SAMPLE PROBLEM 1
Consider a steel pan placed on top of an electric range to
cook spaghetti. The bottom section of the pan is L 0.4 cm
thick and has a diameter of D 18 cm. The electric heating
unit on the range top consumes 800 W of power during
cooking, and 80 percent of the heat generated in the
heating element is transferred uniformly to the pan.
Assuming constant thermal conductivity, obtain the
differential equation that describes the variation of the
temperature in the bottom section of the pan during steady
operation.
SAMPLE PROBLEM 2
A 2-kW resistance heater wire with thermal conductivity k 15
W/m · °C, diameter D 0.4 cm, and length L 50 cm is used to boil
water by immersing it in water. Assuming the variation of the
thermal conductivity of the wire with temperature to be
negligible, obtain the differential equation that describes the
variation of the temperature in the wire during steady
operation.
SAMPLE PROBLEM 3
A spherical metal ball of radius R is heated in an oven to a
temperature of 600°F throughout and is then taken out of
the oven and allowed to cool in ambient air at T 75°F by
convection and radiation. The thermal conductivity of the
ball material is known to vary linearly with temperature.
Assuming the ball is cooled uniformly from the entire outer
surface, obtain the differential equation that describes the
variation of the temperature in the ball during cooling.
