Mathematical Model of Identification of the Skin Surface Temperature caused by the Temperature of Tissue inflammation

Purpose - The main goal is to identify the skin surface temperature in the steady state. Since two types of equations (Laplace and Helmholtz) are considered, it is necessary to derive the Trefftz functions (T-functions) for the Helmholtz equation in the cylindrical system of coordinates (whereas for the Laplace equation they are known).Design/methodology/approach - Approximate solutions of two problems are expressed in the form of linear combination of the T-functions with unknown coefficients. For each problem, minimizing the functional that describes the matching of an approximate solution to the boundary conditions leads to a system of algebraic equations for these coefficients.Findings/novelty - T-functions for the Helmholtz equation are derived. An infinite set of these functions is a complete set of functions. Approximate solutions for temperature of skin surface caused by inflammation are determined both when perfusion is and is not taken into account.Research implications - The method presented in the paper is simpler than the ones used in the literature. The applied method always leads to results that fit the physics of the problem described by the used governing equation.Originality/value - The T-functions for the Helmholtz equation in cylindrical coordinates have been reported in this paper for the first time. The results are discussed with respect to practical applications.