Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy.

The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods.

Dynamic response of a long cylinder under thermal shock in micropolar thermoelasticity.

In this manuscript, the dynamic response of a long cylinder subjected to an asymmetric thermal shock is investigated within the framework of generalized micropolar thermoelasticity. The displacement and micro-rotation are assumed to vanish at the surface. Laplace transformation techniques are used to solve the problem. The solution is obtained in the transformed field using an innovative direct approach. Furthermore, we obtain the inverse transformations using a numerical method based on Fourier expansion. The obtained results are carefully presented through graphical representations and discussed extensively across different relaxation time values. It is evident that the relaxation time parameter significantly influences all the distributions. The displacement distributions are always continuous, whereas all other functions, including temperature variation, stress distribution, and micro-rotation, exhibit discontinuity at the wave front. The results obtained hold significant importance in various technological applications and in the manufacturing of mechanical components.