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Modelling of Heat Flow When Thermal Conductivity, Specific Heat Capacity and Density All are a Function of Temperature

  • Research Article-Mechanical Engineering
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Abstract

This paper deals with experimental procedures to determine thermal conductivity, heat capacity, and density of Pb–Sn (60/40) solder alloy between 27 and 280C. The relationship between temperature and these three physical properties was established. An indirect experimental procedure was developed following the Wiedemann Franz Law to determine the thermal conductivity of the material, while direct experimental approaches were used to obtain the specific heat and density values. The heat flow in our sample was analyzed by finite element modeling (FEM). Two different FEM cases for heat flow were analyzed, one with experimentally determined properties, while empirically developed relations were analyzed for the second case. We have also discussed the importance of determining physical properties at regular intervals of temperature for application in FEM, using the empirical relations. Thus, empirical relations can be used to model the high-temperature manufacturing processes like soldering, brazing, welding, and additive manufacturing with good accuracy.

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Abbreviations

\(\dot{T}\) :

Rate of change of temperature

\(\rho \) :

Density

\(\rho _\mathrm{elec}\) :

Electrical resistivity

\(\sigma \) :

Electrical conductivity

A :

Cross-sectional area

C :

Heat capacity

\(C_\mathrm{p}\) :

Constant pressure heat capacity

\(C_\mathrm{v}\) :

Constant volume heat capacity

e :

Elementary electron charge

H :

Heat generation in body

I :

Total current

\(I_{i}\) :

Induced current

k :

Thermal conductivity

\(k_\mathrm{B}\) :

Boltzmann constant

L :

Lorenz number

l :

Length of sample

m :

Mass

R :

Resistance of circuit

T :

Temperature

t :

Time

V :

Voltage

\(V_{0}\) :

Volume

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Acknowledgements

The authors gratefully acknowledge the facilities provided by the Department of Production Engineering and the Center of Innovation, founded by Prof. Bidyut K Bhattacharyya at NIT, Agartala. All the experiments were conducted initially at the Center of Innovation, at NIT Agartala, India.

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Authors and Affiliations

  1. Department of Production Engineering, National Institute of Technology, Agartala, Agartala, Tripura, 799046, India

    Debtanay Das & Vidyut Dey

  2. Georgia Institute of Technology, Nano Technology/Packaging Research Center, Atlanta, GA, USA

    Bidyut Bhattacharyya

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  1. Debtanay Das
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Correspondence to Debtanay Das.

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Das, D., Dey, V. & Bhattacharyya, B. Modelling of Heat Flow When Thermal Conductivity, Specific Heat Capacity and Density All are a Function of Temperature. Arab J Sci Eng 46, 7649–7659 (2021). https://doi.org/10.1007/s13369-021-05477-y

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