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Principles of Food and Bioprocess Engineering (FS 231) Short Answer Questions on Transfer

1. Explain the following terms and explain when, why, and where are they used: a. (k) b. Convective coefficient (h) c. Overall heat transfer coefficient (U) d.

e. (NRe) f. (NNu) g. Biot number (NBi)

2. What are the SI units of the following quantities?

a. Specific heat (cp) b. Latent heat () c. Thermal conductivity (k) d. Convective heat transfer coefficient (h) e. Overall heat transfer coefficient (U) f. Thermal diffusivity (")

g. (NPr) h. Logarithmic mean area (Alm) i. Logarithmic mean temperature difference ()Tlm) j. Thermal resistance to heat transfer k. Rate of transfer of energy

l. Nusselt number (NNu) m. (NGr) n. Biot number (NBi) o. Heat flux (Q/A)

3. Give approximate values for the following (with SI units): a. Convective heat transfer coefficient for free between a hot cylinder and still air b. Convective heat transfer coefficient for forced convection in a pipe for turbulent flow c. Thermal conductivity of a metal d. Thermal conductivity of an insulator e. Specific heat of water at room temperature f. Viscosity of water at room temperature

4. Are the following statements true or false? a. The logarithmic mean area (of a cylindrical tube) is always greater than the inside surface area and always less than the outside surface area b. The overall heat transfer coefficient (U) for heat flow from a composite slab to air (with convection and conduction taking place) is greater than the convective heat transfer coefficient (h) c. At steady state, the heat flux (Q/A) in the wall of a coaxial tubular heat exchanger is equal to the heat flux in the insulator surrounding it (Neglecting heat losses in the axial direction) d. The lumped parameter analysis is valid for the situation of negligible surface resistance e. Grashof number comes into play for forced convection f. When the Biot number is greater than 40, it can be assumed that the convective heat transfer coefficient (h) is negligible. g. In a counter-current heat exchanger, the exit temperature of the cold fluid can be higher than the inlet temperature of the hot fluid. h. When insulation is added to the outside of a pipe such that the outside radius of the pipe (including the insulation) becomes equal to the critical radius, then the heat loss from the pipe is at its maximum. i. Higher the specific heat of a product, the faster it up.

j. The characteristic dimension (dc) to use in the computation of Grashof number and Nusselt number for a situation involving free convection (at steady state) over a horizontal cylinder is the radius of the cylinder.

k. In a tubular heat exchanger (with )T1 … )T2), )Tlm lies between the values )T1 and )T2 l. Convective heat transfer coefficient is a property of a fluid m. The outlet temperature of the cold fluid is always less than or equal to the outlet temperature of the hot fluid in a co-current heat exchanger n. The outlet temperature of the cold fluid can be greater than the outlet temperature of the hot fluid in a counter-current heat exchanger o. The units of thermal conductivity and convective heat transfer coefficient are the same

p. Prandtl number (NPr) increases with an increase in product flow rate q. Heat transfer during transfer of energy between hot and cold fluids in a tubular heat exchanger starts off as being an unsteady state heat transfer problem and then becomes a steady state heat transfer problem

5. What is Fourier’s law of heat conduction (write down the equation)? What does the negative sign in the equation signify?

6. Does the use of insulation (outside a heated cylindrical tube) always result in a decrease in heat loss? Justify your answer.

7. Why is an insulation used despite the fact that air has a slightly lower thermal conductivity than most insulating materials?

8. Three slabs of identical thickness and length (k1 = 1 W/m K, k2 = 5 W/m K, k3 = 15 W/m K) are stacked next to each other with the slab no. 2 being in between slabs 1 & 3. a. Draw the temperature profiles (at steady state) in the slabs if the free end of slab no. 1 is at 100 /C and the free end of slab no. 3 is at 0 /C. b. Across which slab is the temperature drop the highest?

9. Three slabs (k1 = 1 W/m K, k2 = 5 W/m K, k3 = 15 W/m K & x1= 1 cm, x2 = 7 cm, x3 = 10 cm) are stacked next to each other with the slab no. 2 being in between slabs 1 & 3. Across which slab is the temperature drop the highest when the heat flux is the same in all the 3 slabs? EXPLAIN how you arrived at the answer.

10. What is the main principle governing free convection? 11. What are the differences between forced and free convection?

