ENME 332: Fall, 2008
HW12 Solutions
1). We showed in class that = by performing an energy balance on a real body, but
this is only true if the body was in thermal equilibrium with a black cavity. To show that
for bodies at different temperatures, conside

ENME 332 HW
Due Tuesday, Sept. 14, 5 PM
Fall, 2010
Jungho Kim
1). A copper sphere 2.5 cm in diameter is initially at a uniform temperature of 40C.
The sphere is suspended in a slow-moving air stream at 0C that produces a heat transfer
coefficient of 15 W/

PROBLEM 10.44
KNOWN: Saturated steam condensing on the outside of a brass tube and water flowing on the inside
of the tube; convection coefficients are prescribed.
FIND: Steam condensation rate per unit length of the tube.
SCHEMATIC:
ASSUMPTIONS: (1) Stea

PROBLEM 9.95
KNOWN: Dimensions of double pane window. Thickness of air gap. Temperatures of room and
ambient air.
FIND: (a) Temperatures of glass panes and heat rate through window, (b) Resistance of glass pane
relative to smallest convection resistance.

PROBLEM 9.62
KNOWN: Motor shaft of 20-mm diameter operating in ambient air at T = 27C with surface
temperature Ts 87C.
FIND: Convection coefficients and/or heat removal rates for different heat transfer processes: (a) For a
rotating horizontal cylinder as

PROBLEM 13.17
KNOWN: Temperature and diameters of a circular ice rink and a hemispherical dome.
FIND: Net rate of heat transfer to the ice due to radiation exchange with the dome.
SCHEMATIC:
ASSUMPTIONS: (1) Blackbody behavior for dome and ice. (2) Surfac

PROBLEM 9.70
KNOWN: Diameter, initial temperature and emissivity of long steel rod. Temperature of air and
surroundings.
FIND: (a) Average surface convection coefficient, (b) Effective radiation coefficient, (c,d) Maximum
allowable conveyor time.
SCHEMATI

PROBLEM 8.38
KNOWN: Inlet temperature, pressure and flow rate of air. Tube diameter and length. Pressure of
saturated steam.
FIND: Outlet temperature and pressure of air. Mass rate of steam condensation.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state, (2) Outer

PROBLEM 10.30
KNOWN: Steel bar upon removal from a furnace immersed in water bath.
FIND: Initial heat transfer rate from bar.
SCHEMATIC:
ASSUMPTIONS: (1) Uniform bar surface temperature, (2) Film pool boiling conditions.
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PROPERTIES: Table A-6, Water, li

PROBLEM 10.27
KNOWN: Small copper sphere, initially at a uniform temperature, Ti, greater than that corresponding to
the Leidenfrost point, TD, suddenly immersed in a large fluid bath maintained at Tsat.
FIND: (a) Sketch the temperature-time history, T(t)

PROBLEM 10.45
KNOWN: Insulated container having cold bottom surface and exposed to saturated vapor.
FIND: Expression for growth rate of liquid layer, (t); thickness formed for prescribed conditions;
compare with vertical plate condensate for same conditio

PROBLEM 10.63
KNOWN: Heat dissipation from multichip module to saturated liquid of prescribed temperature and
properties. Diameter and inlet and outlet water temperatures for a condenser coil.
FIND: (a) Condensation and water flow rates. (b) Tube surface

PROBLEM 12.47
KNOWN: Temperature, thickness and spectral emissivity of steel strip emerging from a hot roller.
Temperature dependence of total, hemispherical emissivity.
FIND: (a) Initial total, hemispherical emissivity, (b) Initial cooling rate, (c) Time

PROBLEM 12.44
KNOWN: Temperature of polished stainless steel. Spectral emissivity distribution.
FIND: Total hemispherical emissivity using 5-band integration. Emissive power.
SCHEMATIC:
ASSUMPTIONS: Spectral hemispherical and normal emissivities are equal

PROBLEM 12.28
KNOWN: Various surface temperatures.
FIND: (a) Wavelength corresponding to maximum emission for each surface, (b) Fraction of solar
emission in UV, VIS and IR portions of the spectrum.
ASSUMPTIONS: (1) Spectral distribution of emission from

