1. Convection Contributions by: Janet deGrazia, Stephanie Bryant
Department of Chemical and Biological Engineering University of Colorado Boulder, CO

2. A hot plate is being cooled by flowing air
A hot plate is being cooled by flowing air. The heat transfer coefficient for turbulent air flow is______________ that for laminar air flow.
less than
greater than
the same as
Turbulent Flow
ANSWER: B. greater than
The temperature of the fluid near the surface will be lower for turbulent flow because of fluid mixing. For laminar flow, there will be a defined temperature profile where the fluid is hottest near the surface of the plate and will decrease in temperature further away from the surface. Since the temperature difference between the plate and the fluid is larger for turbulent flow, it will have a larger heat transfer coefficient.
Laminar Flow

3. For cold liquid metal flowing over a hot flat plate in laminar flow, the thermal boundary layer will be ____________ the hydrodynamic boundary layer.
larger than
less than
the same as
ANSWER: A. larger than.
The ratio of the hydrodynamic boundary layer to the thermal boundary layer simplifies to the Prandtl number (which is the ratio of the momentum and thermal diffusivities) raised to some positive exponent. Liquid metals have a small Pr so the thermal boundary layer will be larger.

4. For cold liquid metal flowing over a hot flat plate in laminar flow, the onset of fully-developed flow will take ____________ that of water.
longer than
shorter than
the same as
ANSWER: B. shorter than
The ratio of the xfd(thermal) to xfd(hydrodynamic) simplifies to the Prandtl number. Liquid metals have a smaller Pr than water, so the onset of fully-developed flow will take shorter (x will be smaller).

5. Hot water flows over a cold isothermal flat plate
Hot water flows over a cold isothermal flat plate. If the water temperature increases, the heat transfer coefficient _________________ and the transition flow length ____________. The water is incompressible.
increases, increases
decreases, decreases
stays the same, stays the same
increases, decreases
decreases, increases
ANSWER: C. stays the same, stays the same
Both the heat transfer coefficient and transition flow length are dependent on the fluid. Since the fluid, water, is the same, neither will change.

6. A hot cylinder is cooled by turbulent cross flowing air
A hot cylinder is cooled by turbulent cross flowing air. Which graph could represent the convective heat transfer coefficient (h) as a function of the angular position around the cylinder (θ)? θ h θ
180 h θ
180 B.
C. D.
180
ANSWER: A.
Cross flow over a cylinder is marked by the formation of eddies after the air passes over the top of the cylinder, where θ>90. The exact location the eddies begin depends on the Reynolds number of the fluid. As the Reynolds number increases, the eddies form at a higher θ. Eddies reduce the overall heat transfer coefficient since flow into and out of the eddy area is less than the overall flow. Only plot A has a decrease in h that begins after θ=90.
180 θ
180 h h θ

7. Flowing cold air cools an aligned 4 x 3 hot tube bank
Flowing cold air cools an aligned 4 x 3 hot tube bank. The air is laminar before entering the bank. The convective heat transfer coefficient in row 3 will be _____________ that in row 1.
Cross flow air 1 2 3
greater than
less than
the same as
ANSWER: A. greater than
When the air encounters the first row, the tubes induce turbulence which increases the heat transfer coefficient.

8. Laminar cross flow air enters an aligned tube bank
Laminar cross flow air enters an aligned tube bank. Converting the tube bank from an aligned arrangement into a staggered arrangement would ______________ the heat transfer rate.
Cross flow air
increase
decrease
not change
ANSWER: A. increase
The staggered arrangement alters the flow streamlines to improve mixing of the cross flow air converting the flow to turbulent more quickly than for aligned. Turbulent flow increases the heat transfer coefficient as well as keeps the temperature difference from dropping dramatically.
Aligned
Staggered

9. Turbulent cold air flows over an aligned 3 x 3 hot tube bank
Turbulent cold air flows over an aligned 3 x 3 hot tube bank. Doubling the number of tubes in the _________ direction, while maintaining the same tube spacing, would have the hottest outlet air temperature.
Longitudinal
longitudinal
transverse
either
Cross flow fluid
Transverse
ANSWER: B. the transverse
Heat transfer rates are highest in the first few columns of tubes. The temperature difference between the air and the tubes decreases in the longitudinal direction decreasing the heat transfer rate of each successive column of tubes. Adding tubes in the transverse direction would avoid the decrease and, therefore, have a hotter outlet air temperature.