12. What are the factors that affect the magnitude of convective heat transfer coefficient (h) for: a. Free convection b. Forced convection for flow in a pipe

13. Explain the concept of critical thickness of insulation.

14. Why are good conductors of electricity also good conductors of heat?

15. Name four types of heat exchangers (co-current and counter-current are arrangements of heat exchangers and not types of heat exchangers).

16. What is the expression for thermal resistance to heat transfer in the following situations? (Express your answer in terms of h, k, A, and )x) a. Purely conduction b. Purely convection c. Combination of 1 conduction and 1 convection d. Combination of 2 conductions and 2 convections

17. Can the following terms be less than zero?

a. )Tlm for a co-current heat exchanger b. )Tlm for a counter-current heat exchanger c. Thermal conductivity of an insulator d. Overall heat transfer coefficient e. Convective heat transfer coefficient for free convection f. Logarithmic mean area

18. The inside wall of a heat exchanger is 80 /C and the temperature of the insulation exposed to atmosphere is at 70 /C. Which of the following is a possible value for the temperature of the interface between the insulation and the outside wall of the heat exchanger? EXPLAIN. a. 78 /C b. 70 /C c. 67 /C d. 80 /C e. 82 /C

19. Thi = 80 /CTho = 60 /CTci = 45 /CTco = 65 /C a. Are the above readings for a co-current or counter-current heat exchanger? b. If all the heat lost by the hot fluid is gained by the cold fluid, is the flow rate of the hot or cold fluid higher? (Assume that the specific heats of the cold and hot fluid are the same) EXPLAIN.

20. For a counter-current heat exchanger, the following are the inlet and exit temperatures of the hot and cold fluids:

Thi = 80 /CTho = 60 /CTci = 45 /CTco = 55 /C

Without actually calculating Tlm, EXPLAIN which of the following are possible values for )Tlm. a. 14.7 b. 3.8 c. 19.6 d. 26.3 21. At steady state, the following are the temperatures of the hot and cold fluid at the inlet and exit of a tubular heat exchanger:

Th,i = 95 /C Th,o = 75 /C Tc,i = 45 /C Tc,o = 80 /C Are the above readings for a co- or counter-current heat exchanger? EXPLAIN.

22. Thi = 80 /CTho = 65 /CTci = 55 /CTco = 85 /C The above readings are for: a. Only a co-current heat exchanger b. Only a counter-current heat exchanger c. Either a co-current or a counter-current heat exchanger d. Neither a co-current nor a counter-current heat exchanger EXPLAIN which of the above statements are true.

23. Can the exit temperature of cold water be higher than the exit temperature of hot water in a counter-current heat exchanger? Explain.

24. When does one use Grashof number (NGr)?

25. When and why do we use a logarithmic mean temperature difference?

26. When and why do we use logarithmic mean area?

27. For a problem involving conduction and convection (in a pipe), the following expression for overall heat transfer coefficient is used:

If the Nusselt number in the problem is very high, one of the two terms on the right hand side of the above equation can be neglected. Which is the term that can be neglected? Explain.

28. Make use of the following equation to determine the units of $.

29. Which of the 3 modes of heat transfer does NOT require a medium for transfer of heat?

30. For a problem involving both conduction and convection, the following were the results obtained for h, k, and U (not necessarily in that order): 8 W/m2 K 10 W/m2 K 15 W/m K Assign the appropriate symbol (h, k or U) to the above quantities.

31. What are the NAMES and UNITS of the following quantities used in heat transfer? a. h b. k c. U

32. Insulation (k = 0.1 W/m K) is to be added to the outside surface of a pipe of O.D. 2 cm. If the heat transfer coefficient between the outside of the insulation and the ambient air is 10 W/m2 K, which of the following statements are true? EXPLAIN how you arrived at the answer. a. Adding any amount of insulation will result in a decrease in heat loss b. Heat loss will initially increase and then decrease c. Heat loss will always increase no matter how much insulation is added d. Cannot determine if heat loss will increase or decrease

33. Which of the following are possible values of overall heat transfer coefficient (in SI units) when conduction and convection are taking place. Conduction is taking place within a sheet having a thermal conductivity of 2 (SI units) and the convective heat transfer coefficient for transfer of heat between the slab and the surrounding fluid is 200 (SI units). Assume that the area for heat transfer by conduction and convection are the same. EXPLAIN your answer. a. -2 b. +200 c. +198 d. +202

34. When insulation is added to the outside of a pipe such that the outside radius of the pipe (including insulation) becomes equal to the critical radius, then the heat loss from the pipe is: a. The maximum b. The minimum c. Between the maximum and the minimum EXPLAIN how you arrived at the answer.

