Assume that all air properties may be evaluated at 27°C and determine the constants in the correlation equation: Nu = C (Gr Pr)m

Question

A laboratory experiment has been performed to determine the natural-convection heat

transfer correlation for a horizontal cylinder of elliptical cross section in air. The

cylinder is 1-m-long, has a hydraulic diameter of 1 cm, a surface area of 0.0314 m2, and

is heated internally by electrical resistance heating. Recorded data include power

dissipation, cylinder surface temperature, and ambient air temperature. The power

dissipation has been corrected for radiation effects:



GIVEN

• A horizontal, elliptical cylinder in air

• Hydraulic diameter (Dh) = 1 cm = 0.01 m

• Length (L) = 1 m

• Cylinder surface area (As) = 0.0314 m2

• Experimental data for (Ts – T?) and q shown above FIND

• The constants in the correlation equation Nu = C(Gr Pr)m

ASSUMPTIONS

• All air properties may be evaluated at 27°C

SKETCH



PROPERTIES AND CONSTANTS

for dry air at 27°C

Thermal expansion coefficient (?) = 0.00333 1/K

Thermal conductivity (k) = 0.0256 W/(m K)

Kinematic viscosity (?) = 16.4 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

The Nusselt and Grashof number for the points are given by the following equation





Tabulating these and their logarithms for the experimental data



Performing a least squares fit on the data yields