Experimental measurements of the temperature distribution during the flow of air at atmospheric pressure over the wing of an airplane indicate that the temperature distribution near the surface can be approximated by a linear equation

Question

where a = a constant = 2 m–1

Ts = surface temperature, K

T? = free stream temperature, K

y = perpendicular distance from surface (mm)

(a) Estimate the convective heat transfer coefficient if

Ts = 50°C and T?= – 50°C.

(b) Calculate the heat flux in W/m2

GIVEN

Air flow over an airplane wing

Temperature distribution is given by the expression above

Surface temperature (Ts) = 50°C

Ambient temperature (T?) = – 50°C

FIND

(a) The convective heat transfer coefficient

ch

(b) The heat flux (q/A) in W/m2

ASSUMPTIONS

Steady state conditions

Uniform surface temperature

SKETCH



PROPERTIES AND CONSTANTS

From Appendix 2, Table 28, for air at 0°C, the thermal conductivity (k) = 0.0237 W/(m K)

Answer 1

(a) The heat transfer coefficient is given by Equation (5.1)



where kf is the thermal conductivity of the fluid. Evaluate at the average of the bulk fluid temperature and the surface temperature. (This average is called the film temperature).

For this problem



For the temperature distribution, we find



(b) The rate of heat transfer is given by