# THERMODYNAMICS RANKINE CYCLES

```FME 422 – HEAT TRANSFER 1
Assignment 1
1. The wall of a drying oven is constructed by sandwiching an insulation material of thermal
conductivity 0.05W/m&deg;C between thin metal sheets. The oven air is at 300&deg;C, and the
corresponding convection heat transfer coefficient is 30W/m2 &deg;C. The inner wall surface
absorbs a radiant heat flux of 100W/m2 from the hot objects within the oven. The room air
temperature is 25&deg;C, and the overall coefficient for convection and radiation from the outer
surface is 10W/m2&deg;C.
(a) Draw the thermal circuit for the wall and label all temperatures, heat rates, and thermal
resistances.
(b) What insulation thickness is required to maintain the outer wall surface at a safe-to-touch
temperature of 40&deg;C? (Hint: Neglect the thermal resistance of the thin metal sheets)
2. A steel pipe carries steam at 110&deg;C. The pipe has an inner diameter of 100mm and outer
diameter of 120mm. The pipe is located in a room where the ambient air temperature is 30&deg;C,
and the convective heat transfer coefficient between the pipe and air is 15W/m2 &deg;C. Determine
the heat transfer rate per unit length of the pipe.
To reduce the heat loss from the pipe, it is covered with a 50mm thick layer of insulation of
thermal conductivity 0.2W/m&deg;C. Determine the heat transfer rate per unit length of the
insulated pipe. Assume that the convective resistance of steam is negligible.
3. A long stainless bar of 20mm by 20mm square cross-section is perfectly insulated on three
surfaces and is maintained at a temperature of 400&deg;C on the remaining side. Determine the
maximum temperature in the bar when it is conducting a current of 1000 amperes. The thermal
and electrical conductivities of stainless steel are 16W/m&deg;C and 1.5&times;104 (Ω-m)-1, respectively.
The heat flow at the ends of the bar may be neglected.
4. Derive an equation giving the temperature at the centre of a circular rod conducting an electric
current in terms of current-density (Amps/m2), the wall temperature, and the material
properties.
What is the centre temperature of a 20mm diameter stainless steel with similar properties as in
Question 3 and outer surface temperature of 400&deg;C when conducting a current of 1000A?
```