Analytical Solution of Non Linear DPL Bioheat Transfer Model for Temperature Dependent Metabolic Heat Source During Thermal Therapy
Open Access
- 30 July 2022
- journal article
- Published by Blue Eyes Intelligence Engineering and Sciences Engineering and Sciences Publication - BEIESP in International Journal of Innovative Technology and Exploring Engineering
- Vol. 11 (8), 78-86
- https://doi.org/10.35940/ijitee.h9174.0711822
Abstract
In this research paper, the simulation based modelling of heat transfer in tissue under periodic boundary condition has been considered. The dual phase lag bioheat transfer (DPLBHT) model is implemented for computation of the temperature based thermal therapy treatment. The elements of volumetric heat source such as perfusion of blood, metabolism heat source and external heat source are considered in nonlinear DPL model. In this paper we have taken three cases for metabolic heat source namely, constant, linear and exponential. The combined two numerical methods which are based on finite difference scheme and Runge Kutta (4,5) scheme are exerted to solve the non-linear problem. We compute the exact solution for particular case. Numerical conclusions which are computed by numerical hybrid method are equated with exact result. It has been found that non linear DPL model with exponential metabolic heat source is closed to exact solution. We also expressed the effect of different parameters such as relaxation time, perfusion rate, metabolic heat source parameter, associated blood perfusion heat, heat source because of heat flux and temperature gradient etc.Keywords
This publication has 13 references indexed in Scilit:
- Analysis of classical Fourier, SPL and DPL heat transfer model in biological tissues in presence of metabolic and external heat sourceHeat and Mass Transfer, 2015
- METHOD OF FUNDAMENTAL SOLUTIONS FOR NONLINEAR SKIN BIOHEAT MODELJournal of Mechanics in Medicine and Biology, 2014
- A Study on the Effect of Metabolic Heat Generation on Biological Tissue FreezingThe Scientific World Journal, 2013
- Numerical study of the solidification process in biological tissue with blood flow and metabolism effects by the dual phase lag modelProceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 2012
- Effect of metabolic heat generation and blood perfusion on the heat transfer in the tissues with a blood vesselHeat and Mass Transfer, 1999
- An efficient Runge-Kutta (4,5) pairComputers & Mathematics with Applications, 1996
- Unsteady state heat flow in epidermis and dermis of a human bodyProceedings of the Indian Academy of Sciences - Section A, 1988
- On the Relationship Between Blood Perfusion, Metabolism and Temperature in Biological Tissue Heat BalanceJournal of Biomechanical Engineering, 1980
- THERMAL DILUTION METHODS: ESTIMATION OF TISSUE BLOOD FLOW AND METABOLISMAnnals of the New York Academy of Sciences, 1980
- A mathematical model of the human thermal systemBulletin of Mathematical Biology, 1964