2. Water flows on the inside of a steel pipe of ID 2.5 cm and wall thickness 2 mm.
The convective heat transfer coefficient on the inside is 500 𝑊/𝑚2𝐾, while on the
outside is 12 𝑊/𝑚2𝐾. Calculate the value of Overall Heat transfer coefficient
based on the inside area and the outside area. What is the dominant resistance in
this problem? What is the contribution of the wall conduction resistance?
Estimate the error in calculating the value of U, if the conduction is neglected.
3.
4. Electric heater wires are embedded in a solid wall having
thickness 8 cm and k = 2.5 W/m-K. Calculate the maximum
possible heat generation rate of the maximum temperature
should not exceed 300°C. The boundary conditions on the
walls are:
Heat transfer Coefficient (𝑊/𝑚2
𝐾) Free stream temperature (°C)
Left wall 50 30
Right
wall
75 50
5.
6. Steam in a heating system flows through tubes whose outer diameter is 5 cm and whose walls are
maintained at a temperature of 180°C. Circular aluminium alloy 2024-T6 fins (k =186 W/m°C) of
outer diameter 6 cm and constant thickness 1 mm are attached to the tube. The space between the
fins is 3 mm, and thus there are 250 fins per meter length of the tube. Efficiency of the individual
fin is determined to be 97%. Heat is transferred to the surrounding air at T=25°C, with a heat
transfer coefficient of 40 W/m2°C. Determine the increase in heat transfer from the tube per meter
of its length as a result of adding fins.
7.
8. A hollow cylinder fin (shown below) has dimensions and thermal conductivity as follows: ro = 10 mm, ri =
7.5 mm, L = 70 m, and k = 1 W/mK. The fin is exposed to the ambient temperature Tinf = 150°C and the outer
and inner heat transfer coefficients are ho = 10 W/m2K and hi = 2 W/m2K. The base temperature of the fin is
Tb = 500°C. Calculate the following:
(a) the parameter m of the fin
(b) show that this fin is a long-fin.
9.
10. A composite cylindrical wall is composed of two materials of thermal conductivity kA and kB, which are separated by a
very thin electric resistance heater for which the interfacial contact resistances are negligible. Liquid pumped through the
tube is at a temperature T∞,i and provides a convective coefficient hi at the inner surface of the composite wall. The outer
surface is exposed to ambient T∞,o with ho. At steady state, a uniform heat flux of 𝑞ℎ
′′
is dissipated by the heater.
(a) Sketch the equivalent thermal circuit of the system and express all resistances in terms of relevant variables.
(b) Obtain an expression that may be used to determine the heater temperature Th.
