Computational study on 2D space-time fractional single-phase-lag bioheat model using RBF and Chebyshev polynomial based space-time collocation method

Abstract

The present study concerns the numerical simulation of the two-dimensional space-time fractional single-phase-lag bioheat model to study the heat transfer during hyperthermia. A space-time collocation method employing Gaussian radial basis functions (RBF) and Chebyshev polynomials in space and time directions, respectively, is proposed to solve the model numerically. The meshfree nature of Gaussian RBF enables us to apply the proposed method in an irregular domain. Further, using the Chebyshev polynomials, fewer nodes in the time direction are required to solve the model, which reduces the computational cost. The proposed method can simultaneously obtain the solution for the whole time domain in regular and irregular spatial domains. The effects of various parameters like heat source parameters, relaxation time(phase-lag), and blood perfusion on heat transfer in tissue are simulated in both regular and irregular domains. Furthermore, the temperature profiles in tissue are obtained for different fractional orders to exhibit their effects on heat transfer in tissue. The results indicate that fractional-order models could provide a unified approach to analyzing the heat transfer process in hyperthermia treatment.