Exact analysis for propagation of heat in a biological tissue subject to different surface conditions for therapeutic applications

• Temperature response in skin tissue for therapeutic conditions.
• Thermal behavior in a skin tissue subject to various surface heating.
• Temperature response for Fourier and non-Fourier heat conduction.
• Analytical determination based on separation of variables.
• Non-Fourier temperature response has significance on boundary conditions.
• A greater temperature response from isothermal heating.

The thermal therapy to kill cancereous cells is gradually increasing due to no side effect for the treatment. For this therapeutic application, different boundary conditions can be selected to establish the effective heating. In the present study, the separation of variables was used to determine the exact expression for temperature response in a biological tissue under Fourier and non-Fourier heat conduction subject to a therapeutic application. As the thermal therapy is dependent on the surface conditions, isothermal, isoflux, and convective–radiative boundary conditions are taken in the present study. Depending upon the inner core condition, five different boundary conditions were adopted to show the temperature response in a tissue. For every case study, the temperature response was explicitly derived. From the results, it can be highlighted that the temperature distribution in a thermal therapy is a strong function of Fourier number F, Vernetto number Ve, and dimensionless blood flow parameter β. However, the temperature is also strong function of the boundary condition applied to the surface and it is also dependent on the inner core condition. The average temperature response was plotted as a function Fourier number and biological parameters, and is always a sinusoidal nature for a lower value of Fourier number. The ripple of sinusoidal curves is dependent on the therapeutic boundary condition applied.