Fractal Models For The Effective Thermal Conductivity Of Down Fiber Assembly

Down fiber assembly is widely used as a natural filling material in clothing and groceries. In this paper, according to the definition of porous material, down fiber assembly is treated as dry saturated porous material in which the moisture is regarded as pure vapor. The fractal characteristic of down fiber assembly is analyzed using fractal theory and the fractal thermal conductivity model is been set up. Based on the three ways of heat transfer, the thermal conduction model is then developed for down fiber assembly.For down fiber assembly under different fiber volume fraction, their computed tomography (CT) scan images are obtained using Micro CT technology. The images are then reconstructed and processed into binary images via matlab language. Based on fractal theory, the pore area fractal dimension Df and the pore tortuosity fractal dimension DT of the down fiber assembly with various fiber fractional volume are been solved through matlab program. According to the results, with lower value in pore area fractal dimension Df and higher in pore tortuosity fractal dimension DT, the thermal property of down fiber assembly is better. The lower value of Df represents more uniformity distribution of pores in down fiber assembly; the higher value of DT stands for more complicated pore channels and heat conduction pathways, which means greater thermal resistance for heat transfer and less heat loss in the assembly.According to the condition for the occurrence of hear convection, the heat convection in down fiber assembly is studied through the solution of Rayleigh number (Ra) which is a product of the Prandtl number (Pr) of the fluid and the Grashoff number (Gr). For the range of room and body temperatures encountered by down fiber assembly. Pr for dry air in the assembly is about0.7. Rayleigh number is obtained as20.664through the solution of Grashoff number (Gr) which is far under103where GrPr<103implicates the natural convection in the assembly can be neglected, which means convection is not a cause of heat loss within the assembly.Assume the heat transfer in down fiber assembly at steady-state condition, in the application of the thermal-electrical analogy approach, the fractal model for thermal conductivity of down fiber assembly is established afterward in consideration of its microstructure which is characterized by its pore area fractal dimension Df and pore tortuosity fractal dimension DT.In addition, the relationship of thermal radiative conductivity with fiber radius is established and the thermal radiative flux is then calculated involves the effect of scattering of radiation. The thermal conduction model for down fiber assembly is developed ultimately by taking account of heat conduction and heat radiation. The thermal conductance is predicted through the model and the results are then compared with the experimental ones, which shows good agreement.Hollow polyester fiber has excellent heat-insulating abilities and widely used in the home textile and clothing. On the basis of the thermal conduction model for down fiber assembly, the thermal conductance of hollow polyester fiber assembly is predicted. The comparison of theoretical values with experimental ones exhibits good accordance which verifies the fractal model for thermal conductance in fibrous assembly.