Piotr Furmański

Finite element analysis of concurrent radiation and conduction in participating media

A method is proposed to calculate temperature, conductive and radiative heat flux distributions in a participating medium. The method is based on the simultaneous solution of two non-linear and mutually conjugated equations describing distribution of both temperature and the so-called radiation function in the medium. In the case of isotropic scattering, the latter quantity, is proportional to the local energy density of radiation. The solution of the coupled non-linear equations is based on the finite element spatial discretization combined with the iterative technique.

Effective macroscopic description for heat conduction in heterogeneous materials

Abstract The macroscopic thermal behaviour of heterogeneous materials is studied using the ensemble averaging technique. The non-local constitutive relations for heat conduction are derived. They relate the ensemble averaged heat flux and energy density to the ensemble averaged temperature of the medium. All the effective properties appearing in the relations are defined with help of the newly introduced, so-called microstructure functions. The asymptotic behaviour of the heterogeneous media for slowly varying average temperature fields was investigated. Possible applications of the theory are presented in two examples when analytical results could be easily obtained.

Fixed Grid Simulation of Radiation-Conduction Dominated Solidification Process

In this paper conduction-radiation controlled solidification process of semitransparent materials was numerically analyzed. New approach in this kind of simulations, which is based on the fixed grid front tracking method combined with the immersed boundary technique, was adopted and examined. The presented method enables accurate dealing with solidification processes of semitransparent materials which have different optical and thermophysical properties of solid and liquid phases as well as with absorption, emission, and reflection of the thermal radiation at the solid-liquid interface without applying moving mesh methods. The proposed numerical approach was examined by solving several simplified thermal radiation problems with complex fixed and moving boundaries both in two-dimensional and axisymmetric spaces. For some of them the accuracy of obtained results was proved by comparing with reference works, other showed capabilities of the proposed method. For simplified solidification processes of semitransparent materials three configurations of optical properties, i.e., semitransparent solid phase and opaque liquid phase, opaque solid phase and semitransparent liquid phase, and semitransparent both phases were considered. The interface between solid and liquid phases was treated to be opaque, absorbing, emitting, and reflecting diffusely the thermal radiation. Results of the numerical simulations show that the presented numerical approach works well in this kind of problems and is promising for simulation of real solidification processes of semitransparent materials.

A Thermal Barrier With Adaptive Heat Transfer Characteristics

A thermal barrier with adaptive heat transfer characteristics for applications in zero gravity environments is considered. The barrier consists of a mixture of fluid with a small volume fraction of arbitrarily oriented, randomly distributed particles of ellipsoidal shape. Heat flux control is obtained by changing the orientation of the particles. Heat flow may be increased up to several hundred times by rotating the particles from being parallel to the walls to being transverse to the walls and by increasing their aspect ratio, volume fraction, and relative thermal conductivity. An increase in the size of the particles results in the appearance of wall effects, which may substantially reduce heat flow as compared to the case of an infinite medium. Very large temperature variation is found to occur near the walls where an apparent “slip” of temperature occurs for barriers whose thickness is large compared to the particle size.

Assessment of thermal performance of protective garments: The advanced numerical model

Purpose The paper aims to present the advanced mathematical and numerical models of conjugated heat and mass transfer in a multi-layer protective clothing, human skin and muscle subjected to incident external radiative heat flux. Design/methodology/approach The garment was made of three layers of porous fabric separated by the air gaps, whereas in the tissue, four skin sublayers and muscle layer were distinguished. The mathematical model accounted for the coupled heat transfer by conduction and thermal radiation with the associated phase transition of the bound water in the fabric fibres and diffusion of the water vapour in the clothing layers and air gaps. The skin and muscle were modelled with two equation model which accounted for heat transfer in the tissue and arterial blood. Complex thermal and mass transfer conditions at the internal or external boundaries between the fabric layers, air gaps and skin were assumed. Special attention was paid to modelling of thermal radiation emitted by external heat source, for example, a fire, penetrating through the protective clothing and being absorbed by the skin and muscle. Findings Temporal and spatial variations of temperature in the protective garment, skin and muscle, as well as volume fractions of the water vapour and bound water in the clothing, were calculated for various intensity of incident radiative heat flux. The results of numerical simulation were used to estimate the risk of the first-, second- and third-degree burns. Research limitations/implications Because of the small thickness of the considered system in comparison to its lateral dimensions, the presented model was limited to 1D heat and moisture transfer. The convective heat transfer through the clothing was neglected. Practical implications The model may be applied for design of the new protective clothing and for assessment of thermal performance of the various types of protective garments. Additionally, the proposed approach may be used in the medicine for estimation of degree of thermal destruction of the tissue during treatment of burns. Originality/value The novel advanced thermal model of the multi-layer protective garment, skin and muscle layer was developed. For the first time, non-grey optical properties and various optical phenomena at the internal or external boundaries between the fabric layers, air gaps and skin were accounted for during simulation of thermal interactions between the external heat source (e.g. a fire), protective clothing and human skin.

