The Prandtl number, NPr, is used in heat transfer calculations. Like all dimensi

Question

The Prandtl number, NPr, is used in heat transfer calculations. Like all dimensionless numbers, it represents the ratio of two physical processes, in this case momentum diffusivity to thermal diffusivity. It is defined as

NPr = Cp /k

where Cp is the heat capacity, is the viscosity, and k is the thermal conductivity. For a certain fluid, Cp = 0.5 J/(g oC), k = 0.3 W/(m oC), and =

2000 lbm/(ft h). Calculate NPr in a single dimensional equation. Then convert all properties first to base SI, CGS, and engineering units and then, in each system of units, calculate NPr.

Explanation / Answer

In SI units should be in m^2/s = 2000 lbm/(ft^2/h) = 0.0516128 m^2/hr

= 0.0516128 m^2/3600 sec = 1.4336 x 10^-5 m^2/s

Cp should be in J/Kg*K = 0.5 J/(g oC) = 500  J/Kg*K

k should be in W/(m*K) = 0.3 W/(m oC) = 29.9 W/(m*K)

Substituting all above values

So NPr = Cp /k

NPR = (500  J/Kg*K *1.4336 x 10^-5 m^2/s) / 29.9 W/(m*K)

= 0.0002397 = 2.397 x 10^-4 JmW/(Kg*K^2 *s)

In CGS units

should be in cm^2/s = 2000 lbm/(ft^2/h) = 516.128 cm^2/hr

= 516.128 cm^2/3600 sec = 0.1433 cm^2/s

Cp should be in Cal/g*oC = 0.5 J/(g oC) = 0.00011942 Cal/(goC)

k should be in W/cm-°C = 0.3 W/(m oC) = 0.003 W/cm-°C

So NPR = 0.1433 cm^2/s x 0.00011942 Cal/(goC) /( 0.003 W/cm-°C)

= 0.0057 cm^3* Cal / (s * g * cm)

Now in engineering units

= 2000 lbm/(ft^2/h)

Cp = 0.5 J/(g oC)

k = 0.3 W/(m oC)

NPR = [ 0.5 J/(g oC) x 2000 lbm/(ft^2/h) ]/0.3 W/(m oC)

= 3333,3 (J *lbm * h *W)/(ft^2*m)

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