For 0001kgs internal flow of air in a 2m long 5mm inside dia

For 0.001kg/s internal flow of air in a 2m long 5mm inside diameter thin wall tube, with a mean inlet temperature of 300K and mean outlet temperature of 400K, determine assuming the constant flux model: thermal fluid properties of air at 350K

(A) the Reynolds Number (Is the flow turbulent, based on ReD)?

(B) the heat transfer rate from basic thermodynamics

(C) the heat flux

(D) using the Dittus-Boelter Eqn, the average Nusselt Number (about 40?)

(E) the average h

(F) the average surface temperature (the mean bulk fluid temperature is 350K)

Solution

For air at 350 K, properties are:

Thermal conductivity k = 0.0299 W/m-K

Specific heat Cp = 1.009 kJ/kg-K

Density rho = 1 kg/m^3

Kinematic viscosity neu = 20.94*10^-6 m^2/s

Prandtl number Pr = 0.708

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Pipe area A = 3.14/4*5^2 = 19.625 mm^2

a)

Reynolds number Re = V*D/neu

But V = m/(rho*A) = 0.001 / (1*19.625*10^-6) = 50.96 m/s

Re = 50.96*5*10^-3 / (20.94*10^-6)

Re = 12167

Since Re > 2300, flow is turbulent.

b)

Heat transfer rate Q = m*Cp*(Tout - Tin)

= 0.001*1.009*(400 - 300)

= 0.1009 kW = 100.9 W

C)

Surface area = pi*D*L = 3.14*2*5*10^-3 = 0.0314 m^2

Heat flux = Heat transfer rate / surface area

= 100.9 / 0.0314

= 3213.4 W/m^2

D)

Nu = 0.023 * Re^0.8 * Pr^0.4

= 0.023 * 12167^0.8 * 0.708^0.4

= 37.1

E)

Nu = hD/k

h = Nu*k/D

= 37.1*0.0299 / 0.005

= 222.1 W/m^2-K