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**Unformatted text preview: **Name l’Tprtné §C5H ME 454 Fall 2016 Exam II Total Points — 100 pts. The points for each problem are listed. Be sure to include the symbolic version of the equation when you
are solving a problem. lfyou find yourself running short of time, explain how you would finish the problem
if you had time (for partial credit). 1. 8 pts. What is the physical meaning of the Reynolds Number (Re) and the Nusselt Number (Nu).
Re = Ratio of inertia and viscous forces
Nu = Ratio of convection to pure conduction heat transfer in the fluid 2. 6 pts. What is the film temperature (Tf) and what is it used for? The film temperature is the average of the surface and free stream temperatures
[(TS+T....)/2]. It represents the temperature of the fluid in the boundary layer. It is used to
evaluate fluid properties. 3. 6 pts. What is the importance of non-dimensionalizing the governing equations for convective
heat transfer thus getting the convective heat transfer coefficient as a function of dimensionless
parameters? Non—dimensionalizing the solution globalizes the solution. In other words, it allows you to
use the results (analytical, numerical or experimental) you get by solving one
problem/situation (i.e. the correlation for the heat transfer coefficient) and apply it to a
different problem/situation so long as the geometry and dimensionless parameters are
the same. It also reduces the number of variables. 4. 10 pts. In your plastic manufacturing facility, hot sheets of the plastic are cooled via air convection
from blowers blowing air across the sheet. To increase the rate of production of plastic, you need
to cool the hot sheets faster. Besides adding more blowers, suggest a method to decrease the
time to cool the plastic sheets and explain why this method will improve the rate of cooling. There are many methods to improve the cooling rate (i.e. increase the heat transfer from the sheet
to the fluid). Here are a few. Others exists and will be considered during grading. - Add a turbulence inducing device in front of the leading edge of the plastic. This would force
the flow to be turbulent which, due to mixing in the flow, has higher heat transfer rates. — Increase the velocity of the airflow. This will increase the Reynolds Number over the length of
the sheet which will lead to higher heat transfer. - Redesign the system for liquid cooling (rather than gaseous cooling), e.g. misting in water or
a water quench. In general, liquids have higher convective heat transfer coefficients than
gases, and thus higher convective heat transfer rates. - Blow cooler air over the sheets. From Newton’s Law of Cooling, the heat transfer rate is
proportional to the driving temperature difference. Thus increasing the temperature
difference will increase the h.t. rate. Note, however, that this may not be that economical. v F“ V (V
Name ['Tiikafi"? sax-1%” 5. 30 pts. An array of power transistors, dissipating 6 Watts each, are to be cooled by mounting them
on a square plate and blowing air over them (see below). The average temperature ofthe plate is
not to exceed 65 °C. Determine the maximum number of transistors that can be placed on this plate. You do not need to list your assumptions. All: Power Transistor — 6 W each T3. = 35 °C "—* How many can be on the plate? u33=4m/s Properties: Tplate S 65°C 4————————> k=0.03 W/m-K 25cm v = 1.8 x 10‘5 mZ/s (square plate: A3 = 0.0625 m2) Pr = 0.7 Solution
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on the shell side with a convection coefficient of 10,000 W/mZ-K. The cooling fluid in the tubes is
water. For a heat exchanger effectiveness of 0.27 and the other H.X. parameters specified below,
how long must the tubes (ger passl be to condense the steam. You do not need to list assumptions. Water:
Steam: T ‘_ 15 “C
Tm = The: 70 °c Tc" __ 30 .C
rh = 2.73 kg/s 2°“ m = 102 kg/s (total h0 = 10,000 W 2-K
/m through all tubes) Progerties:
= 4181 J/kg-K
H-X- u = 959x106 N-s/mz
#Tubes=720 k=0.60 W/m-K
Tube Diameter = 0.02 m Pr = 6.6
Thin walled tubes
5 = 0.27 R” = 0.0003 W/mZ-K (Fouling factor) Solution: r . I ‘
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