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Technical Brief

Optimal Distribution of Discrete Heat Sources Under Mixed Convection—A Heuristic Approach

[+] Author and Article Information
Tapano Kumar Hotta

Center of Energy,
Indian Institute of Technology Jodhpur,
Rajasthan 342011, India

C. Balaji

Department of Mechanical Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: balaji@iitm.ac.in

S. P. Venkateshan

Department of Mechanical Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India

The convective heat transfer coefficient for all the five heat sources of a particular configuration is first calculated as defined in Eq. 6 of the manuscript. The maximum convective heat transfer coefficient is the maximum among all the five values of convective heat transfer coefficient obtained thus.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 12, 2013; final manuscript received March 27, 2014; published online July 29, 2014. Assoc. Editor: Jose L. Lage.

J. Heat Transfer 136(10), 104503 (Jul 29, 2014) (7 pages) Paper No: HT-13-1474; doi: 10.1115/1.4027350 History: Received September 12, 2013; Revised March 27, 2014

Steady state experiments are conducted in a low speed horizontal wind tunnel under mixed convection for five discrete heat sources (aluminum) of nonidentical sizes arranged at different positions on a substrate board (bakelite) to determine the optimal configuration. The optimal configuration is one for which the maximum temperature excess (difference between the maximum temperature among the heat sources of that configuration, and the ambient temperature) is the lowest among all the other possible configurations and is determined by a heuristic nondimensional geometric parameter λ. The maximum temperature excess is found to decrease with λ, signifying an increase in heat transfer coefficient. In view of this, the configuration with highest λ is deemed to be the optimal one. The effect of surface radiation on the heat transfer characteristic of heat sources is also studied by painting their surface with black, which reduces their temperature by as much as 12%. An empirical correlation is developed for the nondimensional maximum temperature excess (θ) in terms of λ, by taking into account the effect of surface radiation. The correlation when applied for highest λ of the configuration returns the minimum value of θ at the optimal condition, which is a key engineering quantity that is sought in problems of this class.

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References

Figures

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Fig. 1

Schematic of the low speed horizontal wind tunnel

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Fig. 2

Arrangement of heat sources on the substrate board

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Fig. 3

One typical configuration (out of 17) used for the experiment, λ = 1.6708

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Fig. 4

Variation of maximum temperature excess of different configurations with their λ

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Fig. 5

Variation of maximum convective heat transfer coefficient of different configurations with their λ

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Fig. 6

Variation of temperature excess of five heat sources for the optimal configuration

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Fig. 7

Variation of temperature excess of five heat sources for the optimal configuration with different velocities

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Fig. 9

Parity plot showing the agreement between θdata and θfit for two different regimes

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Fig. 8

Parity plot showing the agreement between θdata and θfit

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