are explored and discussed for systems with more than one (case 1) and no adiabatic wall (case 3).…”

“…Due to adiabatic top and bottom walls, the datum point for heatfunction (P) or the boundary condition, P ¼ 0 was considered at the bottom wall. Similar to the work reported by Deng and Tang [20], conjugate natural convection in square and rectangular cavities were also carried out using heatfunction formulation [21]. Basak and Roy [22] reported various cases of thermal boundary conditions including uniform/non-uniform heating of bottom wall and discretely heated bottom and side walls.…”

Using of Bejan's Heatline Technique for Analysis of Natural Convection in a Divided Cavity with Differentially Changing Conductive Partition

“…By defining h as a continuous scalar function, the dimensional heatfunction can be written in a differential form [23].…”

“…(19) and (20) along the considered boundary. For instance, the following equation can be used to determine the values of heatfunction at the left wall of the cavity [23].…”

“…The same geometry with different boundary conditions was also studied [22]. Mobedi and Oztop [23] studied conjugate heat transfer in an enclosure with a thick solid ceiling using the heatline method. They investigated thermal conductivity ratio effects on heat and fluid flow.…”