Analytical Solution of Non-Linear DPL Bioheat Transfer Model for Temperature Dependent Metabolic Heat Source During Thermal Therapy
Neha Sharma1, Surjan Singh2, Dinesh Kumar3
1Neha Sharma, Department of Mathematics, Eternal University, Baru Sahib, (H.P), India.
2Surjan Singh, Department of Mathematics, Eternal University, Baru Sahib, H.P., India.
3Dinesh Kumar, Department of Mathematics, Government Polytechnic College, Nawada (Bihar) India.
Manuscript received on 30 June 2022 | Revised Manuscript received on 11 July 2022 | Manuscript Accepted on 15 July 2022 | Manuscript published on 30 July 2022 | PP: 78-86 | Volume-11 Issue-8, July 2022 | Retrieval Number: 100.1/ijitee.H91740711822 | DOI: 10.35940/ijitee.H9174.0711822
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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 non-linear 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: Bioheat, Hybrid Method, Metabolic Heat Source, Non-linear, Runge – Kutta Method, Thermal Therapy, Tissues.
Scope of the Article: Heat Transfer