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Visualization of diffusion and convection heat transport in a square cavity with natural convection

Mobedi, Moghtada; Ozkol, Uenver and Sundén, Bengt LU (2010) In International Journal of Heat and Mass Transfer 53(1-3). p.99-109
Abstract
In this study, the total heatfunction equation which includes diffusion and convection transport is divided into the corresponding heatfunction equations. The superposition rule is used to obtain the mathematical definitions of diffusion and convection heatfunctions and corresponding boundary conditions. It is observed that the separate visualization of diffusion and convection heatlines provides significant information on understanding of the mechanism of heat transfer in a convective flow. The direction of the diffusion and convection heat transport as well as the strength of convection compared to the conduction in entire or in a portion of a domain can be visualized. The diffusion heatlines demonstrate a potential flow like behavior... (More)
In this study, the total heatfunction equation which includes diffusion and convection transport is divided into the corresponding heatfunction equations. The superposition rule is used to obtain the mathematical definitions of diffusion and convection heatfunctions and corresponding boundary conditions. It is observed that the separate visualization of diffusion and convection heatlines provides significant information on understanding of the mechanism of heat transfer in a convective flow. The direction of the diffusion and convection heat transport as well as the strength of convection compared to the conduction in entire or in a portion of a domain can be visualized. The diffusion heatlines demonstrate a potential flow like behavior while convective heat flow rotates due to the source term of the convection heatfunction equation, similar to the rotation of fluid flow generated by fluid flow vorticity. The similarity between the streamfunction and the total heatfunction yields a concept of heat flow vorticity, Omega(t). The obtained results show that the maximum absolute value of the convection heatfunction may be an appropriate parameter for determination of the convection strength. The diffusion and convection heatfunction equations for natural convection in a differentially heated square cavity for four different length of the heated surface on the right vertical wall as s(p) = L/4, L/2, 3L/4 and L and a fixed length of the cooled surface on the right vertical wall as L/4 are obtained and corresponding heatlines are drawn. The values of the conduction heatfunction are positive while the sign of convection heatfunction values is negative for the studied cases. Based on the distribution of total heatlines, two regions are detected in the cavity, an active region with the positive values of heatlines signifying dominant conduction heat transfer and a passive region with the negative heatfunction values in where convection heat flow is dominant and heat only rotates in a closed contour pattern. The variations of average Nusselt number, average of heat flow vorticity. maximum absolute values of convection heatfunction and streamfunction at different Rayleigh numbers and lengths of the heated surface are presented. (C) 2009 Elsevier Ltd. All rights reserved. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Diffusion, Heatlines, Convective flow, Vorticity, Convection
in
International Journal of Heat and Mass Transfer
volume
53
issue
1-3
pages
99 - 109
publisher
Pergamon
external identifiers
  • wos:000272877900012
  • scopus:71749100423
ISSN
0017-9310
DOI
10.1016/j.ijheatmasstransfer.2009.09.048
language
English
LU publication?
yes
id
9ff8f4ca-c3d4-4686-a7c9-bb21aeab2412 (old id 1533849)
date added to LUP
2010-01-27 14:16:23
date last changed
2018-06-10 03:18:50
@article{9ff8f4ca-c3d4-4686-a7c9-bb21aeab2412,
  abstract     = {In this study, the total heatfunction equation which includes diffusion and convection transport is divided into the corresponding heatfunction equations. The superposition rule is used to obtain the mathematical definitions of diffusion and convection heatfunctions and corresponding boundary conditions. It is observed that the separate visualization of diffusion and convection heatlines provides significant information on understanding of the mechanism of heat transfer in a convective flow. The direction of the diffusion and convection heat transport as well as the strength of convection compared to the conduction in entire or in a portion of a domain can be visualized. The diffusion heatlines demonstrate a potential flow like behavior while convective heat flow rotates due to the source term of the convection heatfunction equation, similar to the rotation of fluid flow generated by fluid flow vorticity. The similarity between the streamfunction and the total heatfunction yields a concept of heat flow vorticity, Omega(t). The obtained results show that the maximum absolute value of the convection heatfunction may be an appropriate parameter for determination of the convection strength. The diffusion and convection heatfunction equations for natural convection in a differentially heated square cavity for four different length of the heated surface on the right vertical wall as s(p) = L/4, L/2, 3L/4 and L and a fixed length of the cooled surface on the right vertical wall as L/4 are obtained and corresponding heatlines are drawn. The values of the conduction heatfunction are positive while the sign of convection heatfunction values is negative for the studied cases. Based on the distribution of total heatlines, two regions are detected in the cavity, an active region with the positive values of heatlines signifying dominant conduction heat transfer and a passive region with the negative heatfunction values in where convection heat flow is dominant and heat only rotates in a closed contour pattern. The variations of average Nusselt number, average of heat flow vorticity. maximum absolute values of convection heatfunction and streamfunction at different Rayleigh numbers and lengths of the heated surface are presented. (C) 2009 Elsevier Ltd. All rights reserved.},
  author       = {Mobedi, Moghtada and Ozkol, Uenver and Sundén, Bengt},
  issn         = {0017-9310},
  keyword      = {Diffusion,Heatlines,Convective flow,Vorticity,Convection},
  language     = {eng},
  number       = {1-3},
  pages        = {99--109},
  publisher    = {Pergamon},
  series       = {International Journal of Heat and Mass Transfer},
  title        = {Visualization of diffusion and convection heat transport in a square cavity with natural convection},
  url          = {http://dx.doi.org/10.1016/j.ijheatmasstransfer.2009.09.048},
  volume       = {53},
  year         = {2010},
}