The paper presents investigations related to solving of a direct and inverse problem of a non-stationary heat conduction equation for a cylinder. The solution of the inverse problem in the form of temperature distributions has been obtained through minimization of a functional being the measure of the difference between the values of measured and calculated temperatures in M points of the heated cylinder. The solution of the conduction equation was presented in the convolutional form and then numerically integrated approximating one of the integrand with a step function described with parameter Θ ∈ (0, 1]. The influence of the integration parameter Θ on the obtained solution of the inverse problem (including a number of temperature measurement points inside the heated body) has been analyzed. The influence of the parameter Θ on the sensitivity of the obtained temperature distributions has been investigated.

Main goal of the paper is to present the algorithm serving to solve the heat conduction inverse problem. Authors consider the heat conduction equation with the Riemann-Liouville fractional derivative and with the second and third kind boundary conditions. This type of model with fractional derivative can be used for modelling the heat conduction in porous media. Authors deal with the heat conduction inverse problem, which, in this case, consists in identifying an unknown thermal conductivity coefficient. Measurements of temperature, in selected point of the region, are the input data for investigated inverse problem. Basing on this information, a functional describing the error of approximate solution is created. Minimizing of this functional is necessary to solve the inverse problem. In the presented approach the Ant Colony Optimization (ACO) algorithm is used for minimization.

Thermochemical treatment processes are used to produce a surface layer of the workpiece with improved mechanical properties. One of the important parameters during the gas nitriding processes is the temperature of the surface. In thermochemical treatment processes, there is a problem in precisely determining the surface temperature of heat-treated massive components with complex geometries. This paper presents a simulation of the heating process of a die used to extrude aluminium profiles. The maximum temperature differences calculated in the die volume, on the surface and at the most mechanically stressed edge during the extrusion of the aluminum profiles were analysed. The heating of the die was simulated using commercial transient thermal analysis software. The numerical calculations of the die assumed a boundary condition in the form of the heat transfer coefficient obtained from experimental studies in a thermochemical treatment furnace and the solution of the nonstationary and non-linear inverse problem for the heat conduction equation in the cylinder. The die heating analysis was performed for various heating rates and fan settings. Major differences in the surface temperature and in the volume of the heated die were obtained. Possible ways to improve the productivity and control of thermochemical treatment processes were identified. The paper investigates the heating of a die, which is a massive component with complex geometry. This paper indicates a new way to develop methods for the control of thermochemical processing of massive components with complex geometries.