An analytical solution of non-Fourier Chen-Holmes bioheat transfer equation

2005 ◽  
Vol 50 (23) ◽  
pp. 2791-2792 ◽  
Author(s):  
Gou Chenhua ◽  
Cai Ruixian
Keyword(s):  
Analytical Solution ◽  
Transfer Equation ◽  
Bioheat Transfer ◽  
Bioheat Transfer Equation

Analytical Solution for the Time-Fractional Pennes Bioheat Transfer Equation on Skin Tissue

2014 ◽  
Vol 1049-1050 ◽  
pp. 1471-1474 ◽  
Author(s):  
Zhou Jin Cui ◽  
Gui Dong Chen ◽  
Rui Zhang
Keyword(s):  
Analytical Solution ◽  
Exact Solutions ◽  
Transfer Equation ◽  
Laplace Transformation ◽  
Bioheat Transfer ◽  
Skin Tissue ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Conditions ◽  
Robin Boundary ◽  
Bioheat Transfer Equation

This study focuses on analytical solution of a fractional Pennes bioheat transfer equation on skin tissue. The method of separating variables, finite Fourier sine transformation, Laplace transformation and their corresponding inverse transforms are used to solve this equation with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin boundary value conditions. The exact solutions are discussed and derived in the form of generalized Mittag-Leffler function. In addition, numerical results are presented graphically for various values of order factional derivative.

Theoretical Analysis of Transient Bioheat Transfer in Multi-Layer Tissue

2015 ◽  
Author(s):  
Daipayan Sarkar ◽  
A. Haji-Sheikh ◽  
Ankur Jain
Keyword(s):  
Transfer Equation ◽  
Physical Phenomenon ◽  
Separation Of Variables ◽  
Blood Perfusion ◽  
Bioheat Transfer ◽  
Skin Tissue ◽  
Transient Temperature ◽  
Theoretical Understanding ◽  
Transient Model ◽  
Bioheat Transfer Equation

Heat conduction in skin tissue is a problem of significant technological importance. A theoretical understanding of such a problem is essential as it may lead to design potential therapeutic measures for needed cancer therapy or novel medical devices for various applications including hyperthermia. To understand the physical phenomenon of energy transport in biological systems a transient model is chosen for this study. The most common transport equation to estimate temperature distribution in humans was developed by H.H. Pennes and is popularly known as the Pennes bioheat transfer equation. A generalized Pennes bioheat transfer equation accounts for the effect of various physical phenomena such as conduction, advection, volumetric heat generation, etc. are considered. In this paper, a general transient form of the Pennes bioheat transfer equation is solved analytically for a multilayer domain. The boundary value problem considers the core of the tissue is maintained at uniform temperature of 37°C, convective cooling is applied to the external surface of the skin and the sidewalls are adiabatic. The computation of transient temperature in multidimensional and multilayer bodies offers unique features. Due to the presence of blood perfusion in the tissue, the reaction term in the Pennes governing equation is modeled similar to a fin term. The eigenvalues may become imaginary, producing eigenfunctions with imaginary arguments. In addition the spacing between the eigenvalues between zero and maximum value varies for different cases; therefore the values need to be determined with precision using second order Newton’s method. A detailed derivation of the temperature solution using the technique of separation of variables is presented in this study. In addition a proof of orthogonality theorem for eigenfunctions with imaginary eigenvalues is also presented. The analytical model is used to study the thermal response of skin tissue to different parameters with the aid of some numerical examples. Results shown in this paper are expected to facilitate a better understand of bioheat transfer in layered tissue such as skin.

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