Effect of microstructure of fibrous insulation materials on heat transfer

Insulation materials are used to reduce to heat transfer between two media with different temperatures, thus, allow for more efficient usage of thermal energy. Fibrous insulation materials are the most common used insulation materials for both industrial and domestic usage. Fibrous insulation materials are used in a wide range of application areas from common building applications to spacecraft applications. Heat transfer in fibrous insulation materials arise from conduction and radiation mechanisms. As heat conductivity of air and radiative properties of the insulation materials depend on temperature so does the overall thermal conductivity of fibrous insulation materials depend significantly on temperature. Due to their ability to suppress any air movement inside, convective heat transfer in the fibrous insulation materials can be neglected. Generally, heat transfer calculations of fibrous insulation materials are done with the emprical correlations which are based on lumped formulation assumption. However, it is not possible to make any comment on how to increase the insulation performance of the material using these kind of formulations. In this thesis, effects of the morphologic properties of the fibrous insulation materials upon the materials' thermal conductivity is investigated. The heat transfer of the material by the radiation and the conduction is investigated seperatly and the effective heat conduction coefficient of the fibrous insulation materials is found. Conductive term for the fibrous insulation materials are acquired using emprical formulations based on the conductive terms of the gas and the solid phases. There are two approaches: parallel mode and the Bhattacharya model. While using these models, the heat conductivity of the solid phase is corrected using an empirical relation to correctly take into account the loose arrangement of the fibers relative to a continuous solid. As for the radiative term, a statistical model, Monte Carlo Ray Tracing (MCRT) method is used. Monte Carlo method relies on randomly generated numbers and probability density functions and is used for a wide range of problems. In this thesis, the Monte Carlo method is used to compute the pi number, one-dimensional definite integra l and the view factor of simple geometries where the view factor can be analytically calculated and the change of the relative error based on the sampling number is demonstrated. After that a simulation area for which an analytical solution is present in the literature is constructed with symmetric boundary condition to show that the symmetric boundary condition can be used to reduce the simulation area and it is validated by the analytical solution given. The change of the relative error based on the sampling number is determined for the validation geometry. With the use of the MCRT method, the view factors which play a very important role in the radiative heat transfer can easily be calculated for even complex geometries. In this method, a ray is emitted from a plate which acts as a heat source from a location on the plate defined by a probablility density functions, and in a direction which again is defined by a probability density function and is traced. This is repeated several times. After desired number of rays are emitted, the number of rays that reach the sink plate devided by the total number of rays emitted from the source plate gives the view factor from the source plate to the sink plate. If a porous media (fibrous insulation material) is placed between the source and the sink plates, the procedure gets more complicated. In this case, a ray emmited from the source plate can either be scattered or absorbed and reemitted. The ray is traced until it eventually reaches to sink plate or returns to the source plate. Again, after desired number of rays are emitted, the number of rays that reach the sink plate devided by the total number of rays emitted from the source plate gives the steady state energy transmittance of the fibrous insulation material. The energy transmittance of the insulation material is actually the view factor of the source plate to the sink plate. Number of fibers in the simulation area, mean diameter of the fibers, absorbtion coefficient of the fibers, solid volume fraction (the ratio of fiber volume to the total volume of the material), the temperatures of the source and the sink plates, the number of rays to be emitted and the asymmetry factor of the phase function are provided as input parameters to the code which is based on the MCRT method. The steady state energy transmittance of the fibrous insulation material is given as output in addition to the view factors between the fibers among themselves and the temperature of each fiber by the code. In MCRT method, the ray emitted from the heat source is absorbed and scattered several times before reaching the sink plate. When a fiber absorbs a ray, according to conversation of energy the ray is emitted isotropically while the scattering is a little bit more complex. The most important parameter of the scattering is the size parameter (χ). When the size parameter is high (χ>10), it means that the wavelength of the ray is small compared to the diameter of the fiber. In this case, the scattering occurs according to the geometric scattering laws. In the geometric scattering region, the fiber acts as a mirror that reflects the ray. When the size parameter is between 10 and 0.1 (10>χ>0.1) it means that the wavelength of the ray is comparable to the fiber diameter and in this case the scattering occurs according to the Mie scattering laws. As the Mie equations are hard to solve and complicated, simpler phase function equations such as Linear Anisotropic Scattering, Henvey-Greenstein etc. are used. These phase functions take into account both the forward and backward scattering with asymmetry factor. It can be seen from the literature that the scattering in the fibrous insulation materials is dominantly in a forward direction. Using MCRT method, it is possible to observe the effect of the solid volume fraction, fiber diameter and absorbtion coefficient of the fiber on the effective heat conductivity of the fibrous insulation material. The ability to see the effects of various microstrucrural properties of the material is a valuable asset in designing the optimum insulation material compositon regarding the heat insulation. In order to verify the numerical studies done in the thesis, an experimental setup (Guarded Hot Plate) is designed and constructed according to ISO 8302 specifications. The morphologic properties of the insulation materials which are used in the guarded hot plate are measured by the Scanning Electron Microscope, and are also used in the numerical studies. The guarded hot plate experimental setup obtain the effective heat transfer coefficient by one-dimensional Fourier heat transfer law. The experimental setup consists of two horizontal plates which have a homogeneous and steady temperature distribution (±1°C) along their faces. The insulation material for which the effective heat transfer coefficient is desired to be measured is placed between these two plates. Because the temperature difference and the distance between the plates are known, by measuring the power supplied to the hot plate, one can find the effective thermal conduction coefficient of the insulation material by applying the one-dimensional Fourier law. Comparing the numerical and the experimental studies, it is concluded that the MCRT method gives satisfactory and realistic results for the thermal analysis of the fibrous insulation materials.