Natural convection on a convectively heated vertical wall, one of the fundamental issues of heat and mass transfer in many engineering applications, is investigated in this work. The configuration is governed by the Rayleigh number (RaL or Ra), the Prandtl number (Pr), and the non-dimensional convective heat transfer coefficient (CiL or Ci). A scaling analysis for the dynamics of the boundary layer flow and heat transfer is carried out. The scales of the velocity/thickness of the boundary layer flow and the temperature/thickness of the thermal boundary layer related to the non-dimensional governing parameters are obtained. The scales are validated using the numerical results by large eddy simulation. The results show that the non-dimensional velocity of the boundary layer flow is proportional to CiL2/5RaL2/5; the thickness from the wall to the layer of the maximal velocity is inversely proportional CiL1/5RaL1/5; the non-dimensional thickness of the thermal boundary layer is inversely proportional CiL1/5RaL1/5; the non-dimensional temperature in the thermal boundary layer is proportional to CiL4/5RaL−1/5. The reduction factor describing the thermal resistance of the thermal boundary layer is further discussed, which is proportional to Ci4/5Ra−1/5.
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February 2019
Research Article|
February 22 2019
Scales of natural convection on a convectively heated vertical wall
Special Collection:
Selected Papers from the 10th National Congress on Fluid Mechanics of China
Bingchuan Nie;
Bingchuan Nie
1
School of Civil Engineering, Beijing Jiaotong University
, Beijing 100044, China
2
Beijing’s Key Laboratory of Structural Wind Engineering and Urban Wind Environment
, Beijing 100044, China
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Feng Xu
Feng Xu
a)
1
School of Civil Engineering, Beijing Jiaotong University
, Beijing 100044, China
2
Beijing’s Key Laboratory of Structural Wind Engineering and Urban Wind Environment
, Beijing 100044, China
a)Author to whom correspondence should be addressed: fxu@bjtu.edu.cn
Search for other works by this author on:
a)Author to whom correspondence should be addressed: fxu@bjtu.edu.cn
Note: This paper is part of the special issue from the 10th National Congress on Fluid Mechanics of China
Physics of Fluids 31, 024107 (2019)
Article history
Received:
November 30 2018
Accepted:
January 05 2019
Citation
Bingchuan Nie, Feng Xu; Scales of natural convection on a convectively heated vertical wall. Physics of Fluids 1 February 2019; 31 (2): 024107. https://doi.org/10.1063/1.5083671
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