Principles of Food and Bioprocess Engineering (FS 231) Short Answer Questions on Heat Transfer 1. Explain the following terms and explain when, why, and where are they used: a. Thermal conductivity (k) b. Convective heat transfer coefficient (h) c. Overall heat transfer coefficient (U) d. Thermal resistance e. Reynolds number (NRe) f. Nusselt number (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. Prandtl number (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. Grashof number (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 convection 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 heats 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.