Piotr Buliński, Ziemowit Ostrowski, Wojciech Adamczyk, Artur Fityka, Andrzej J. Nowak. Validation of a numerical model of locally cooled tissues. CAMES 2015 (22)

Measurements of heat transfer and temporal temperature distribution can be used as input in the diagnostic tools and methods of skin lesions, with special attention paid to malignant melanoma identification. Such approach requires mutual use of skin temperature and heat flux measurements combined with numerical simulation. A mild skin cooling process by a brass compress is considered in this paper. The temperature distribution on the skin and the heat flux between metal and tissues are measured. They are used in the course of validation study of the proposed numerical model. A numerical model of heat transfer in living tissues is described by Pennes' bioheat equation augmented with additional models of passive thermoregulation and vasoconstriction effects. The information regarding material properties of tissues and cooling compress involved in the simulation is essential to accurately solve this problem. Therefore, the main purpose of this work is to determine the accurate material property information by means of laboratory experiments.

*Keywords:* bioheat transfer, LFA, melanoma, thermal conductivity, thermal diffusivity.

Michał Dudek, Marek Jaszczur, Zygmunt Kolenda, Inga Polepszyc. Thermodynamic modeling of high-temperature combined cycle for hydrogen and electricity co-production. CAMES 2015 (22)

The high (HTGR) and very high (VHTR) temperature nuclear reactors are the most innovative designs and belong to the most advanced fourth generation gas-cooled reactor technology. These types of reactors are designed to have an outlet temperature between 800-1000° C for the HTGR and the VHTR respectively. Such systems are able to generate electrical energy and supply process heat in a broad spectrum of high-temperature and energy-intensive non-electric and thermal processes. In this paper, a numerical analysis of the high temperature HTGR/VHTR combined cycle with co-production of hydrogen and electricity is conducted. The presented cycle consists of three subsidiary circuits with gas turbine and two steam turbines for electric energy generation, and two heat exchangers for hydrogen production at high or medium temperature. The results show that such a combination allows a significant increase of thermal efficiency to about 50% at the reactor outlet temperature of 1273 K and a decrease in cost of hydrogen production.

*Keywords:* high temperature nuclear reactor, HTR, VHTR, hydrogen production, combined cycle.

Barbara Gambin, Eleonora Kruglenko, Antoni Andrzej Gałka, Ryszard Wojnar. Macroscopic thermal properties of quasi-inear cellular medium on example of the liver tissue. CAMES 2015 (22)

There are two main topics of this research: (i) one topic considers overall properties of a nonlinear cellular composite, treated as a model of the liver tissue, and (ii) the other topic concerns the propagation of heat
in the nonlinear medium described by the homogenised coefficient of thermal conductivity. For (i) we give a method and find the effective thermal conductivity for the model of the liver tissue, and for the point (ii) we present numerical and analytical treatment of the problem, and indicate the principal difference of heat propagation in linear and nonlinear media. In linear media, as it is well known, the range of the heat field is infinite for all times *t* > 0, and in nonlinear media it is finite. Pennes' equation, which should characterize the heat propagation in the living tissue, is in general a quasi-nonlinear partial differential equation, and consists of three terms, one of which describes Fourier's heat diffusion with conductivity being a function of temperature *T* . This term is just a point of our analysis. We show that a nonlinear character of the medium (heat conductivity dependent on the temperature) changes in qualitative manner the nature of heat transfer. It is proved that for the heat source concentrated
initially (*t* = 0) at the space point, the range of heated region (for *t* > 0) is finite. The proof is analytical, and illustrated by a numerical experiment.

*Keywords:* heat transport, asymptotic homogenisation, effective heat conductivity.

Oliwia Nowakowska, Zbigniew Buliński. Mathematical modelling of heat transport in a section of human forearm. CAMES 2015 (22)

The paper presents numerical analysis of heat transfer in the human forearm and influence of its internal structure on the temperature distribution inside. For this purpose three geometrical models of a human forearm were developed: model containing continuous muscle tissue only, model in which muscle tissue and bones were considered and model which contained muscle tissue bones and main blood vessels. In those models heat transfer in the muscle tissues and bones were described by Pennes' bioheat equation, while for blood flowing through main vessels (artery and vein) full set of governing equations were solved. Moreover, simplified one-dimensional description of skin was developed in order to reduce model complexity. Results obtained with all models were confronted against each other to reveal influence of the main blood vessels on the temperature distribution in a forearm.

*Keywords:* bioheat transfer, Pennes' equation, human forearm, temperature distribution, simplified skin model.

Marek Rojczyk, Helcio R.B. Orlande, Marcelo J. Colaço, Ireneusz Szczygieł, Andrzej J. Nowak, Ryszard A. Białecki, Ziemowit Ostrowski. Inverse heat transfer problems: an application to bioheat transfer. CAMES 2015 (22)

In this work, we applied the Markov chain Monte Carlo (MCMC) method for the estimation of parameters appearing in the Pennes' formulation of the bioheat transfer equation. The inverse problem of parameter estimation was solved with the simulated transient temperature measurements. A one-dimensional (1D) test case was used to explore the capabilities of using the MCMC method in bioheat transfer problems, specifically for the detection of skin tumors by using surface temperature measurements. The analysis of the sensitivity coefficients was performed in order to examine linear dependence and low sensitivity of the model parameters. The solution of the direct problem was verified with a commercial code. The results obtained in this work show the ability of using inverse heat transfer analysis for the detection of skin tumors.

*Keywords:* inverse problems, Bayesian framework, Markov chain Monte Carlo method, Pennes' equation, skin tumor.

Anna Wachowicz-Pyzik, Leszek Paj±k, Bartosz Papiernik, Michał Michna. The application of numerical modeling to geothermal investments. CAMES 2015 (22)

Among numerous applications of numerical modeling in many different fields of science, there is numerical modeling applied to the issues related to geothermal investments [1]. A number of important parameters and properties can be estimated based on numerical modeling. In the case of geothermal investments, we can determine several factors, which may influence operation of the heating plants, e.g.: exploitation and size of extraction and/or injection of groundwaters, selection of an optimal spacing of boreholes (in the case of geothermal doublets), and water temperature or pressure [2]. This paper presents the issues related to the numerical modeling of geothermal reservoirs as well as a variety of computer software packages commonly used in creation of static and dynamic models, such as: Visual MODFLOW, TOUGH, FEFLOWor Petrel [3, 4]. The process of numerical modeling is presented in four general steps: (1) archival data collection and analysis (often using statistical methods), (2) creation of the static and (3) dynamic numerical models of a reservoir, and (4) environmental, financial and technical assessments based on a mathematical model of surface installation [5]. Each step is presented in details and the most important reservoir parameters, which influence the utilization of geothermal energy, are discussed. At the end, the main directions in current utilization of geothermal waters in Poland and the future opportunities of geothermal heat generation, including the financial aspects related to geothermal investments, are discussed.

*Keywords:* numerical modeling, geothermal investments, geothermal heating plants.