A long plastic rod of 20-mm diameter (k = 0.3 W/m · K and rhocp = 1040 kJ/m3 · K) is uniformly heated in an oven as preparation for a pressing operation. For best results, the temperature in the rod should not be less than 200°C. To what uniform temperature should the rod be heated in the oven if, for the worst case, the rod sits on a conveyor for 3 min while exposed to convection cooling with ambient air at 25°C and with a convection coefficient of 10 W/m2 · K? A further condition for good results is a maximum–minimum temperature difference of less than 10°C. Is this condition satisfied? If not, what could you do to satisfy it?

The temperature that would satisfy is 286.7°C

Explanation:

Given data:

d = 20 mm = 0.02 m

Le = characteristic length = 0.02/4 = 5x10⁻³m

K = 0.3 W/m K

ρCp = 1040 kJ/m³ K = 1.04x10⁶

t = 3 min = 180 s

h = 10 W/m² K

According transient heat analysis:

200°C is the limiting temperature, the temperature should not be less to 200°C, then, we suppose a temperature of 210°C (10°C), and find the temperature:

radiation

explanation:

heat is transmitted by radiation

molecules are free to separate from each other and will take on the shape of the container. molecules move completely at random and high speeds. they vibrate in a fixed position and do not move around much. molecules expand to the edge of their container.