LESSON 3
ONE DIMENSIONAL – STEADY STATE CONDUCTION
SAMPLE PROBLEM
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
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
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
