Present
paper deals with the solution of time and space fractional Pennes bioheat equation. We consider time fractional derivative and space fractional derivative in the form of Caputo fractional derivative of order and Riesz–Feller fractional derivative of order respectively. We obtain solution in terms of Fox’s H-function with some special cases, by using Fourier–Laplace transforms.
This paper deals with the study of heat transfer and thermal damage in triple layer skin tissue using fractional bioheat model. Here, we consider three types of heating viz. sinusoidal heat flux, constant temperature and constant heat flux heating on skin surface. An implicit finite difference scheme is obtained by approximating fractional time derivative by quadrature formula and space derivative by central difference formula. The temperature profiles and thermal damage in the skin tissue are obtained to study the effect of fractional parameter [Formula: see text] on diffusion process for constant temperature and heat flux boundary heating on skin surface. A parametric study for sinusoidal heat flux at skin surface has also been made.
This paper deals with the study of fractional bioheat equation for heat transfer in skin tissue with sinusoidal heat flux condition on skin surface. Numerical solution is obtained by implicit finite difference method. The effect of anomalous diffusion in skin tissue has been studied with different frequency and blood perfusion respectively, the temperature profile are obtained for different order fractional bioheat equation. (2010): 35R11, 80M20, 65M06.
Mathematics subject classification
This paper deals with the study of fractional bioheat equation for hyperthermia treatment in cancer therapy with external electromagnetic (EM) heating. Time fractional derivative is considered as Caputo fractional derivative of order α ∈ (0, 1]. Numerical solution is obtained by implicit finite difference method. The effect of anomalous diffusion in tissue has been studied. The temperature profile and thermal damage over the entire affected region are obtained for different values of α.
Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation.
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