By Lienhard J.H.IV, Lienhard J.H.V.

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Does the temperature proﬁle suggest any simplifying assumptions that might be made in subsequent analysis of the wall? 2 Verify eqn. 15). 3 q = 5000 W/m2 in a 1 cm slab and T = 140◦ C on the cold side. 5 % carbon) • Ice • Spruce • Insulation (85 % magnesia) • Silica aerogel Indicate which situations would be unreasonable and why. 4 Explain in words why the heat diﬀusion equation, eqn. 1). 5 A 1 m rod of pure copper 1 cm2 in cross section connects a 200◦ C thermal reservoir with a 0◦ C thermal reservoir.

Write a diﬀerential equation that expresses T (t) for the sphere, assuming lumped thermal capacity. • Identify a dimensionless group, analogous to the Biot number, than can be used to tell whether or not the lumpedcapacity solution is valid. • Show that the lumped-capacity solution is valid. • Integrate your diﬀerential equation and plot the temperature response for the sphere. 18 As part of a space experiment, a small instrumentation package is released from a space vehicle. It can be approximated as a solid aluminum sphere, 4 cm in diameter.

51(∆T ◦ C)1/4 W/m2 K. Plot Tsphere as a function of t. Verify the lumpedcapacity assumption. 27 A 3 cm diameter, black spherical heater is kept at 1100◦ C. It radiates through an evacuated space to a surrounding spherical shell of Nichrome V. 3 cm thick. It is black on the inside and is held at 25◦ C on the outside. Find (a) the temperature of the inner wall of the shell and (b) the heat transfer, Q. 28 The sun radiates 650 W/m2 on the surface of a particular lake. At what rate (in mm/hr) would the lake evaporate away if all of this energy went to evaporating water?

### A heat transfer textbook by Lienhard J.H.IV, Lienhard J.H.V.

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