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Heat transfer Final exam Summer
Typology: Papers
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conduction within the sphere is extremely fast relative to convection
on the surface, and temperature distribution in the sphere is uniform.
(solid), two boundary conditions (spatial) and one initial condition (in
time) must be known.
in temperature of an object over time, the total change in thermal
energy in the object can be calculated as: mc(T(t)-T(0)) ; where c is
the specific heat, m is the objects mass, T(t) is the object’s
temperature at the t , and T(0) is the initial temperature.
adiabatic or insulated surface means the surface temperature must be
equal to zero.
surface holds for both steady-state and unsteady-state conditions.
silica glass panes 1 cm thick, with air in between. Under steady
conditions, linear (constant gradient) temperature profiles are
found in both silica panes, as well as the air.
a) If the room (and the inner surface of the inner glass pane) is
at a temperature of 25
o
C , while outdoors it is - 25
o
C with a
convection coefficient of 18 W m
- 2
- 1
, what is the rate of
heat loss through the window?
b) What is the rate of heat loss if the room temperature is
decreased to 20
o
c) Finally, what is the rate of heat loss for a room temperature
of 25
o
C , but with one of the panes (and the air) removed?
with a thickness of L=10 cm (considered as characteristic
length) is given as T(x)=-3000x
2
+100x+500 (“T” in Kelvins and
“x” in meters). On both sides, the wall is losing heat by
convection to a liquid at 300 K. Determine the Biot number on
each side of the wall. Note that the thermal and/or material
properties of the wall are not known.
rod, which has a radius of 5 cm. The rod is cooled by the
surrounding water at T ∞
= 20 °C. Due to the directionality of the
flow, convection heat transfer coefficients on each side of the
rod are different. To simplify the problem, we can assume that,
uniformly h 1
=50 W/m
2
× K on the right-hand side of the dashed
rectangle and it is h 2
=25 W/m
2
× K on the left-hand side.
Determine the maximum allowable heat generation rate within
the rod for the centerline temperature to not exceed 3000 K at
steady-state. The thermal conductivity of the rod is k= 1 W/m
quenched in a large bath having a constant temperature of 320
K with a convection heat transfer of 75 W/m
2
K. The
thermophysical properties of the sphere material are: ρ=
kg/m
3
, c=1600 J/kg × K, and k=1.7 W/m × K. (Use characteristic
length Lc=V/A to determine applicability of lumped method; Use
radius of the sphere for one term approximation)
a) Calculate the time required for the surface of the sphere to
reach 415 K.
b) Determine the heat flux (W/m
2
) at the outer surface of the
sphere at the time determined in part a).
c) Determine the energy (J) that has been lost by the sphere
during the process of cooling to the surface temperature of
