King Saud University
Free Convection problems1. A fine wire having a diameter of 0.02
mm is maintained at a constant temperature of 54 C by an electric
current. The wire is exposed to air at 1 bar and 0 C. Calculate the
electric power necessary to maintain the wire temperature if the
length is 50 cm.
2. A vertical cylinder 76.2 mm in diameter and 121.9 mm high is
maintained at 397.1 K at its surface. It loses heat by natural
convection to air at 294.3 K. Heat is lost from the cylindrical
side and the flat circular end at the top. Calculate the heat loss
neglecting radiation losses. Use the simplified equation of table
(4.7-2) in Geankoplis and those equations for the lowest range of
NGr NPr. The equivalent L to use for the top flat surface is 0.9
times the diameter.
3. A 6-m-long section of an 8-cm-diameter horizontal hot water
pipe passes through a large room whose temperature is 20C. If the
outer surface temperature of the pipe is 70C, determine the rate of
heat loss from the pipe by natural convection.
4. Consider a 0.6-m x 0.6-m thin square plate in a room at 30C.
One side of the plate is maintained at a temperature of 90C, while
the other side is insulated, as shown in Figure Q2. Determine the
rate of heat transfer from the plate by natural convection if the
plate is (a) vertical, (b) horizontal with hot surface facing up,
and (c) horizontal with hot surface facing down.
5. An orange 102 mm in diameter having a surface temperature of
21.1 C is placed on an open shelf in a refrigerator held at 4.4 C.
Calculate the heat loss by natural convection, neglecting
radiation. As an approximation, the simplified equation for
vertical planes can be used with L replaced by the radius of the
sphere (M1).
6. Air at 1 atm abs pressure in enclosed between two vertical
plates where L = 0.6 m and = 30 mm. The plates are 0.4 m wide. The
plate temperatures are T1 = 394.3 K and T2 = 366.5 K. Calculate the
heat transfer rate across the air gap. Repeat for the case where
the two plates are horizontal and the bottom plate is hotter than
the upper plate. Compare the results.
Eng. Mohamed Gaily
Office: A B 81, Building 3
