3rd Homework
1) In manufacturing process, a transparent film is being bonded to a substrate as shown in the
sketch. To cure the bond at a temperature T0, a radiation source is used to provide a heat flux q0”,
all of which is absorbed at the bonded surface. The back of the substrate is maintained at T1 while
the free surface of the film is exposed to air at T ∞ and a convection heat transfer coefficient h.
(a) Show the thermal circuit representing the steady-state heat transfer situation.
(b) Assume the following conditions: T∞=20⁰C, h=50W/m2.K, and T1=30⁰C. Calculate the heat
flux that is required to maintain the bonded surface at T0=60⁰C.
2) The composite wall of an oven consists of three materials, two of which are of known thermal
conductivity, kA=20 W/m.K, and kC=50 W/m.K, and known thickness, LA=0.30 m, LC=0.15 m,
and LB=0.15 m. Under steady-state operating conditions, measurements reveal an outer surface
temperature of Ts,o=20⁰C, an inner surface temperature of Ts,i=600⁰C, and an oven air temperature
of T∞=800⁰C. The inside convection coefficient h is known to be 25 W/m2.K. What is the value of
kB?
3) A firefighter’s protective clothing, referred to as a turnout coat, is typically constructed as an
ensemble of three layers separated by air gaps, as shown schematically.
3rd Homework
Representative dimensions and thermal conductivities for the layers are as follows:
The air gap between the layers are 1 mm thick, and heat is transferred by conduction and
radiation exchange through the stagnant air. The linearized radiation coefficient for a gap may be
approximated as hrad=σ(T1+T2)( T12+T22) ≈4 σTavg3, where Tavg represents the average temperature
of surfaces comprising the gap, and the radiation flux across the gap may be expressed as
qrad”=hrad(T1-T2).
Represent the turnout coat by a thermal circuit, labeling all the thermal resistances. Calculate and
tabulate the thermal resistances per unit area for each of the layers, as well as for the conduction
and radiation processes in the gaps. Assume that the value of Tavg= 470K may be used to
approximate the radiation resistance of both gaps.
4) A composite cylindrical wall is composed of two materials of thermal conductivity k A and kB,
which are separated by a very thin, electric resistance heater for which interfacial contact
resistances are negligible.
Liquid pumped through the tube is at a temperature T∞,i and provide a convection coefficient hi at the
inner surface of the composite. The outer surface is exposed to ambient air, which is at T∞,o and
provide a convection coefficient of ho . Under steady-state conditions, a uniform heat flux of qh” is
dissipated by heater.
(a) Sketch the equivalent thermal circuit of the system.
3rd Homework
(b) Obtain an expression that may be used to determine the heater temperature.
(c) Obtain an expression for the ratio of heat flows to the outer and inner fluids, qo’ / qi’. How might
the variables of the problem be adjusted to minimize this ratio?