10. Laminar cold air flows over two aligned hot tube banks each with 8 tubes. One bank has 4 rows of 2 tubes each. The other has 2 rows of 4 tubes each. Which tube bank will have the greater outlet air temperature?
Cross flow fluid B.
Cross flow fluid
ANSWER: A.
Heat transfer rates are highest in the first few column of tubes. The temperature difference between the air and the tubes decreases as the number of columns increases, decreasing the heat transfer rate of each successive column of tubes. Therefore, reducing the number of columns will give the greater outlet air temperature. C. D.
Both will have the same outlet temperature
Not enough information

11. For incompressible flow within a cylinder, which statements are true?
I. The mean velocity is best used to determine the Reynold’s number.
II. When flow is fully developed, the velocity profile does not change with distance along the tube.
III. Transition to turbulent flow has a lower Reynold’s number than for external flow.
IV. Flow becomes fully developed faster for fluids with a high Prandtl number.
Answer: D. I, II, III
IV is not always true since the Prandtl number is dependent on both kinematic viscosity and thermal diffusivity, whereas fully developed flow only depends only on viscosity. In theory, a fluid with a lower thermal diffusivity and higher Prandtl number could have the same fully developed flow length as a lower Prandtl number fluid.
I is true since mean velocity is constant for an incompressible fluid through a tube
II is true since the definition of fully developed flow is a constant velocity profile
III is true based on experimental results
A. I, II B. I, III C. I, II, IV D. I, II, III
E. All the statements are true

12. Water flows through a tube of length L with an mean inlet temperature (Ti). The tube is held at a uniform surface temperature (Ts) greater than Ti. Which temperature profile best represents the mean temperature of the water as if flows through the tube? T Ti Ts
Tube
Water Ti Ts L
C. D.
ANSWER: B.
At the entrance region to the tube the temperature difference is greatest. As the temperature difference between the water and the tube decreases, the rate of heat transfer will decrease quicker. T T T

13. Water enters a tube of length L with an mean inlet temperature (Ti)
Water enters a tube of length L with an mean inlet temperature (Ti). The water is heated with a uniform heat flux through the tube. Which temperature profile best represents the mean temperature of the water as if flows through the tube?
Water Ti L
Uniform heat flux T Ti
Tube
C. D.
ANSWER: D.
A uniform heat flux means that a fixed amount of water will be increased a fixed amount of temperature. This is a linear plot. T Ti T Ti T Ti

14. Water flows through a tube of length L with an mean inlet temperature (Ti). The tube is held at a uniform surface temperature (Ts) greater than Ti. Assuming fully developed, laminar flow, the outlet temperature (To) _______ when the mass flow rate is doubled.
stays the same
increases
decreases
Water Ti Ts L To
ANSWER: C. decreases
The heat transfer along the tube will be the same, but the heat will need to be distributed across more mass, which means a lower mean outlet temperature increase.

15. Water flows through a tube of length L with an mean inlet temperature (Ti). The tube is held at a uniform surface temperature (Ts) greater than Ti. Assuming fully developed, laminar flow, the heat flow _______ when the mass flow rate is doubled.
stays the same
increases
decreases
Water Ti Ts L
ANSWER: B. increases
With more mass flow, the heat transferred will result in a smaller increase in temperature of the water. Since the temperature difference will be larger than for the lower flow, there will be additional heat flow.

16. A spacecraft contains a freshly hard boiled egg
A spacecraft contains a freshly hard boiled egg. The atmosphere inside the spacecraft is air at room temperature and atmospheric pressure. While the spacecraft is in space, the rate of cooling is ___________ that while the spacecraft is on earth.
greater than
less than
equal to
ANSWER: B. less than
Free convection is directly proportional to gravity. As gravity is reduced, the rate of free convection decreases.

17. A suspended spherical block of dry ice at -79°C is exposed to atmospheric air at 30°C. The air close to the dry ice moves _________. up
down
circular around the sphere
nowhere
Atmospheric air
30 °C
Dry Ice
-79 ° C
ANSWER: B. down
The air close to the dry ice will cool, increase in density, and travel downwards.

