Question

Measurement of thermal diffusivity in an unsteady-state experiment. A solid slab, 1.90 cm thick, is brought to thermal equilibrium in a constant-temperature bath at 20.0°C. At a given instant (t0) the slab is clamped tightly between two thermostatted copper plates, the sur- faces of which are carefully maintained at 40.0°C. The midplane temperature of the slab is sensed as a function of time by means of a thermocouple. The experimental data are: t (sec) 0 120 240 360 480 600 T (C) 20.0 24.4 30.5 34.2 36.5 37.8 12B.1. to thermal equilibrium in mostatted copper pa the slab is Determine the thermal diffusivity and thermal conductivity of the slab, given that p- 1.50 g/cmand C-0.365 cal/g.C. Answer: a 1.50 x 103 cm2/s; k 7.9 x 10*cal/s cm Cor 0.19 Btu/hr ft

Answer 1

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Center of slab Surface of slab at/b2 1.0 0.8 0.2 0.6 0.6 0.4 Т,-T T1-To T-To 0.6 0.2 0.2 0.8 0.1 0.040.01 0.2 0.4 0.6 0.8 1.0 ylb Fig. 12.1-1. Temperature profiles heat conduction in a slab of finite thickness 2b. The initial temperature of the slab is To and T, is the tempera ture imposed at the slab surfaces for time0. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd edition, Oxford University Press (1959), p. 101.J for unsteady-state