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Title: Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues
Authors: Kumar D.
Kumar P.
Rai K.N.
Published in: Mathematical Biosciences
Abstract: This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge–Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. © 2017 Elsevier Inc.
Citation: Mathematical Biosciences (2017), 293(): 56-63
Issue Date: 2017
Publisher: Elsevier Inc.
Keywords: Kirchoff number
Model selction criterion AIC
Non-linear DPL bioheat transfer model
Periodic heat flux boundary conditions
Skin tissues
Temperature dependent blood perfusion
ISSN: 255564
Author Scopus IDs: 57202478211
Author Affiliations: Kumar, D., DST-CIMS, Institute of Science, BHU, Varanasi, India
Kumar, P., Department of Mathematical Sciences, IIT(BHU), Varanasi, India
Rai, K.N., Department of Mathematical Sciences, IIT(BHU), Varanasi, India
Funding Details: The first and third authors are thankful to the DST-CIMS, BHU for providing the necessary facility during the preparation of the paper. The second author is also thankful to the UGC, New Delhi, India for the financial support under the SRF (17- 06/2012/(i) EU-V) scheme.
Corresponding Author: Kumar, D.; DST-CIMS, Institute of Science, BHU, Varanasi, India; email:
Appears in Collections:Journal Publications [ME]

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