Analytical and numerical solution of heat generation and conduction equation in relaxation mode: Laplace transforms approach | Zendy

Lawal Mohammed | Zendy; K. Jha Basant | Zendy; O Akusu Patrick | Zendy; R Mat Isa Ahmad | Zendy; R Nasiru | Zendy

Open Access

Analytical and numerical solution of heat generation and conduction equation in relaxation mode: Laplace transforms approach

Author(s) -

Lawal Mohammed,

K. Jha Basant,

O Akusu Patrick,

R Mat Isa Ahmad,

R Nasiru

Publication year - 2015

Publication title -

international journal of the physical sciences

Language(s) - English

Resource type - Journals

ISSN - 1992-1950

DOI - 10.5897/ijps2015.4285

Subject(s) - laplace transform , thermal conduction , relaxation (psychology) , heat equation , thermodynamics , mode (computer interface) , heat generation , chemistry , mechanics , mathematical analysis , physics , mathematics , psychology , social psychology , computer science , operating system

In this article analytical solution of one-dimensional heat equation in relaxation mode of heat generation and conduction using Laplace transforms method is presented. The model adopted takes into account finite velocity of heat propagation, and relaxation of heat source capacity. The properties of heat source terms in four different cases are incorporated in the model and investigated. Temperature distributions and variations with conduction mode and relaxation time are analyzed. High relaxation time is observed to lowers the temperature profile, whereas enhanced temperature distribution changes at particular values of α, andfor source capacity proportional to temperature. How the steady state solution is achieved for some selected values of coefficients is also discussed. Key words: Relaxation time, conduction mode, pulsed heat source, Laplace transforms.

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