Consider fully developed laminar flow of a fluid inside a wide rectangular duct with both the upper and lower surface at uniform surface temperature, as schematically shown in the figure below. The effect of the two sides of the duct is neglected (W>> H), and at a location far from the entrance the velocity distribution is assumed to be uniform, u(x) = Cu whereas the temperature distribution has a parabolic profile given by T(x)= Ts + CT (1 –(2x/H)2). From the given velocity and temperature distributions, calculate the Nusselt number, which is given by its definition as where Tb is the average bulk temperature of the flowing fluid at the specified location, and k is the thermal conductivity of the fluid.
GIVEN
Fully developed laminar flow of fluid inside rectangular duct
Uniform upper and lower surface temperature
Uniform velocity distribution u(x) = Cu
Parabolic temperature distribution T(x)= Ts + CT (1 –(2x/H)2
FIND
Nusselt number
SKETCH
The bulk temperature of a fluid is given by formula
Substituting velocity and temperature distribution in above equation we get
Now, Nu is given by definition as
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