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

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Write the equation qrad /qcond = fn(N, Θ ≡ Th /Tc ), where N is a dimensionless group containing σ , k, L, and Tc . 2 (and for other values if you wish). 1 W/m·K . Further suppose that you wish to operate in such a way that the conduction and radiation heat ﬂuxes are identical. Identify the operating point on your curve and report the value of Th that you must maintain. 17 A blackened copper sphere 2 cm in diameter and uniformly at 200◦ C is introduced into an evacuated black chamber that is maintained at 20◦ C.

It is initially at room temperature and is suddenly placed in a 200◦ C gas ﬂow. 18 kJ/kg·K, respectively. Evaluate the response of the thermocouple. 3 Solution. 116 s = ρcV = Therefore, eqn. 116 ◦ C (20 − 200)◦ C This result is plotted in Fig. 12, where we see that, for all practical purposes, this thermocouple catches up with the gas stream in less than 5 s. Indeed, it should be apparent that any such system will come within 95% of the signal in three time constants. Notice, too, that if the response could continue at its initial rate, the thermocouple would reach the signal temperature in one time constant.

Calculate (a) the heater temperature, (b) the heat transfer from the methanol to the heater, and (c) the heat transfer from the heater to the air. 6 W/m2 K) and by radiation to a parallel black wall at 80◦ C. What is the temperature of the heater if it delivers 9000 W/m2 ? 35 An 8 oz. can of beer is taken from a 3◦ C refrigerator and placed in a 25◦ C room. 3 W/m2 K). How long will it take to reach 12◦ C? Ignore thermal radiation, and discuss your other assumptions. 36 A resistance heater in the form of a thin sheet runs parallel with 3 cm slabs of cast iron on either side of an evacuated cavity.