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International Heat Transfer Conference 6

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

APPLICATION ОF SIMILARITY TRANSFORMATION TO UNSTEADY STATE HEAT MIGRATION PROBLEMS IN HUMAN SKIN AND SUBCUTANEOUS TISSUES

V. P. Saxena
Department of Applied Mathematics S.V.R. College of Engineering and Technology, Surat, INDIA.

DOI: 10.1615/IHTC6.2700
pages 65-68

Abstract

The object of this paper is to illustrate application of similarity transformation method to solve unsteady state heat migration problems in human skin and subcutaneous tissues.
An in-vivo tissue, unlike other media, contains metabolic heat generation and heat addition or removal by the blood supply due to tissue vascularity. The equation Δ ·(λΔT)+mbcb(Tb-T) + Sm =ρс δT/δt provides a thermal model for a living biological medium. The effect of blood flow is accounted for by the term mbcb (Tb-T) and the effect of metabolism on energy transport through tissue appears as a term Sm .
The above equation is considered for one dimensional heat migration from dry skin and sub-cutaneous tissues in cool environment in which insensible perspiration is negligible. Suitable values are assigned to the physical parameters mb and Sm and appropriate boundary conditions are imposed to bring the problem nearer to a realistic situation.
At first stage λ(in-vivo thermal conductivity of the tissue) is taken as function of temperature, time and position and a similarity transformation λ =x/√(at + 1) is employed to reduce the equation to a non-linear ordinary differential equation. Later is solved for various particular cases of λ.

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