Conduction Heat Transfer

A Treatise on Electricity and Magnetism, Vol. 1

Summary Personnel operating in extreme environments require equipment that protects against multiple hazards Currently, protection against both thermal and ballistic threats requires the combination of multiple high-performance materials that increases equipment weight and complexity Here, we hypothesized we could achieve simultaneous protection by manufacturing a porous network of aligned fibers, combining the mechanical properties of continuous fibers with the thermal properties of porous aerogels Choosing para-aramid polymers as the building block, we engineered precursor solutions to be fluid-like during fiber spinning and solid-like during fiber formation This allowed for the fabrication of porous, continuous para-aramid fiber sheets (pAFS) with fiber diameters an order of magnitude lower than that of commercial para-aramid fibers Although exhibiting moderately reduced single-fiber mechanics, these pAFS had fragment projectile resistance comparable with commercial para-aramids, while providing 20-fols heat-insulation capability With these synergistic properties, the nanofiber sheets act as a multifunctional material that can provide improved simultaneous protection

para-Aramid Fiber Sheets for Simultaneous Mechanical and Thermal Protection in Extreme Environments

Numerical calculations of relative Young’s modulus and thermal conductivity have been performed on computer-generated microstructures of wall-based (closed-cell) and strut-based (open-cell) cellular materials (foams) and inverse foams. The results are compared to rigorous upper bounds (Wiener-Paul, Hashin-Shtrikman), model-based predictions (power-law, exponential) and cross-property predictions (CPRs). It is shown that closed-cell foams exhibit higher property values than open-cell and inverse foams, Kelvin foams higher than random foams, and the difference between closed-cell and open-cell foams is larger than that between Kelvin and random foams. While the properties of closed-cell foams are higher than the power-law prediction, those of inverse and open-cell random foams are between the exponential and power-law predictions, and open-cell Kelvin foams follow the Gibson-Ashby power-law prediction for open-cell foams. The Pabst-Gregorova CPR is shown to predict Young’s modulus with accuracy better than ±0.02 relative property units (better than any model-based relation and any other CPR).

Young’s modulus and thermal conductivity of closed-cell, open-cell and inverse ceramic foams – model-based predictions, cross-property predictions and numerical calculations

The effective Young’s modulus and thermal conductivity of porous materials can be rigorously bounded from above via micromechanical bounds (upper Wiener–Paul bounds and upper Hashin–Shtrikman bounds), and several model relations are commonly used as tentative approximate predictions (Maxwell-type, Coble–Kingery-type, power-law and exponential relations). Based on numerical calculations on computer-generated digital model microstructures, both periodic and random, it is shown that these model relations provide rough approximations that are more or less appropriate for microstructures with essentially convex pores, but are not suitable for microstructures with concave pores. On the other hand, the Pabst–Gregorova cross-property relation provides a very accurate (better than 0.04 relative property units) analytical prediction for the relative Young’s modulus of isotropic porous materials with isometric pores, both convex and concave, when the relative thermal conductivity is known. It is shown that this cross-property relation is the best prediction currently available for isotropic porous materials with isometric pores.

Young’s modulus and thermal conductivity of model materials with convex or concave pores – from analytical predictions to numerical results

A critical assessment of model relations describing the porosity dependence of elastic properties (Young's modulus) and thermal properties (thermal conductivity) is given. It is shown that there are essentially five types of admissible predictive model relations for the relative Young's modulus and thermal conductivity of isotropic porous materials. The cross-property relations resulting from the complete analogy between the model relations for the elastic moduli and thermal conductivity of isotropic porous materials are reviewed and compared. Finally, it is shown that the fact that relative Young's moduli are not equal to relative thermal conductivities except for materials with translational symmetry, i.e. the mere existence and necessity of non-trivial cross-property relations, proves so-called minimum solid area models to be wrong.

W. Pabst

Papers

Critical Assessment 18: elastic and thermal properties of porous materials – rigorous bounds and cross-property relations