Air flows in a circular tube in which there is uniform heating along the length

Question

Air flows in a circular tube in which there is uniform heating along the length of the tube. The wall temperature is measured at four locations and the values are presented in the table below.

x (ft) Twall (oF)
3 51.12
4 54.45
5 57.78
6 61.11


The inner diameter of the tube is 0.5 inches. These measurements were made at locations where the local heat transfer coefficient is a constant. For fully developed laminar flow with a uniform heat flux,



where k, the local thermal conductivity of the fluid, may be taken to be 0.016 Btu/hr-ft-oF. The local heat transfer coefficient is defined as



where the heat flux and temperatures are local values. In the problem being considered, both q and h are constant, therefore, Twall %u2013 Tb is the same at the selected locations.

(a) If , cp 0.24 Btu/lbm-oF, find the value of q.
(b) What are the values of Tb at x = 3, 4, 5, and 6 ft?

Explanation / Answer

Q= hA(Tw - Tb) = m*Cp*(Tb2 - Tb1)

q = Q/A = h(Tw - Tb) = (m/A)*Cp(Tb2 - Tb1) = D/(4(x2 - x1)) *Cp*(Tb2 - Tb1) *rho*V

q = (0.5/12)/4 *0.24 *(54.45-51.12)/(4-3) *0.075*V

q = 0.000624*V

Nu = hD/k = 0.453*Re^0.5*Pr^0.33

h = 0.453*k/D *(VD/neu)^0.5*Pr^0.33

h = 0.453*(0.016/3600)/(0.5/12) *[(V*(0.5/12)/(1.6*10^-4)]^0.5 *0.707^0.33

h = 6.93*10^-4 *V^0.5

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