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So Far: Conservation of Mass and Energy Pressure Drop in Pipes Flow Measurement Instruments

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 and Heat Transfer Conduction, Convection, Radiation Heat Exchangers.

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So Far: Conservation of Mass and Energy Pressure Drop in Pipes Flow Measurement Instruments

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  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 and Heat Transfer Conduction, Convection, Radiation Heat Exchangers

  2. 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?

  3. (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.

  4. 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 the total energyrequired for the electric heaters, in kW-hr? (f) If steam is used, what is the total mass of steam required, in kg?

  5. At the location of our brewery, electricity costs $0.14/kW-hr and the steam can be generated for $0.03 per kg. Each day, the system is cleaned for one hour and the time between batches is very small. The system operates 7 days per week. (g) What is the mashing cost, per month, when electric resistance heaters are used? (h) What is the monthly cost with steam?

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

  7. Heat Transfer Equipment Mash Mixer – External heating jacket Steam in Wort Steam out

  8. Heat Transfer Equipment Mash Mixer – External heating jacket

  9. Heat Transfer Equipment Wort kettle – Internal calandria Steam

  10. Heat Transfer Equipment Wort kettle – Internal calandria

  11. Heat Transfer Equipment Wort kettle – External calandria Steam

  12. Heat Transfer Equipment Plate Heat Exchanger

  13. Heat Transfer Equipment Plate Heat Exchanger

  14. Heat Transfer Equipment Shell and tube heat exchanger

  15. Heat Transfer Transfer of energy from a high temperature to low temperature Conservation of Energy Ein – Eout = Esystem Qin = m(u2 – u1) = mcv(T2-T1) Wort Qin

  16. Heat Transfer Rate of Ein – Rate of Eout = 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/m3 and specific heat of 4.0 kJ/kg.K. Qout min Wort

  17. Heat Transfer Rate of Ein – Rate of Eout = Rate of E Accumulation H2O Wort

  18. Heat Transfer Rate of Ein – Rate of Eout = 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. H2O Wort

  19. Conduction Transfer of microscopic kinetic energy from one molecule to another 1-D Heat Transfer, Fourier Equation: or A 0.5 m2, 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.

  20. 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? What is the temperature at the interface of the stainless steel and insulation? Draw the temperature profile of the system.

  21. Conduction Hollow cylinders (pipes) 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. Determine the rate of heat loss from the pipe. r1 r2

  22. Convection Transfer of heat due to a moving fluid Natural convection – buoyant forces drive flow Forced convection – mechanical forces drive flow Fluid Wall Tfluid Temperature Twall

  23. Convection Overall Heat Transfer Coefficient For “thin walled” heat exchangers, Ai = Ao

  24. 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/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. The diameter of the pipe is 4.0 cm.

  25. Convection Condensation Constant temperature process Occurs when a saturated comes in contact with a surface with temperature below Tsat for the vapor Film coefficients: 5,000-20,000 W/m2.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.

  26. 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:

  27. 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.

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

  29. 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.

  30. Fouling Layers of dirt, particles, biological growth, etc. effect resistance to heat transfer We cannot predict fouling factors well 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

  31. 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/m2.K and 800 W/m2.K, respectively. The fouling factors on the product and coolant sides are 0.0008 and 0.00001 m2K/W. Assume that the heat exchanger is thin walled. • Determine the heat transfer rate • Determine the LMTD • Determine the overall heat transfer coefficient • Determine the outside area required • Determine the length of tube required

  32. 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

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