Question

ONLY PART C is needed

10. (19.22) Nonsteady-state heat flow may be described by the following partial differential equation эт ㄒㄧ 2 at where DT is the thermal diffusivity; this expression is the thermal equivalent of Fick's second law of diffiusion (Equation 5.4b). The thermal diffusivity is defined according to D_ k In this expression, k, p, 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 19.1. Density values are included in Table B.1, Appendix B c) From the form of the governing partial differential equation, it should come as no surprise that the temperature distribution in a semi-infinite solid can be calculated from an equation which is analogous to equation 5.5 in the text Consider the case of a solid initially at 25C whose surface is suddenly heated to 125C. Calculate and plot the temperature profiles for the materials in part (b) at t-30 minutes after the surface is heated Table 19.1 Thermal Properties for a Variety of Materials Material WkgK Aluminum 23.6 2.20 17.0 398 128 14.2 315 2.71 118 2.08 19.7 138 178 1025 Steel 12.0 51.9 16.0 316 Stainless steel 502 15.9 Brass (70Cu-30Zm) Kovar (54Fe-29Ni-17Co) 5.1 17 Invar (64Fe-36Ni) 10 2.75 0.72 Super Invar (63Fe-32Ni-5Co) 10 2.68 Alumina (ALO 7.6 Magnesia (Mgo Spinel (MgALO) 37.7 7.6 15.0 Fused silica (SiO) Soda-lime glass Borosilicate (Pyrex) glass 740 9.0 1.7 1.4 Polyethylene (high density) 106-198 0.46-0.50 0.12 1925 145-180 1170 90-150 Polytetrafluoroethylene (Teflon) Phenol-formaldehyde, phenolic 126-216 0.25 0.15 1590-1760 122 144 Nylon 6,6 1670 0.14 To convert to cal/g-K, multiply by 2.39 x 10 to convert to Btulb. "F, multiply by 2.39 x 10 To convert to F),multiply by 0.56 To convert to cal/s-cm-K, multiply by 2.39 x 10to convert to Btu/ft-hF, multiply by 0.578. Value measured at 100°C. Mean value taken over the temperature range O'C to 1000°C

Answer 1

In this solution some basic concepts and formulas of Heat transfer are used. For more information, refer to any standard textbook or drop a comment below. Please give a Thumbs Up, if solution is helpful.

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