35. The outside surface area of a cylinder is 1.2 m2 and the inside surface area is 0.8 m2. Without actually computing the logarithmic mean area, EXPLAIN which of the following are possible values for the logarithmic mean area (in m2)? There may be more than 1 correct answer. a. 0.8 b. 1.2 c. 0.99 d. 2.01 e. 0.39 f. 1.19

36. Can the overall heat transfer coefficient (U) for heat flow from a composite slab to (with convection and conduction taking place) be greater than the convective heat transfer coefficient (h)? Explain.

37. Match the following columns:

(i) NBi < 0.1 a. Buoyancy (or density difference) driven flow

(ii) 0.1 < NBi < 40.0 b. Resistance due to convection is very low

(iii) NNu is very high c. Lumped parameter analysis

(iv) NGr d. Heisler chart 38. Saturated steam at a pressure of 198.53 kPa (corresponding saturation temperature = 120 /C) and a quality of 95% is condensing in the annular space of a 5 m long double pipe heat

exchanger. The exiting steam has a quality of 90%. Apple juice (cp = 3000 J/kg K) is flowing in the inner tube at the rate of 1 kg/s. It enters at 20 /C and exits at 70 /C. What is the logarithmic mean temperature difference?

39. In the laboratory analysis of the following experiments, was a steady state or unsteady state heat transfer analysis performed? Explain. a. Thermal conductivity lab (Determination of thermal conductivity of a food product). b. Heat exchanger lab (Determination of the overall heat transfer coefficient for a co-current and counter-current heat exchanger). c. Convective heat transfer coefficient lab (Determination of the convective heat transfer coefficient between a cylinder and air).

40. Can the Temperature Ratio (TR) = be greater than 1.0 for the case where

a. NBi < 0.1 (Lumped parameter analysis) b. NBi > 0.1 (Heisler chart) EXPLAIN your answer in both cases.

41. Can the be greater than 1.0 for:

a. Heating b. Cooling EXPLAIN your answer in both cases.

42. Detail the steps involved in determining the time taken for a product (" = 1.3 x 10-7 m2/s) at the center of a cylindrical can (r = 10 cm, L = 10 cm) initially at 10 /C to reach 25 /C if the surrounding fluid temperature is 80 /C. Neglect the resistance to heat transfer due to convection and also that due to the can.

43. Both the Nusselt number and Biot number are given by the expression “hdc/k”. How are they different? (Where or when are they used?)

44. Is the lumped parameter analysis more applicable to metals or insulators? EXPLAIN.

45. Is the lumped parameter analysis valid if the temperature of the surrounding fluid is not constant? Justify your answer. Hint: The starting point for the lumped parameter method is given by the following equation: 46. What is the characteristic dimension, dc, in the following situations? a. Forced convection in a vertical pipe b. Free convection outside a vertical cylinder c. Unsteady state heat transfer taking place on one side of a slab d. Unsteady state heat transfer taking place on both sides of a slab

47. What are the quantities represented in the Heisler chart? What are their units?

48. When does one use (NFo)?

49. When subjected to similar conditions, will the initial rate of cooling/heating of the center of an infinitely long cylinder be greater than or less than that for a finite cylinder of the same radius? Explain physically and mathematically.

50. Outline the procedure to determine the center temperature of a canned food at any given time during thermal processing.

51. Outline the procedure to determine the time it will take for the center temperature of a canned food product being thermally processed to reach a certain desired value.

52. a. What are the 3 modes of heat transfer? b. Explain how heat transfer takes place by each of these modes by giving an example

53. Explain the difference between steady state heat transfer and unsteady state heat transfer. Be specific as to what factors change (or do not change) as a function of what quantity.

54. Give an example of a situation where: a. Steady state conditions exist from a heat transfer standpoint b. Unsteady state conditions exist from a heat transfer standpoint c. Unsteady state conditions change to steady state conditions

55. In what specific category (or type) of heat transfer are the following quantities used? a. Biot number b. Reynolds number c. Grashof number d. Fourier number e. Nusselt number f. Prandtl number

56. For a situation involving convection on either side of a slab (of high thermal conductivity), draw the temperature profile in the surrounding fluids (one at 0 /C and the other at 100 /C)

and the slab when the convective heat transfer coefficient at the end exposed to 100 /C (h1) is much greater than the convective heat transfer coefficient at the other end (h2).