Atmospheric air at 10°C enters a 2 m long smooth rectangular duct with a 7.5 cm x 15 cm cross-section. The mass flow rate of the air is 0.1 kg/s. If the sides are at 150°C, estimate (a) the heat transfer coefficient, (b) the air outlet temperature, (c) the rate of heat transfer, and (d) the pressure drop.

GIVEN



FIND



ASSUMPTIONS

Steady state

The duct is smooth

SKETCH


The hydraulic diameter of the duct is



The Reynolds number is





(a) Therefore, entrance effects may be significant.



(b) The outlet temperature is found by rearranging



No further iteration is needed since the result is close to the initial guess.

(c) The rate of heat transfer is given by



(d) The friction can be estimated from the lowest line for Figure 7.7: Re = 47,585 ? f ? 0.021. The

pressure drop is given by

Physics & Space Science

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Determine how well the above data are predicated by the appropriate correlation given in the text. Express your results in terms of the per cent difference between the experimentally determined Nusselt number and that from the equation.

An experiment was conducted in which the heat transfer from a sphere in sodium was
measured. The sphere, 0.5 in. in diameter was pulled through a large sodium bath at a
given velocity while an electrical heater inside the sphere maintains the temperature at a
set point. The following table gives the results of the experiment

GIVEN
A sphere is pulled through a sodium bath at a given velocity
Sphere diameter = 0.5 in. = 0.0127 m
Sphere temperature is kept constant
Experimental data given above
FIND
The standard deviation between the data and the appropriate correlation
SKETCH

Physics & Space Science