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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: Heat Transfer Energy Balance Example The power goes out at your brewery due to an overheated transformer, shutting down your fermentation cooling mechanism. Consider a 25 m3 cylindroconical vessel that is full with a product at 10oC, specific heat of 3.4 kJ/kg.K, and density of 1025 kg/m3. Assuming that the sum of heat gains from the surroundings and conversion from fermentation is 7 kW, determine the temperature after 4 hours. How would the 7 kW load change over time? 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 Pasteurisers – Plate heat exchangers, Tunnel Refrigeration equipment – Shell and tube heat exchangers, evaporative condensers Steam and hot water equipment – Shell and tube Heat Transfer Equipment Steam in Wort Steam out Mash Tun – External heating jacket Heat Transfer Equipment Mash Tun – External heating jacket Heat Transfer Equipment Steam Wort kettle – Internal calandria Heat Transfer Equipment Steam Wort kettle – External calandria Heat Transfer Equipment Wort kettle – Internal calandria Heat Transfer Equipment Plate Heat Exchanger Heat Transfer Equipment Plate Heat Exchanger Heat Transfer Equipment Shell and tube heat exchanger Heat Transfer Equipment Watch Peppermill Hotel and Casino Heat Exchanger Video Heat Transfer Transfer of energy from a high temperature to low temperature Conservation of Energy Ein – Eout = Esystem Qin = m(u2 – u1) = mc(T2-T1) Qin Wort Heat Transfer Rate of Ein – Rate of Eout = Rate of E Accumulation Qout Q out m ( hin h out ) 0 Q out m c p T in T out min Wort Calculate the rate of heat transfer required to cool 100 L/min of wort from 85 to 25C. The wort has a density of 975 kg/m3 and specific heat of 4.0 kJ/kg.K. Heat Transfer Rate of Ein – Rate of Eout = Rate of E Accumulation H2O Wort Q in , H 2O m H c p,H O O 2 2 T H O ,in T H O , out 0 2 2 Q out , wort m wort c p , wort T wort , in T wort , out 0 m wort c p , wort T wort , in T wort , out m H 2O c p,H 2O T H 2 O , in TH 2 O , out 0 Heat Transfer Rate of Ein – Rate of Eout = Rate of E Accumulation H2O Wort Wort is being cooled with chilled water in a heat exchanger. The wort enters at 85C with a flow rate of 100 L/min and it exits the heat exchanger at 25C. The chilled water enters at 5C 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. Conduction Transfer of microscopic kinetic energy from one molecule to another 1-D Heat Transfer, Fourier Equation: T Q kA x or T Q R R x kA A 0.5 m2, 1.75 cm thick stainless steel plate (k = 50 W/m.K) has surface temperatures of 22.5 and 20C. Calculate the rate of heat transfer through the plate. Conduction Same equations apply for multi-layer systems 1-D Heat Transfer, Fourier Equation: Q T R Total R Total x1 k1 A x2 k2 A x3 ... k3 A 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. Conduction Hollow cylinders (pipes) r1 R Total r2 x kA m Am r2 r1 2 L r2 ln r1 A 3 cm diameter, 15 m long pipe carries hot wort at 85C. The pipe has 1.0 cm thick insulation, which has thermal conductivity of 0.08 W/m.K. The insulation exterior surface temperature is 35C. Determine the rate of heat loss from the pipe. Convection Transfer of heat due to a moving fluid Natural convection – buoyant forces drive flow Temperature Forced convection – mechanical forces drive flow Fluid Wall Tfluid Twall Q convection hA T fluid T wall Heat Transfer Overall Heat Transfer Coefficient QÝ U o A T R conduction x T R total R convection kA 1 hA For “thin walled” heat exchangers, Ai = Ao 1 Uo 1 h outside x kw 1 h inside Convection A tube-in-tube heat exchanger carries hot wort at 85C in the inner tube and chilled water at 5C 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. 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. Radiation Vibrating atoms within substance give off photons Energy Radiated T 4 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: Q surf A surf T surf 4 T surr 4 Radiation Sometimes, we’ll make an analogy to convection T T Q h A rad rad surf surf surr A 3 cm diameter, 15 m long pipe carries hot wort at 85C. The pipe has 1.0 cm thick insulation, which has thermal conductivity of 0.08 W/m.K. The insulation exterior surface temperature is 35C and its emissivity is 0.85. The temperature of the surroundings is 20C. Determine the rate of heat loss by radiation. T1 T T2 Length Temperature Temperature Log Mean Temperature Difference Parallel Flow Counter Flow T1 T T2 Length Log Mean Temperature Difference Tm T1 T 2 ln T1 T2 A tube-in-tube, counterflow heat exchanger carries hot wort at 85C in the inner tube and chilled water at 5C 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. Fouling Layers of dirt, particles, biological growth, etc. effect resistance to heat transfer 1 U o , dirty 1 Uo Ro Ri 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 Heat Exchanger Sizing Beer, dispensed at a rate of 0.03 kg/s, is chilled in an ice bath from 18C to 8C. 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. 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 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