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Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 139592 Total View: 1750723
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article Open Access http://dx.doi.org/10.26855/jamc.2021.12.008

Hybrid Analytical/Numerical Solution of the Unsteady Heat Conduction Equation Subject to Unequal Robin Boundary Conditions

Antonio Campo

School of Mechanical Engineering (Escuela de Ingeniería Mecánica), Pontifical Catholic University of Valparaíso (Pontificia  Universidad Católica de Valparaíso), Viña del Mar, Valparaíso, Chile.

*Corresponding author: Antonio Campo

Published: November 23,2021

Abstract

The primary objective of the present study is to utilize the Method of Lines (MOL) for the analysis of the unsteady, heat conduction in a slab with different Robin boundary conditions. A hot fluid is in contact with the left side of the slab and a cold fluid is in contact with the right side. In the heat conduction equation, MOL discretizes the second spatial derivative while leaving the time derivative continuous. This operation leads to a system of adjoint ordinary differential equations of first order for each line in the special computational domain that is solved analytically (not numerically) with the potent eigenvalue method. The computational procedure uses a symbolic algebra code that produces the collection of eigenvalues and eigenvectors. Based on this, a sequence of piecewise temperature-time variations at each line are expressed in terms of linear combinations of exponential functions of time. A limiting test case involves a slab with asymmetric Dirichlet boundary conditions, a particular case of asymmetric Robin boundary conditions. The combination of MOL, the eigenvalue method and a symbolic algebra code delivers a set of analytical/numerical temperature-time variations exhibiting excellent quality for the entire time domain.

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How to cite this paper

Hybrid Analytical/Numerical Solution of the Unsteady Heat Conduction Equation Subject to Unequal Robin Boundary Conditions

How to cite this paper: Antonio Campo. (2021) Hybrid Analytical/Numerical Solution of the Unsteady Heat Conduction Equation Subject to Unequal Robin Boundary ConditionsJournal of Applied Mathematics and Computation5(4), 303-314.

DOI: http://dx.doi.org/10.26855/jamc.2021.12.008