1. So Far: Conservation of Mass and Energy Pressure Drop in Pipes Flow Measurement Instruments Flow Control (Valves) Types of Pumps and Pump Sizing This Week: Energy Balance Heat Transfer

2. Conservation of Energy For steady flow systems Energy = Heat (Q), Work (W), mass (h) No Phase Change, E = m c ΔT Phase Change, E = m h fg where h fg = enthalpy of vaporization or fusion

3. A 2 m 3 water tank is filled with 1.25 m 3 of hot water at 80  C and 0.75 m 3 of cold water at 10  C. Assume that the specific heat of water is 4.2 kJ/kg.K. a) Determine the temperature in the tank after it has been filled. b) How much heat must be added to the tank to bring its temperature to 65  C? c) If a 30 kW electric heater is used, how long will the heating process take?

4. 500 kg of grain (25  C) is mixed with hot (80  C) and cold (10  C) water for mashing. The water to grain ratio (by weight) is 3:1 and the specific heat capacities of the water and grain are 4.2 and 1.7 kJ/kg.K, respectively. a) If the desired “mash in” temperature is 38  C, how much hot and cold water should be added?

5. (Continued) A three step mashing process, with 20 minute-long rests at 50, 62 and 72  C, is desired. The mash should be heated quickly, but not too quickly between rests; with an optimal rate of 1  C per minute. Neglect heat losses to the surroundings. b) Plot the mash temperature vs. time. c) Determine the heating power required, in kW. d) Determine the total heat required for the mashing process, in kJ.

6. Two types of heat sources are available for mashing, electric resistance heaters and steam. The steam enters a heating jacket around the mash as dry, saturated steam at 300 kPa and it exits the system as wet, saturated steam at the same pressure (enthalpy of vaporization = 2150 kJ/kg). (e) What is steam flow rate required, in kg/s? (f) If steam is used, what is the total mass of steam required, in kg?

7. At the location of our brewery, electricity costs $0.14/kW-hr and the steam can be generated for $0.03 per kg. (g) What is the mashing cost when electric resistance heaters are used? (h) What is the cost with steam?

8. Energy Balance Example The power goes out at your brewery due to an overheated transformer, shutting down your fermentation cooling mechanism. Consider a 25 m 3 cylindroconical vessel that is full with a product at 10 o C, specific heat of 3.8 kJ/kg.K, and density of 1025 kg/m 3. Assuming that the sum of heat gains from the surroundings and conversion from fermentation is 7 kW, determine the temperature after 8 hours. How would the 7 kW load change over time?

9. Heat Transfer Equipment Mash Tun – External heating jacket Kettle – External jackets/panels, internal coils, internal or external calandria Wort cooler – Plate heat exchanger Fermenter – Internal or external coils or panels Pasteurizers – Plate heat exchangers, Tunnel Refrigeration equipment – Shell and tube heat exchangers, evaporative condensers Steam and hot water equipment – Shell and tube

10. Heat Transfer Equipment Mash Tun – External heating jacket Steam in Steam out Wort

11. Heat Transfer Equipment Mash Tun – External heating jacket

12. Heat Transfer Equipment Wort kettle – Internal calandria Steam

13. Heat Transfer Equipment Wort kettle – External calandria Steam

14. Heat Transfer Equipment Wort kettle – Internal calandria

16. Heat Transfer Equipment Plate Heat Exchanger

17. Heat Transfer Equipment Plate Heat Exchanger

18. Heat Transfer Equipment Shell and tube heat exchanger

19. Heat Transfer Transfer of energy from a high temperature to low temperature Conservation of Energy E in – E out =  E system Q in = m(u 2 – u 1 ) = mc(T 2 -T 1 ) Wort Q in

20. Heat Transfer Rate of E in – Rate of E out = Rate of E Accumulation Calculate the rate of heat transfer required to cool 100 L/min of wort from 85 to 25  C. The wort has a density of 975 kg/m 3 and specific heat of 4.0 kJ/kg.K. Wort Q out m in

21. Heat Transfer Rate of E in – Rate of E out = Rate of E Accumulation Wort H2OH2O

22. Heat Transfer Rate of E in – Rate of E out = Rate of E Accumulation Wort is being cooled with chilled water in a heat exchanger. The wort enters at 85  C with a flow rate of 100 L/min and it exits the heat exchanger at 25  C. The chilled water enters at 5  C with a flow rate of 175 L/min. The specific heat of the wort and water are 4.0 and 4.2 kJ/kg.K Determine the exit temperature of the chilled water. Wort H2OH2O

23. Conduction Transfer of microscopic kinetic energy from one molecule to another 1-D Heat Transfer, Fourier Equation: A 0.5 m 2, 1.75 cm thick stainless steel plate (k = 50 W/m.K) has surface temperatures of 22.5 and 20  C. Calculate the rate of heat transfer through the plate.

