The following equation has been proposed for the heat transfer coefficient in natural convection from long vertical cylinders to air at atmospheric pressure:
Where Tf = the film temperature = 1/2 (Ts + T?) and Tf is in the range 0 to 200°C The corresponding equation in dimensionless form is
Compare the two equations, to determine those values of C, m and n in the second
equation that will give the same results as the first equation.
GIVEN
Empirical equations shown above
FIND
Values of C, m and n
ASSUMPTIONS
Air behaves as an ideal gas
Equating this to the empirical equation
The exponents of the variables must be the same, so
The value of the constant C is determined by
for dry air at 100°C and one atmosphere
k = 0.0307 W/(m K)
The gas constant for air (R) = 287 J/(kg K)
The absolute pressure of one atmosphere (P) = 101,000 N/m2
The non-dimensional empirical equation is
COMMENTS
The units of the constant in the empirical equation must be W/(m2 K1/3).
The non-dimensional empirical equation closely resembles that for turbulent
natural convection from vertical cylinders.
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