 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13554 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8194
|
| In English (Mech. Solids): | | 5360 |
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| << Previous article | Volume 60, Issue 7 / 2025 | Next article >> |
| M. Khalid, I. Abbas, S. M. Sayed, and O.H. El-Kalaawy, "Hybrid Numerical Analysis of a Nonlinear DPL Bioheat Model in Spherical Tissue with Experimental and FEM Validation," Mech. Solids. 60 (7), 6402-6417 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
7 |
Pages |
6402-6417 |
| DOI |
10.1134/S002565442560463X |
| Title |
Hybrid Numerical Analysis of a Nonlinear DPL Bioheat Model in Spherical Tissue with Experimental and FEM Validation |
| Author(s) |
M. Khalid (Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt, Mohamed.khaled1301@science.bsu.edu.eg)
I. Abbas (Mathematics Department, Faculty of Science, Sohag University, Egypt, ibrabbas7@science.sohag.edu.eg)
S. M. Sayed (Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt, smsayed71@gmail.com)
O.H. El-Kalaawy (Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt, Ohkalaawy7@gmail.com) |
| Abstract |
This study presents a highly nonlinear dual-phase lag (DPL) bioheat model for simulating
heat transfer in spherical biological tissues subjected to a focused laser heat source. The formulation
integrates temperature-dependent metabolic heat generation and blood perfusion with an external
laser heat source, yielding a strongly coupled nonlinear system of governing equations. The numerical
solution is obtained through a hybrid framework that combines the implicit finite difference method
with Newton-Raphson iterations, ensuring robust and efficient convergence in the strongly nonlinear
regime. Results reveal that accounting for strong nonlinearity produces substantially higher peak temperatures and significantly modified heat penetration profiles compared to the linear counterpart.
These findings are further supported by numerical simulations, experimental measurements, an alternative finite element approach, and comparisons made with existing literature, underscoring the
necessity of nonlinear modeling for the accurate forecasting of thermal response and further enhancement of the accuracy and safety of laser biotherapy. |
| Keywords |
Nonlinear DPL model, Spherical tissue, Thermal damage, Implicit Finite difference, Newton–Raphson iteration |
| Received |
29 August 2025 | Revised |
16 October 2025 | Accepted |
17 October 2025 |
| Link to Fulltext |
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