24. Conduction Same equations apply for multi-layer systems 1-D Heat Transfer, Fourier Equation: How would the rate of heat transfer change if a 2.5 cm thick layer of insulation (k = 0.05 W/m.K) were added to the “low” temperature side of the plate?

25. Convection Transfer of heat due to a moving fluid Natural convection – buoyant forces drive flow Forced convection – mechanical forces drive flow Temperature T fluid T wall FluidWall

26. Heat Transfer Overall Heat Transfer Coefficient For “thin walled” heat exchangers, A i = A o

27. Convection A tube-in-tube heat exchanger carries hot wort at 85  C in the inner tube and chilled water at 5  C in the outer tube. The tube wall thickness is 4 mm and its thermal conductivity is 100 W/m.K. The wort film coefficient is 750 W/m 2.K and the chilled water film coefficient is 3000 W/m 2 K. Determine the overall heat transfer coefficient and the rate of heat transfer per meter of heat exchanger length. The diameter of the pipe is 4.0 cm.

28. Convection Condensation Constant temperature process Occurs when a saturated comes in contact with a surface with temperature below T sat for the vapor Film coefficients: 5,000-20,000 W/m 2.K Boiling Constant temperature process Some surface roughness promotes boiling Bubbles rise – significant natural convection Fraction of surface “wetted” effects Q Fig 9, page 114 in Kunze.

29. Log Mean Temperature Difference Parallel FlowCounter Flow Length Temperature T1T1 TT T2T2 Length Temperature T1T1 TT T2T2

30. Log Mean Temperature Difference A tube-in-tube, counterflow heat exchanger carries hot wort at 85  C in the inner tube and chilled water at 5  C in the outer tube. The tube wall thickness is 4 mm and its thermal conductivity is 100 W/m.K. The wort film coefficient is 750 W/m2.K and the chilled water film coefficient is 3000 W/m2K. Determine the overall heat transfer coefficient and the rate of heat transfer per meter of heat exchanger length. Calculate the LMTD.

31. Fouling Layers of dirt, particles, biological growth, etc. effect resistance to heat transfer We cannot predict fouling factors analytically Allow for fouling factors when sizing heat transfer equipment Historical information from similar applications Little fouling in water side, more on product Typical values for film coefficient, p. 122

32. Heat Exchanger Sizing Beer, dispensed at a rate of 0.03 kg/s, is chilled in an ice bath from 18  C to 8  C. The beer flows through a stainless steel cooling coil with a 10 mm o.d., 9 mm i.d., and thermal conductivity of 100 W/m.K. The specific heat of the beer is 4.2 kJ/kg.K and the film heat transfer coefficients on the product and coolant sides are 5000 W/m 2.K and 800 W/m 2. K, respectively. The fouling factors on the product and coolant sides are 0.0008 and 0.00001 m 2 K/W. Assume that the heat exchanger is thin walled. a. Determine the heat transfer rate b. Determine the LMTD c. Determine the overall heat transfer coefficient d. Determine the outside area required e. Determine the length of tube required

33. Radiation Vibrating atoms within substance give off photons Emissivity of common substances Polished aluminum: 0.04 Stainless steel:0.60 Brick:0.93 Water:0.95 Snow:1.00 Radiation between surface and surroundings:

34. Radiation Sometimes, we’ll make an analogy to convection A 3 cm diameter, 15 m long pipe carries hot wort at 85  C. The pipe has 1.0 cm thick insulation, which has thermal conductivity of 0.08 W/m.K. The insulation exterior surface temperature is 35  C and its emissivity is 0.85. The temperature of the surroundings is 20  C. Determine the rate of heat loss by radiation.

35. Heat Losses Total Heat Loss = Convection + Radiation Preventing heat loss, insulation Air – low thermal conductivity Air, good Water – relatively high thermal conductivity Water, bad Vessels/pipes above ambient temperature – open pore structure to allow water vapor out Vessels/pipes below ambient temperature - closed pore structure to avoid condensation

36. Conduction Hollow cylinders (pipes) r2r2 r1r1