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Application of Homotopy Perturbation Method Using Laplace Transform Intended for Determining the Temperature in the Heterogeneous Casting-Mould System

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Abstract

In this article, we established an application of homotopy perturbation method using Laplace transform (LT-HPM) to elaborate the analytical solution of heat conduction equation in the heterogeneous casting-mould system. The solution of the problem is provided with our supposition of an ideal contact between the cast and the mould. In the proposed method, we have chosen initial approximations of unknown constants which can be implemented by imposing the boundary and initial conditions. Examples have been discussed and confirmed the usefulness of this method.

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Abbreviations

\(E_{1}\) :

Region of casting

\(E_{2}\) :

Region of mould

L :

Laplace operator

\(L^{-1}\) :

Laplace inverse operator

t :

Time

R :

Thermal resistance (\(\mathrm{m}^{2} \mathrm{K}/\mathrm{w}\))

\(\mathfrak {I}_{\varGamma _{j}}\) :

Thermal conductivity (W/mK)

\(\varGamma _{1}\) :

Temperature in region \(E_{1}\) (K)

\(\varGamma _{2}\) :

Temperature in region \(E_{2}\) (K)

\(\tau \) :

Spatial location (m)

\(\kappa _{j}\) :

Thermal diffusivity (\(\mathrm{m}^{2} /\mathrm{s}\))

\(\delta _{i}\) :

Component of boundary

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Authors and Affiliations

  1. Department of Mathematics, Jaypee University of Engineering and Technology, Guna, MP, 473226, India

    Rajnee Tripathi

  2. Department of Applied Science and Humanities, KNIT, Sultanpur, 228118, India

    Hradyesh Kumar Mishra

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  1. Rajnee Tripathi
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Correspondence to Hradyesh Kumar Mishra.

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Tripathi, R., Mishra, H.K. Application of Homotopy Perturbation Method Using Laplace Transform Intended for Determining the Temperature in the Heterogeneous Casting-Mould System. Differ Equ Dyn Syst 30, 301–314 (2022). https://doi.org/10.1007/s12591-018-0417-7

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