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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:

 width=

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

 width=

 width=

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

 width=

 width=

May 26 2020 View more View Less

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