Research on structure optimization control of heat insulation material for problem A
The new heat insulation material A has excellent heat insulation properties and is
widely used in high-tech fields such as aerospace, military industry, petrochemical, construction, and transportation.
At present, the thermal conductivity of a fabric woven from a single fiber of thermal insulation material A can be directly measured; however, the thermal conductivity of a single fiber of thermal insulation material A (which can be assumed to be a constant value in the experimental environment of this question), because Its diameter is too small and its aspect ratio (ratio of length to diameter) is too large to be measured directly. The thermal conductivity of a single fiber is the basis of the thermal conductivity of fabrics, and it is also the basis for establishing various fiber-based fabric thermal conductivity models. Establishing a heat transfer mechanism model between the thermal conductivity of a single thermal insulation material A fiber and the overall thermal conductivity of the fabric has become a research focus. This model can not only obtain the thermal conductivity of a single fiber of thermal insulation material A, and solve the current technical problem that the thermal conductivity of a single fiber of thermal insulation material A cannot be measured; On the basis of the relational model of efficiency, control the weaving structure of the fabric and optimize the design to produce fabrics with excellent thermal insulation properties that better meet the needs of
high-tech fields such as aerospace, military industry, petrochemical, construction, and transportation.
The fabric is a network structure formed by stacking and interweaving a large number of single fibers. This topic only studies the plain weave fabric, as shown in Figure 1 and Figure 2. Fabrics made of fibers with different diameters have different basic structural parameters, that is, fiber bending angle, fabric thickness, warp density, weft density, etc., which affect the thermal conductivity of the fabric. In this question, assume that the vertical section of any single fiber A is circular, and each fiber in the fabric is always a curved cylinder
. Warp and weft bending angle 10° < θ ≤ 26.565°.
Thermal conductivity is one of the most important indicators of the physical properties of fibers and fabrics. There are gaps between the fibers of the fabric, and the air in the gaps is static air, and the static air thermal conductivity is 0.0296 W/(mK). When calculating the thermal conductivity of the fabric,
both the heat transfer between the fibers and the heat transfer of the air in the gap cannot be ignored.
Figure 1. Schematic diagram of plain weave fabric section
Figure 2. Three-dimensional image of plain weave fabric
We use the Hotdisk device to heat and measure the fabric in a laboratory environment of 25°C. The constant power of the Hotdisk is 1mW, and the action time is 1s. At 0.1s, the heat flow is just transferred to the other side of the fabric. experimental test
See Appendix 1 for the time-varying data of the temperature of the fabric on the side of the heat source between 0 and 0.1s.
Please build a mathematical model and answer the following questions:
Question 1 : Assuming that the temperature in Attachment 1 is the surface temperature of the fabric on the heat source side, and only considering the heat transfer of fibers and the gas in the gap, establish a mathematical model of the relationship between the overall thermal conductivity of the plain weave fabric and the thermal conductivity of a single fiber. Under the conditions of the experimental sample parameters in Appendix 2, the overall thermal conductivity of the plain weave fabric shown in Figure 2 is measured
is 0.033W/(mK), please calculate the thermal conductivity of a single A fiber according to the established mathematical model.
Question 2 : Assumptions: 1) The diameter of any single A fiber made into the fabric is between 0.3 mm and 0.6 mm. 2) For the data on the surface temperature of the fabric on the side of the heat source changing with time, please refer to Appendix 1. 3) Changes in the overall density and specific heat of the fabric due to temperature and fabric structure are negligible. How to choose a single A
The diameter of the fiber and the adjustment of the warp density, weft density and bending angle of the fabric make the overall thermal conductivity of the fabric the lowest.
Question 3 : If the temperature in Attachment 1 is actually the temperature of the air on the surface of the fabric on the heat source side, then convective heat transfer will occur on this side, assuming that the convective heat transfer coefficient on the fabric surface is 50 W/(m2 K), please answer the question again
Question 1 and Question 2.
