The homogeneous soft tissue domain subjected to an external heat source is considered. Thermal processes in this domain are described using the well known Pennes equation and next the Cattaneo-Vernotte one. Within recent years the prevailing view is that the Cattaneo-Vernotte equation better describes the thermal processes proceeding in the biological tissue (it results from the specific internal tissue structure). Appearing in this equation the delay time of heat flux with respect to the temperature gradient (tau(q)) is of the order of several seconds and the different values of tau(q) are taken into account. At the stage of numerical modeling the finite difference method is used. In the final part of the paper, the examples of computations are shown.

The non-homogeneous fragment of biological tissue is considered. Its shape roughly corresponds to the fragment of cross-section of the upper or lower limb. The tissue domain is protected by a layer of protective clothing. The purpose of numerical computations is to examine the effectiveness of the clothing insulation layer on the action of the external heat fluxes of differing intensity. Thermal processes in the tissue domain are described by the system of the Pennes equations. This system is supplemented by the appropriate boundary-initial conditions and the energy equations determining the transient temperature field in the fabric and air gap sub-domains (the air gap is treated as a solid body). At the stage of numerical computations, the program MSC. Marc has been used. In the final part of the paper, the examples of numerical simulations and also the conclusions are presented.

In the paper the problem of explicit FDM scheme stability for the bio-heat transfer equation (the Pennes equation) is discussed. To formulate the appropriate condition the von Neumann approach is applied. The first chapter contains the known derivation of FDM stability condition for the Fourier equation. In the second part, a similar condition is found for the case of the bio-heat transfer equation containing both the perfusion and metabolic heat sources.

Thermal processes in the domain of a human forearm are considered. The external surface of forearm is in the direct thermal contact with the environment. The steady state problem is considered. From the mathematical point of view, the task is described by the system of the Poisson-type equations, the boundary conditions given on the contact surface between tissue sub-domains, the boundary conditions determining heat transfer between blood vessels and tissue and the boundary conditions on the external surface of the system. The non-homogeneous forearm domain is reconstructed as accurately as possible (3D task). At the stage of numerical modelling, the finite element method has been used. In the final part of the paper the example of computations is presented.

In the paper the simplified model of thermal processes proceeding in the domain of biological tissue secured with protective clothing is discussed. In particular, the simplification of the mathematical model consists in the omission of the real layer of fabric for which the transient temperature field is determined by the Fourier equation and the introduction in this place of the additional thermal resistance appearing in the boundary condition determining the heat exchange between tissue and environment. In this way both the mathematical model of the thermal processes in the system considered and also numerical realization are greatly simplified. To verify the effectiveness of the approach proposed, the solution of the basic problem and the simplified one have been solved (1D task) using the finite difference method and the results have been compared. It turned out that the results are close and from the practical point of view such simplification is fully acceptable.

In the paper the problem of thermal processes proceeding in the domain of biological tissue secured with protective clothing is discussed. In particular, the mathematical model of heat exchange corresponding to conditions of high temperature in the system environment - layer of protective clothing - air gap - skin tissue is formulated in the form of a certain boundary - initial problem. Next, the numerical algorithm based on the boundary element method is presented. In the final part of the paper the examples of numerical simulations are shown.