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Simulation studies on multi-mode heat transfer from an open cavity with a flush-mounted discrete heat source

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Abstract

Prominent results of a simulation study on conjugate convection with surface radiation from an open cavity with a traversable flush mounted discrete heat source in the left wall are presented in this paper. The open cavity is considered to be of fixed height but with varying spacing between the legs. The position of the heat source is varied along the left leg of the cavity. The governing equations for temperature distribution along the cavity are obtained by making energy balance between heat generated, conducted, convected and radiated. Radiation terms are tackled using radiosity-irradiation formulation, while the view factors, therein, are evaluated using the crossed-string method of Hottel. The resulting non-linear partial differential equations are converted into algebraic form using finite difference formulation and are subsequently solved by Gauss–Seidel iterative technique. An optimum grid system comprising 111 grids along the legs of the cavity, with 30 grids in the heat source and 31 grids across the cavity has been used. The effects of various parameters, such as surface emissivity, convection heat transfer coefficient, aspect ratio and thermal conductivity on the important results, including local temperature distribution along the cavity, peak temperature in the left and right legs of the cavity and relative contributions of convection and radiation to heat dissipation in the cavity, are studied in great detail.

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Abbreviations

A :

aspect ratio

F ik :

view factor of an element i with reference to another element k of the cavity

h :

convection heat transfer coefficient (W/m2 K)

J(i, j):

radiosity of an element (i, j) of the enclosure (W/m2)

k :

thermal conductivity of the cavity walls and heat source (W/m K)

L :

height of open cavity (m)

L 1 :

distance between bottom end of the cavity and the start of heat source (m)

L h :

height of the discrete heat source (m)

M :

total number of grids along the leg

M 1 :

total number of grids between bottom end of the cavity and the start of heat source

M 2 :

total number of grids between bottom end of the cavity and the end of heat source

N :

total number of grids across the cavity

n′:

total number of elements in the cavity

Pr :

Prandtl number of air

q v :

volumetric heat generation in the heat source (W/m3)

S :

spacing between the legs of the cavity (m)

t :

thickness of each wall of the cavity (m)

T :

temperature at any location in the cavity (K or °C)

T max :

maximum temperature in the cavity (K or °C)

T ∞ :

ambient air temperature (K or °C)

x :

co-ordinate direction along the cavity

y :

co-ordinate direction across the cavity

δ c :

convergence criterion, in percentage, \( {\left| {\raise0.7ex\hbox{${(T_{{{\text{new}}}} - T_{{{\text{old}}}} )}$} \!\mathord{\left/ {\vphantom {{(T_{{{\text{new}}}} - T_{{{\text{old}}}} )} {T_{{{\text{new}}}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${T_{{{\text{new}}}} }$}} \right|} \times 100\% \)

Δx :

height of the wall element in non-heat source portion along the cavity (m)

Δx h :

height of the wall element in heat source portion (m)

Δy :

height of the wall element in non-heat source portion across the cavity (m)

ε :

surface emissivity of the walls of the cavity

σ :

Stefan–Boltzmann constant (5.6697 × 10−8 W/m2 K4)

cond, x, in:

conduction heat transfer into an element along the cavity

cond, x, out:

conduction heat transfer out of an element along the cavity

cond, y, in:

conduction heat transfer into an element across the cavity

cond, y, out:

conduction heat transfer out of an element across the cavity

conv:

convection heat transfer from an element

conv, horz:

convection heat transfer from the horizontal surface of the unique element

conv, vert:

convection heat transfer from the vertical surface of the unique element

gen:

volumetric heat generation in an element

i :

any arbitrary element along the cavity

j :

any arbitrary element across the cavity

new, old:

temperatures from current and previous iterations, respectively

rad:

heat transfer by surface radiation from an element

rad, horz:

radiation heat transfer from the horizontal surface of the unique element

rad, vert:

radiation heat transfer from the vertical surface of the unique element

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology, [Formerly, Regional Engineering College Warangal], Warangal, 506 004, AP, India

    C. Gururaja Rao, V. Nagabhushana Rao & C. Krishna Das

Authors
  1. C. Gururaja Rao
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  2. V. Nagabhushana Rao
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  3. C. Krishna Das
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Correspondence to C. Gururaja Rao.

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Gururaja Rao, C., Nagabhushana Rao, V. & Krishna Das, C. Simulation studies on multi-mode heat transfer from an open cavity with a flush-mounted discrete heat source. Heat Mass Transfer 44, 727–737 (2008). https://doi.org/10.1007/s00231-007-0301-4

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  • DOI: https://doi.org/10.1007/s00231-007-0301-4

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