Analytical Solutions to the Problem of Transient Heat Transfer in Living Tissue

1978 ◽  
Vol 100 (4) ◽  
pp. 202-210 ◽  
Author(s):  
A. Shitzer ◽  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Temperature Profile ◽  
Analytical Solutions ◽  
Biological Tissue ◽  
Geometrical Parameter ◽  
Convective Transport ◽  
Transient Heat Transfer ◽  
Living Tissue ◽  
Cylindrical Coordinates

An analytical model of transient heat transfer in living biological tissue is considered. The model includes storage, generation, conduction, and convective transport of heat in the tissue. Solutions for rectangular and cylindrical coordinates are presented and discussed. Transient times for reaching the “locally fully developed” temperature profile were found to be of the order of 5–25 min. These transients are dominated by a geometrical parameter and, to a lesser extent, by a parameter representing the ratio of heat supplied by blood flow to heat conducted in the tissue.

Modeling Transient Heat Transfer Through the Skin and Superficial Tissues—1: Surface Insulation

1986 ◽  
Vol 108 (2) ◽  
pp. 183-188 ◽  
Author(s):  
D. A. Hodson ◽  
G. Eason ◽  
J. C. Barbenel
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Transient Heat Transfer ◽  
Transient Problem ◽  
Finite Slab ◽  
Infinite Slab ◽  
Flow Through ◽  
Superficial Tissues

Two models of transient heat transfer through the skin and superficial tissues are presented. One model comprises a finite slab and semi-infinite slab, representing the epidermis and subdermal tissues, respectively, and a heat-generating interface representing the thermal effect of blood flow through the dermis. A model is also considered where the three tissue regions are represented more conventionally by three finite slabs. A transient problem arising from surface insulation is examined and analytical solutions derived from the first model are compared with numerical solutions derived from the second.

scholarly journals Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces

2021 ◽  
Author(s):  
Raseelo Joel Moitsheki ◽  
Partner Luyanda Ndlovu ◽  
Basetsana Pauline Ntsime
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Properties ◽  
Analytical Solutions ◽  
Nonlinear Problems ◽  
Transient Heat Transfer ◽  
Temperature Dependent ◽  
Approximate Analytical Solutions ◽  
Extended Surfaces ◽  
Insight Into

In this chapter we provide the review and a narrative of some obtained results for steady and transient heat transfer though extended surfaces (fins). A particular attention is given to exact and approximate analytical solutions of models describing heat transfer under various conditions, for example, when thermal conductivity and heat transfer are temperature dependent. We also consider fins of different profiles and shapes. The dependence of thermal properties render the considered models nonlinear, and this adds a complication and difficulty to solve these model exactly. However, the nonlinear problems are more realistic and physically sound. The approximate analytical solutions give insight into heat transfer in fins and as such assist in the designs for better efficiencies and effectiveness.

scholarly journals THERMAL MODELS OF BIOHEAT TRANSFER EQUATIONS IN LIVING TISSUE AND THERMAL DOSE EQUIVALENCE DUE TO HYPERTHERMIA

2002 ◽  
Vol 14 (02) ◽  
pp. 86-96 ◽  
Author(s):  
TZU-CHING SHIH ◽  
HONG-SEN KOU ◽  
CHIHNG-TSUNG LIAUH ◽  
WIN-LI LIN
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Heating Temperature ◽  
Bioheat Transfer ◽  
Living Tissue ◽  
Thermal Dose ◽  
Bioheat Equation ◽  
Transfer Equations ◽  
Polynomial Expression

This review focuses both on the basic formulations of bioheat equation in the living tissue and on the determination of thermal dose during thermal therapy. The temperature distributions inside the heated tissues, generally controlled by heating modalities, are obtained by solving the bioheat transfer equation. However, the major criticism for the Pennes' model focused on the assumption that the heat transfer by blood flow occurs in a non-directional, heat sink- or source-like term. Several bioheat transfer models have been introduced to compare their convective and perfusive effects in vascular tissues. The present review also elucidates thermal dose equivalence that represents the extent of thermal damage or destruction of tissue in the clinical treatment of tumor with local hyperthermia. In addition, this study uses the porous medium concept to describe the heat transfer in the living tissue with the directional effect of blood flow, and the polynomial expression of thermal dose in terms of the curve fitting of the experimental isosurvival curve data by Dewey et al. Results show that the values of factor R is a function of the heating temperature instead of the two different constants suggested by Sapareto and Dewey.

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