Simplified thermo-fluid model of an engine cowling in a small airplane

Purpose – The purpose of this study is to developed a simplified thermo-fluid model of an engine cowling in a small airplane. An aircraft engine system is composed of different elements operating at various temperatures and in conjunction with the composite nacelle creates a region with high intensity of heat transfer to be covered by the cooling/ventilation systems. Therefore a thermal analysis, accounting for the complex heat transfer modes, is necessary in order to verify that an adequate cooling is ensured and that temperatures of the nacelle are maintained within the operating limits throughout the whole aircrafts flight. Design/methodology/approach – Simplified numerical simulations of conductive, convective and radiative heat transfer in the engine bay of the small airplane I-23 in a tractor arrangement were performed for different air inlet and outlet configurations and for varying conditions existing in air inlets during the flight. The model is based on the control volume approach for heat and ...

Wall effects in heat conduction through a heterogeneous material

Abstract It is shown that wall effects may significantly alter heat flow through heterogeneous material. These effects can be accurately modelled using the concept of the apparent wall heat transfer coefficient α w . A method for exact evaluation of α w is proposed and is used for testing of the ad hoc formulae available in literature. The formula proposed by Kubie (1987) gives the smallest errors and is recommended for use in simplified heat transfer calculations.

A mixture theory for heat conduction in heterogeneous media

Abstract A mixture theory based on the ensemble-averaging technique is proposed for studying the thermal behaviour of heterogeneous media. Balance equations with partial heat fluxes and interaction terms are introduced for a two-component medium. Relations between these quantities and the ensemble-averaged (mean) temperatures of separate components are derived. The limits of application of widely used postulates of proportionality of the interaction term of difference in mean temperature of components is discussed. The effective conductivities of components in the mixture and the interaction coefficient are introduced and related to the so-called microstructure functions, which are functions of the microgeometry of the medium and the thermal properties of its components. Examples of the application of the theory to the calculation of the mean properties of a heterogeneous medium are presented.

Modelling of the Mushy Zone Permeability for Solidification of Binary Alloys

An ensemble averaging technique is used to obtain both macroscopic equations of transport phenomena in a two-phase region and new models of permeability and thermal conductivity of the columnar mushy zone through the analysis of most likely configurations of the local microstructure. The obtained formulae are incorporated into a FEM computer code for the macroscopic analysis of binary mixture solidification with convection. The influence of various models of mushy zone permeability on temporal shapes of the two-phase region as well as on velocity and temperature fields is studied for a test case of solidification of a dilute solution of ammonium chloride and water in a square cavity. For this case, relatively small differences in liquid flow patterns and temporal shapes of the two-phase region are observed for significantly different models of mushy zone permeability.

Comparison of different bioheat transfer models for assessment of burns injuries

Two bioheat transfer models i.e.: the classical Pennes model and a more realistic two-equation model which accounted for blood vessel structure in the skin as well as heat transfer in the tissue and arteria blood were coupled with heat and mass transfer model in the protective multilayer garment. The clothing model included conductive-radiative heat transfer with water vapor diffusion in pores and air gaps as well as sorption and desorption of water in fibers. Thermal radiation was modeled rigorously e.g.: both the tissue and fabrics were assumed non-gray, absorbing, emitting and anisotropically scattering. Additionally different refractive indices of fabrics, air and tissue and resulting optical phenomena at separating interfaces were accounted for. Both bioheat models were applied for predicting skin temperature distributions and possibility of burns for different exposition times and radiative heat fluxes incident on external surface of the protective garment. Performed analyses revealed that heat transfer in the skin subjected to high heat flux is independent of the blood vessel structure.Two bioheat transfer models i.e.: the classical Pennes model and a more realistic two-equation model which accounted for blood vessel structure in the skin as well as heat transfer in the tissue and arteria blood were coupled with heat and mass transfer model in the protective multilayer garment. The clothing model included conductive-radiative heat transfer with water vapor diffusion in pores and air gaps as well as sorption and desorption of water in fibers. Thermal radiation was modeled rigorously e.g.: both the tissue and fabrics were assumed non-gray, absorbing, emitting and anisotropically scattering. Additionally different refractive indices of fabrics, air and tissue and resulting optical phenomena at separating interfaces were accounted for. Both bioheat models were applied for predicting skin temperature distributions and possibility of burns for different exposition times and radiative heat fluxes incident on external surface of the protective garment. Performed analyses revealed that heat tran...