MENG 2002 – Heat Transfer and Thermodynamics

MENG 2002 – Heat Transfer and Thermodynamics Practice Questions
A 12 cm x 18 cm circuit board houses 100 closely spaced logic chips, each dissipating 0.07 W, on its
surface. The heat transfer from the back surface of the board is negligible. If the heat transfer
coefficient on the surface of the board is 10 W/ (m2 . ° C), determine
(a) the heat flux on the surface of the circuit board, in W/m2 ,
(b) the surface temperature of the chips, and
(c) the thermal resistance between the surface of the circuit board and the cooling medium, in
°C/W.
Consider the ambient temperature to be 40°C.
(8 marks)
Steam at 7 bar and 250°C enters a pipeline and flows along it at constant pressure.
If the steam rejects heat steadily to the surroundings, at what temperature will droplets of water
begin to form in the vapour?
Using the steady-flow energy equation, and neglecting changes in velocity of the steam, calculate
the heat rejected per kilogram of steam flowing.
(10 marks)
A nozzle is a device for increasing the velocity of a steadily flowing fluid. At the inlet to a certain nozzle
the specific enthalpy of the fluid is 4025 kJ/kg and the velocity is 70 m/s. At the exit from the nozzle
the specific enthalpy is 3090 kJ/kg. The nozzle is horizontal and there is a negligible heat loss from it.
Calculate:
(i) the velocity of the fluid at exit;
(ii) the rate of flow of fluid when the inlet area is 0.1 m2 and the specific volume at inlet is
0.25 m3/kg;
(iii) the exit area of the nozzle when the specific volume at the nozzle exit is 0.5 m3/kg.
(12 marks)
0.05 kg of steam at 15 bar is contained in a rigid vessel of volume 0.0076 m3 .
What is the temperature of the steam?
If the vessel is cooled, at what temperature will the steam be just dry saturated?
Cooling is continued until the pressure in the vessel is 11 bar; calculate the final dryness fraction
of the steam, and the heat rejected between the initial and the final states.
(12 marks)
Steam from a superheater at 7 bar, 300°C is mixed in steady adiabatic flow with wet steam at 7 bar,
dryness fraction 0.9. Calculate the mass of wet steam required per kilogram of superheated steam to
produce steam at 7 bar, dry saturated.
(8 marks)
The gases in the cylinder of an internal combustion engine have a specific internal energy of 800 kJ/kg
and a specific volume of 0.06 m3/kg at the beginning of expansion. The expansion of the gases may
be assumed to take place according to a reversible law, pv1.5 = constant, from 55 bar to 1.4
bar. The specific internal energy after expansion is 230 kJ/kg. Calculate the heat rejected to the
cylinder cooling water per kilogram of gases during the expansion stroke.
(10 marks)
1 kg of a fluid is compressed reversibly according to a law pv = 0.25, where p is in bar and v is
in m3/kg. The final volume is 1/4 of the initial volume. Calculate the work done on the fluid and sketch
the process on a p-v diagram.
(10 marks)
A 50-m-long section of a steam pipe whose outer diameter is 10 cm passes through an open
space at 15 °C. The average temperature of the outer surface of the pipe is measured to be 150
°C. If the combined heat transfer coefficient on the outer surface of the pipe is 20 W/(m2. °C),
determine
(a) the rate of heat loss from the steam pipe,
(b) the annual cost of this energy lost if steam is generated in a natural gas furnace that has an
efficiency of 75 percent, and the price of natural gas is $0.52/therm (1 therm = 105,500 kJ), and
(c) the thickness of fiberglass insulation [k = 0.035 W/(m.°C)] needed in order to save 90 percent of
the heat lost. Assume the pipe temperature to remain constant at 150°C.
(10 marks)
A fluid at 0.8 bar occupying 0.1 m3 is compressed reversibly to a pressure of 4 bar according
to a law pvn = constant. The fluid is then heated reversibly at constant volume until the pressure
is 4.5 bar; the specific volume is then 0.7 m3/kg. A reversible expansion according to a law pv2 =
constant restores the fluid to its initial state. Sketch the
cycle on a p-v diagram and calculate:
(i) the mass of fluid present;
(ii) the value of n in the first process;
(iii) the net work of the cycle.
(12 marks)
Consider a 2-m-high and 3.2 m wide double-pane window consisting of two 5-mm-thick layers of
glass [ k=0.8 W/(m.°C)] separated by a 15-mm-wide stagnant air space [k = 0.028 W/(m.°C)] as
shown in the figure below.
Determine the steady rate of heat transfer through this double-paned window and the temperature
of its inner surface for a day during which the room is maintained at 26 °C while the temperature
of the outdoors is -7 °C.
Take the convection heat transfer coefficients on the inner and outer surfaces of the window to be h
1 = 12 W/(m2.°C) and h 2 = 30 W/(m2.°C), and disregard any heat transfer by radiation.
(12 marks)