From Problem 1.71, consider the wire leads connecting the transistor to the circuit board. The leads are of thermal conductivity k, thickness t, width w, and length L. One end of a lead is maintained at a temperature T c corresponding to the transistor case, while the other end assumes the temperature T b of the circuit board. During steady-state operation, current flow through the leads provides for uniform volumetric heating in the amount q . , while there is convection cooling to air that is at T ∞ and maintains a convection coefficient h . Derive an equation from which the temperature distribution in a wire lead may be determined. List all pertinent assumptions. Determine the temperature distribution in a wire lead, expressing your results in terms of the prescribed variables.
From Problem 1.71, consider the wire leads connecting the transistor to the circuit board. The leads are of thermal conductivity k, thickness t, width w, and length L. One end of a lead is maintained at a temperature T c corresponding to the transistor case, while the other end assumes the temperature T b of the circuit board. During steady-state operation, current flow through the leads provides for uniform volumetric heating in the amount q . , while there is convection cooling to air that is at T ∞ and maintains a convection coefficient h . Derive an equation from which the temperature distribution in a wire lead may be determined. List all pertinent assumptions. Determine the temperature distribution in a wire lead, expressing your results in terms of the prescribed variables.
Solution Summary: The author explains the equation from which the temperature distribution in a wire lead may be determined.
From Problem 1.71, consider the wire leads connecting the transistor to the circuit board. The leads are of thermal conductivity k, thickness t, width w, and length L. One end of a lead is maintained at a temperature
T
c
corresponding to the transistor case, while the other end assumes the temperature
T
b
of the circuit board. During steady-state operation, current flow through the leads provides for uniform volumetric heating in the amount
q
.
,
while there is convection cooling to air that is at
T
∞
and maintains a convection coefficient h.
Derive an equation from which the temperature distribution in a wire lead may be determined. List all pertinent assumptions.
Determine the temperature distribution in a wire lead, expressing your results in terms of the prescribed variables.
2.16 A standard 4-in. steel pipe (ID = 4.026 in., OD =
4.500 in.) carries superheated steam at 1200°F in an
enclosed space where a fire hazard exists, limiting
the outer surface temperature to 100°F. In order to
minimize the insulation cost, two materials are to be
(a) Specify the thickness for each insulating mate-
rial. (b) Calculate the overall heat transfer coefficient
based on the pipe OD. (c) What fraction of the
total resistance is due to (1) steam-side resistance,
(2) steel pipe resistance, (3) insulation (the combina-
tion of the two), and (4) outside resistance? (d) How
much heat is transferred per hour per foot length of
pipe?
used: first a high-temperature (relatively expensive)
insulation is to be applied to the pipe, and then
magnesia (a less expensive material) will be applied
on the outside. The maximum temperature of the
magnesia is to be 600°F. The following constants are
known:
steam-side coefficient
h = 100 Btu/hr ft² °F
high-temperature
insulation
conductivity
k =…
Number 16.
Q3. What is the analogical reason between heat transfer by conduction and flow of electricity through ohmic resistance? Use a composite wall of a building to illustrate the concept. A composite slab with three layers of thermal conductivities k1, k2, k3 and thickness t1, t2, t3 respectively, are placed in a close contact. Derive an expression from the first principle for the heat flow through the composite slab per unit surface area in terms of the overall temperature difference across the slab.
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