https://doi.org/10.1140/epjp/s13360-026-07640-6
Regular Article
Computational analysis of nonlinear bioheat transfer equation of multilayered brain tissue with porosity during tumor thermal therapy
1
Department of Mathematics, Institute of Science, Banaras Hindu University, 221005, Varanasi, India
2
Department of Mathematics and Statistics, Mathematics Applications Consortium for Science and Industry (MACSI), University of Limerick, V94 T9PX, Limerick, Ireland
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Received:
3
February
2026
Accepted:
31
March
2026
Published online:
19
April
2026
Abstract
The present model incorporates a bioheat transport framework within multilayered brain tissue, accounting for blood perfusion and thermal conductivity as temperature-dependent variables, while also considering porosity during magnetic fluid hyperthermia. Additionally, the skin’s surface is subjected to a nonlinear boundary condition of heat-flux kind. The treatment’s temperature level is crucial for tumor eradication, which is forecasted by resolving the current model utilizing the Crank–Nicolson scheme. To validate the current scheme, we compared with the Laplace transform solution in specific situation against both types of boundary conditions. The analysis indicates that augmenting the nonlinear thermal conductivity coefficient (
) and the blood perfusion coefficient (
) reduces the temperature profile. Moreover, augmenting the porosity parameter (
) substantially reduces tissue temperature. Furthermore, augmenting the magnetic parameters 
and f boosts the heating profile specifically within the tumor. An elevation in the convective heat transfer coefficient (
) under Robin conditions reduces outer-layer temperatures, whereas an increased ambient temperature (
) elevates the boundary temperature. The Neumann condition reduces outer-layer temperatures by increasing heat flux (
). A comparative investigation demonstrates that the nonlinear model produces lower peripheral tissue temperatures and more effectively protects healthy tissue than the linear model, suggesting its superior appropriateness for therapeutic heating applications.
© The Author(s) 2026
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