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.

Physics & Space Science

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