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Effect of surface radiation heat transfer on the optimal distribution of discrete heat sources under natural convection

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Abstract

Experiments have been conducted for natural convection heat transfer from protruding discrete heat sources, mounted at different positions on a substrate, to determine the optimal configuration, and to study the effect of surface radiation on them, which reduces their temperature upto 12 %. The optimal configuration has been determined by a non-dimensional geometric distance parameter (λ). An empirical correlation has been proposed between the non-dimensional steady state temperature (θ) and λ, by taking into account the effect of surface radiation heat transfer.

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Abbreviations

A :

Area of the heat source, m 2

F :

Shape factor between the surfaces of heat sources

g :

Gravitational acceleration, 9.81   m/s 2

Gr :

Grashof number, \(g\beta(T_{hs}-T_{\infty})L^{3}/\nu^{2}\)

\(Gr^{\ast}\) :

Modified Grashof number, \(g \beta(\Updelta T_{ref})L^{3}/\nu^{2}\)

h :

Heat transfer coefficient, W/m 2 °C

I :

Heat source input current, A

k :

Thermal conductivity, W/m K

L :

Length of the heat source, m

Nu :

Nusselt number, h conv L/k f

\(q^{\ast}\) :

Non-dimensional heat flux, \(Q_{supplied}L/Ak_{f}T_{\infty}\)

Q :

Rate of heat transfer, W

Ra :

Rayleigh number, GrPr

t :

Thickness of the substrate, m

t i :

Thickness of the insulation, m

T :

Temperature, K

v :

Volume of the heat source, m 3

V :

Heat source input voltage, V

X, Y :

Centroid, with the origin fixed at the left bottom corner of the heat source 51, m

Z :

Geometric parameter, X/Y

∑ d 2 i :

Sum of the square of the distances, for each configuration, from the centroid of each heat source of that configuration, to the centroid of that particular configuration, m 2

β:

Isobaric thermal expansion coefficient of air, 1/T mean , K −1

\(\Updelta T_{ref}\) :

Reference temperature, Q supplied L/Ak f ,   K

\(\varepsilon\) :

Hemispherical emissivity of the surfaces of heat source

λ:

Non-dimensional geometric distance parameter

σ:

Stefan Boltzmann constant, 5.67 × 10−8, W/m 2 K 4

θ:

Non-dimensional temperature, \((T_{maximum}-T_{\infty})/\Updelta T_{ref}\)

\(\infty\) :

Ambient

i :

For each heat source

c :

For each configuration

cond:

Conduction

conv:

Convection

f:

Fluid (air)

rad:

Radiation

hs:

Heat source

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Authors and Affiliations

  1. Department of Mechanical Engineering, Heat Transfer and Thermal Power Laboratory, IIT Madras, Chennai, 600036, India

    Tapano Kumar Hotta, Pullarao Muvvala & S. P. Venkateshan

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  1. Tapano Kumar Hotta
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  2. Pullarao Muvvala
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  3. S. P. Venkateshan
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Correspondence to S. P. Venkateshan.

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Hotta, T.K., Muvvala, P. & Venkateshan, S.P. Effect of surface radiation heat transfer on the optimal distribution of discrete heat sources under natural convection. Heat Mass Transfer 49, 207–217 (2013). https://doi.org/10.1007/s00231-012-1072-0

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