Graded meshes in bio-thermal problems with transmission-line modeling method

•Graded meshes can be 9 times faster than regular meshes.•Model for heat fluxes and sources in biological bodies.•Consider biothermal characteristics on the boundary.•Error parameter allow quantitatively control of numerical approximation.•Increase temperature's data without increased memory and run time.

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.