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Nonsteadystate 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 c_{p} represent the thermal conductivity, the mass density, and the specific heat at constant pressure, respectively.
(a) What are the SI units for D_{T}?
(b) Determine values of D_{T} for copper, brass, magnesia, fused silica, polystyrene, and polypropylene using the data in Table.
Tabulation of the Thermal Properties for a Variety of Materials

c_{p} 
α_{l} 
k 
L 
Material 
(J/kgK)^{a} 
[(?C)^{−1} × 10^{−6}]^{b} 
(W/mK)^{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 (Al_{2}O_{3}) 
775 
7.6 
39 
— 
Magnesia (MgO) 
940 
13.5d 
37.7 
— 
Spinel (MgAl_{2}O_{4}) 
790 
7.6d 
15.0e 
— 
Fused silica (SiO_{2}) 
740 
0.4 
1.4 
— 
Soda–lime glass 
840 
9.0 
1.7 
— 
Borosilicate (Pyrex^{TM}) 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 (Teflon^{TM}) 
1050 
126–216 
0.25 
— 
Phenolformaldehyde, 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
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