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.

Question

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

Answer 1

The Correlation of the heat transfer rate will be illustrated with Run #1. The film temperature

(Tf) = (Ts + T?)/2 = (478°C + 300°C)/2 = 389°C. for sodium at 389°C

Thermal conductivity (k) = 71.6 W/(m K)

Kinematic viscosity (?) = 3.08 × 10–7 m2/s

Prandtl number (Pr) = 0.0050

The Reynolds number is



The Nusselt number for spheres in liquid metals for 3.6 × 104 < ReD < 2 × 105 is given



The heat flux from the sphere is



Similarly for the other test runs