PROBLEM 12.27
KNOWN: Spectral distribution of the emissive power given by Plancks distribution.
FIND: Approximations to the Planck distribution for the extreme cases when (a) C2/T > 1, Wiens
law and (b) C2/T < 1, Rayleigh-Jeans law.
ANALYSIS: Plancks dist

PROBLEM 12.24
KNOWN: Isothermal enclosure of surface area, As, and small opening, Ao, through which 70W
emerges.
FIND: (a) Temperature of the interior enclosure wall if the surface is black, (b) Temperature of the
wall surface having = 0.15.
SCHEMATIC:
AS

PROBLEM 12.20
2
KNOWN: Solar flux at outer edge of earths atmosphere, 1368 W/m .
FIND: (a) Emissive power of sun, (b) Surface temperature of sun, (c) Wavelength of maximum solar
emission, (d) Earth equilibrium temperature.
SCHEMATIC:
De= 1.29 107 m
ASSUMP

PROBLEM 12.4
KNOWN: Temperature, absorptivity, transmissivity, radiosity and convection conditions for a
semitransparent plate.
FIND: Plate irradiation and total hemispherical emissivity.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Uniform su

PROBLEM 9.109
KNOWN: Diameter and temperature of cylinder. Velocity and temperature of fluid in cross flow.
Four different fluids.
FIND: Whether heat transfer by free convection is significant.
SCHEMATIC:
D = 25 mm
Fluid
V = 0.05 m/s
T = 20C
g
Ts = 35C
AS

PROBLEM 10.65
KNOWN: Copper sphere of 10 mm diameter, initially at 50C, is placed in a large container filled
with saturated steam at 1 atm.
FIND: Time required for sphere to reach equilibrium and the condensate formed during this period.
SCHEMATIC:
ASSUM

PROBLEM 10.13
KNOWN: Nickel-coated heater element exposed to saturated water at atmospheric pressure;
thermocouple attached to the insulated, backside surface indicates a temperature To = 266.4C when
7
3
the electrical power dissipation in the heater elem

PROBLEM 9.39
KNOWN: Width and thickness of sample material. Rate of heat dissipation at bottom surface of
sample and temperatures of top and bottom surfaces. Temperature of quiescent air and surroundings.
FIND: Thermal conductivity and emissivity of the s

PROBLEM 8.60
KNOWN: Hot fluid passing through a thin-walled tube with coolant in cross flow over the tube. Fluid
flow rate and inlet and outlet temperatures.
FIND: Outlet temperature, Tm,o, if the flow rate is increased by a factor of 2 with all other con

PROBLEM 7.21
KNOWN: Surface characteristics of a flat plate in an air stream.
FIND: Orientation which minimizes convection heat transfer.
SCHEMATIC:
ASSUMPTIONS: (1) Surface B is sufficiently rough to trip the boundary layer when in the
upstream position

PROBLEM 7.4
KNOWN: Liquid metal in parallel flow over a flat plate.
FIND: An expression for the local Nusselt number.
SCHEMATIC:
ASSUMPTIONS: (1) Steady, incompressible flow, (2) < t, hence u(y) u, (3) Boundary layer
approximations are valid, (4) Constant

PROBLEM 7.3
KNOWN: Velocity and temperature of air in parallel flow over a flat plate.
FIND: (a) Velocity boundary layer thickness at selected stations. Distance at which boundary layers
merge for plates separated by H = 3 mm. (b) Surface shear stress and

PROBLEM 6.32
KNOWN: Local Nusselt number correlation for flow over a roughened surface.
FIND: Ratio of average heat transfer coefficient to local coefficient.
SCHEMATIC:
ANALYSIS: The local convection coefficient is obtained from the prescribed correlatio

PROBLEM 6.29
KNOWN: Experimental measurements of the heat transfer coefficient for a square bar in
cross flow.
FIND: (a) h for the condition when L = 1m and V = 15m/s, (b) h for the condition when L
= 1m and V = 30m/s, (c) Effect of defining a side as the

PROBLEM 6.13
KNOWN: Variation of local convection coefficient with distance x from a heated plate with a
uniform temperature Ts.
FIND: (a) An expression for the average coefficient h12 for the section of length (x2 - x1) in terms of
C, x1 and x2, and (b)