18. A thin square plate is in a room held at an ambient temperature of 25 °C. One side of the plate is insulated while the other is kept at a constant 100 °C. Orienting the plate _________ will result in the most free convection heat transfer.
Vertical
vertically
horizontally
either way
Horizontal
ANSWER: B. horizontally
In the vertical orientation, the rate of heat transfer decreases since the temperature of air moving up the plate will increase. Air being heated by the horizontal plate leaves the surface holding a constant temperature difference between the plate and the air.
Insulated

19. A thin plate has one side insulated and the other is kept at a constant temperature. The ambient temperature is less than the temperature of the plate. Which orientation would result in the highest heat transfer rate?
B. C D.
E. A and B will have the same heat transfer rate
ANSWER: C.
Heated air should be removed as quickly as possible to allow for more cold air to be heated and, thus, the highest heat transfer rate. For options A and B, the air will need to move across more heated surface than compared to C, which decreases the turnover rate of air for A and B. For option D, the heated air will form a film across the plate slowly creeping to the sides and result in poor transfer.

20. An array of fins and cold air are cooling an electronic chip
An array of fins and cold air are cooling an electronic chip. If the spacing of the fins is barely widened, while keeping the same individual fin geometry, the rate of heat transfer will _________________.
increase
decrease
stay the same
Not enough information
Answer: A. increase
The increase in spacing allows for more air to be between the fins which means that more heat can be carried by the air from the fins.
vs.

21. An array of fins and cold air are cooling an electronic chip
An array of fins and cold air are cooling an electronic chip. If the number of the fins is halved, while keeping the same individual fin geometry and spacing, the rate of heat transfer will _________________.
increase
decrease
stay the same
Not enough information
ANSWER: B. decrease
Since the spacing between the fins stays the same, but the number of fins has been halved, less air will be in contact on the fins. Less air means less heat can be carried and removed.
vs.

22. Which fluid would be better at removing heat from an array of fins
Which fluid would be better at removing heat from an array of fins? Assume all the fluids to be at ambient temperature and are quiescent.
Air
Ethylene glycol
Hydrogen
ANSWER: B. Ethylene glycol
Ethylene glycol has the highest Prandtl number, therefore the highest Rayleigh number. Free convection increases with increasing Rayleigh number.

23. Laminar air flows over an isothermal plate
Laminar air flows over an isothermal plate. The local heat transfer rate _________ as the position in the x direction increases, because the thermal boundary layer ___________.
decreases, decreases
increases, decreases
decreases, increases
increases, increases
stays the same, stays the same
Air
ANSWER: C. decreases, increases
The local Nusselt number depends on x via the Reynolds number. As x increases, the Reynold’s number increases by a factor of xa where a is a value less than 1. The local heat transfer coefficient is proportional to 1/x, indicating, overall, that the local heat transfer rate decreases with an increasing x position. The thermal boundary layer increases in general. x

24. Engine oil flows through a uniformly heated pipe
Engine oil flows through a uniformly heated pipe. The entrance length for thermal effects will be _________ the entrance length for hydrodynamic effects.
longer than
shorter than
the same as
ANSWER: A. longer than
The ratio of the xfd(thermal) to xfd(hydro) simplifies to the Prandtl number. Engine oil has a very large Pr, so the onset of thermal fully-developed flow will occur further down the pipe (x is larger).

25. Steam flows through a uniformly heated pipe
Steam flows through a uniformly heated pipe. The entrance length for thermal effects will be _________ the entrance length for hydrodynamic effects. Consider steam to have the properties of water vapor.
longer than
shorter than
About the same as
ANSWER: C. about the same as
The ratio of the xfd(thermal) to xfd(hydro) simplifies to the Prandtl number. Gases have a Pr of about 1.

26. Cold air flows between two very long parallel plates
Cold air flows between two very long parallel plates. The air enters at 25°C . The top plate is held at 70°C. The bottom plate is, initially, 25°C and insulated on one side. After some time, the bottom plate could reach _______________.
70 °C, constant
10 °C
25 °C
35 °C
70 °C
Cold Air
25°C at entrance
ANSWER: C. 35°C
As the cold air moves between the plates, it will develop a temperature profile where the air closer to the top plate is approximately 70°C and the air closer to the bottom plate is colder than 70°C. Since the cold plate is not isothermal, the air close to the cold plate will transfer heat warming the cold plate up. Given that there is a gap between the plates and the air is moving, the cold plate cannot reach 70°C, but will be heated up from 25°C. Only Answer C is between those two temperatures.
25 °C, initially