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Nonsteady-state heat flow may be described by the following partial differential equation width where DT is the thermal diffusivity this expression is the thermal equivalent of Fick’s second law

Nonsteady-state heat flow may be described by the following partial differential equation:

where DT is the thermal diffusivity; this expression is the thermal equivalent of Fick’s second law of diffusion (Equation 6.4b). The thermal diffusivity is defined according to

In this expression, k, ρ, and cp represent the thermal conductivity, the mass density, and the specific heat at constant pressure, respectively.

(a) What are the SI units for DT?

(b) Determine values of DT for copper, brass, magnesia, fused silica, polystyrene, and polypropylene using the data in Table.

Tabulation of the Thermal Properties for a Variety of Materials

 cp αl k L Material (J/kg-K)a [(?C)−1 × 10−6]b (W/m-K)c [ΩW/(K)2 × 10−8] Metals Aluminum 900 23.6 247 2.20 Copper 386 17.0 398 2.25 Gold 128 14.2 315 2.50 Iron 448 11.8 80 2.71 Nickel 443 13.3 90 2.08 Silver 235 19.7 428 2.13 Tungsten 138 4.5 178 3.20 1025 Steel 486 12.0 51.9 — 316 Stainless steel 502 16.0 15.9 — Brass (70Cu–30Zn) 375 20.0 120 — Kovar (54Fe–29Ni–17Co) 460 5.1 17 2.80 Invar (64Fe–36Ni) 500 1.6 10 2.75 Super Invar (63Fe–32Ni–5Co) 500 0.72 10 2.68 Ceramics Alumina (Al2O3) 775 7.6 39 — Magnesia (MgO) 940 13.5d 37.7 — Spinel (MgAl2O4) 790 7.6d 15.0e — Fused silica (SiO2) 740 0.4 1.4 — Soda–lime glass 840 9.0 1.7 — Borosilicate (PyrexTM) glass 850 3.3 1.4 — Polymers Polyethylene (high density) 1850 106–198 0.46–0.50 — Polypropylene 1925 145–180 0.12 — Polystyrene 1170 90–150 0.13 — Polytetrafluoroethylene (TeflonTM) 1050 126–216 0.25 — Phenol-formaldehyde, phenolic 1590–1760 122 0.15 — Nylon 6,6 1670 144 0.24 — Polyisoprene — 220 0.14 —

Density values are included in Table B.1, Appendix B.

Table B.10 Compositions of Metal Alloys for Which Data Are Included in Tables B.1 Through B.9

May 26 2020 View more View Less