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Constructal design of a non-uniform heat generating disc based on entropy generation minimization

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Abstract

Non-uniform heat generating phenomenon is ubiquitous in real electronic devices. Based on this point, this paper researches the entropy generation rate (EGR) performance of a non-uniform heat generating (NUHG) disc. In this NUHG model, constructal design of the radial-pattern disc is performed with the conditions of constant- and variable-cross-sectional highly conductive routes (HCRs), respectively. The overall generation of heat over the entire disc area stays invariable, while the geometry of the disc is free to morph. The influence of heat generation non-uniformity on the optimized geometry of the disc is studied. The results manifest that increasing the thermal conductivity ratio and area ratio of HCRs both can reduce the EGR. Increasing the number of elements involved in the disc will compel the optimal HCRs to stretch towards the centre. In the areas with more heat generation and severer heat conduction requirement, more high conductivity material should be arranged to converge more heat flow and reduce the EGR aroused during the heat transfer process. The dimensionless EGR slumps by 11.5% on account of the employment of variable-cross-sectional HCR stratagem. Henceforth, the variable-cross-sectional HCR structure can reduce the EGR and improve its thermal performance. Additionally, the results obtained by minimizing EGR are compared with those obtained by minimizing maximum temperature difference. The primary novelty of this paper is introducing entropy generation minimization theory into the constructal design of radial-pattern disc with both non-uniform heat generation and constant- and variable-cross-sectional HCRs, which can provide benefits to the designs of practical electronic devices and the improvement of heat transfer performance.

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Abbreviations

A :

Area (\(\hbox {m}^{{2}}\))

D :

Breadth (m)

f(r, y):

Heat generating rate function

\(k_{0} \) :

Thermal conductivity of heat generating area [W/(m K)]

\(k_\mathrm{{p}} \) :

Thermal conductivity of highly conductive routes [W/(m K)]

\(\tilde{{k}}\) :

Thermal conductivity ratio \(k_\mathrm{{p}} /k_{0} \)

L :

Length (m)

m :

Breadth ratio

N :

Number of sectorial elements

p :

Non-uniform heat generating coefficient

\(q^{{\prime }{\prime }{\prime }}\) :

Heat generating constant per unit volume (W/m\(^{{3}}\))

\(\dot{{S}}_{\mathrm{gen}} \) :

Entropy generation rate (W/K)

T :

Temperature (K)

\(\alpha \) :

Apex angle (rad)

\(\Delta \) :

Change in physical quantities

\(\nabla \) :

Gradient

\(\phi \) :

Area ratio of highly conductive routes to whole disc

m:

Minimized

mm:

Twice minimized

opt:

Optimized

\(\sim \) :

non-dimensionalized

EGR:

Entropy generation rate

EGM:

Entropy generation minimization

HCR:

Highly conductive route

HT:

Heat transfer

MTD:

Maximum temperature difference

MTDM:

Maximum temperature difference minimization

NUHG:

Non-uniform heat generation

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 51779262, 51579244 and 51979278), Natural Science Foundation of Hubei Province (Grant No. 2016CFB504) and Independent Project of Naval University of Engineering (No. 425317Q017). The authors wish to thank the reviewers for their careful, unbiased and constructive suggestions, which led to this revised manuscript.

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Authors and Affiliations

  1. Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan, 430205, People’s Republic of China

    Huijun Feng, Jiang You, Lingen Chen, Yanlin Ge & Shaojun Xia

  2. School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan, 430205, People’s Republic of China

    Huijun Feng, Jiang You, Lingen Chen, Yanlin Ge & Shaojun Xia

  3. School of Power Engineering, Naval University of Engineering, Wuhan, 430033, People’s Republic of China

    Jiang You

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  1. Huijun Feng
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Feng, H., You, J., Chen, L. et al. Constructal design of a non-uniform heat generating disc based on entropy generation minimization. Eur. Phys. J. Plus 135, 257 (2020). https://doi.org/10.1140/epjp/s13360-020-00273-3

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