In the experimental determination of the heat transfer coefficient between a heated steel ball and crushed mineral solids, a series of 1.5% carbon steel balls were heated to a temperature of 700°C and the center temperature-time history of each was measured with a thermocouple as it cooled in a bed of crushed iron ore that was placed in a steel drum rotating horizontally at about 30 rpm. For a 5-cm-diameter ball, the time required for the temperature difference between the ball center and the surrounding ore to decrease from 500°C initially to 250°C was found to be 64, 67, and 72 s, respectively, in three different test runs. Determine the average heat transfer coefficient between the ball and the ore. Compare the results obtained by assuming the thermal conductivity to be infinite
with those obtained by taking the internal thermal resistance of the ball into account.
GIVEN
Heat steel balls are put in crushed iron ore
Balls are 1.5% carbon steel balls
Initial temperature of balls (To) = 700°C
Ball diameter = 5 cm = 0.05 m
Temperature difference between the ball center and the ore
Center temperature of the balls decreases from 500°C to 250°C
Time taken was found to be 64, 67, and 72 s, respectively, in three different test runs
FIND
The average heat transfer coefficient between the ball and the ore.
Compare the results obtained
(a) by assuming the thermal conductivity to be infinite with
(b) those obtained by taking the internal thermal resistance of the ball into account
ASSUMPTIONS
Temperature of the iron ore is uniform and constant
SKETCH
(a) Assuming the internal resistance of the balls is negligible. The temperature-time history is given by
Solving for the heat transfer coefficient
The average heat transfer coefficient is 322 W/(m2 K)
(b) The chart method will be used to take the internal thermal resistance into account. Figure 3.11 (a) can be used to determine the Biot number for the balls
is not detailed enough to distinguish between the first two test runs
Neglecting the internal resistance resulted in a calculated heat transfer coefficient 9% lower than using the chart method.
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