so far: conservation of mass and energy pressure drop in pipes flow measurement instruments
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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: Short Course in Thermodynamics - Energy Balance, Steam Heat Transfer. Energy Balance Example - PowerPoint PPT PresentationTRANSCRIPT
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So Far:Conservation of Mass and EnergyPressure Drop in PipesFlow Measurement InstrumentsFlow Control (Valves) Types of Pumps and Pump Sizing
This Week:Short Course in Thermodynamics
- Energy Balance, SteamHeat Transfer
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Energy Balance ExampleThe 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?
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Energy Balance Example
Water at 20oC and 15 kg/s is mixed with water at 80oC and 25 kg/s. This mixture then passes through a cooler, which decreases it’s temperature to 34oC.Determine:
a. the temperature after mixingb. rate of heat transfer in the cooler
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Heat Transfer EquipmentMash Tun – External heating jacketKettle – External jackets/panels, internal coils, internal or external calandriaWort cooler – Plate heat exchangerFermenter – Internal or external coils or panelsPasteurisers – Plate heat exchangers, TunnelRefrigeration equipment – Shell and tube heat exchangers, evaporative condensersSteam and hot water equipment – Shell and tube
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Heat Transfer Equipment
Mash Tun – External heating jacket
Steam in
Steam out
Wort
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Heat Transfer Equipment
Mash Tun – External heating jacket
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Heat Transfer Equipment
Wort kettle – Internal calandria
Steam
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Heat Transfer Equipment
Wort kettle – External calandria
Steam
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Heat Transfer Equipment
Wort kettle – Internal calandria
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Heat Transfer Equipment
Plate Heat Exchanger
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Heat Transfer Equipment
Plate Heat Exchanger
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Heat Transfer Equipment
Shell and tube heat exchanger
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Heat Transfer Equipment
Watch Peppermill Hotel and Casino Heat Exchanger Video
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Heat TransferTransfer of energy from a high temperature to low temperature
Conservation of EnergyEin – Eout = Esystem
Qin = m(u2 – u1) = mc(T2-T1)
WortQin
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Heat TransferRate 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 25C. The wort has a density of 975 kg/m3 and specific heat of 4.0 kJ/kg.K.
Wort
Qout
min
0)( outinout hhmQ
outinpout TTcmQ
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Heat TransferRate of Ein – Rate of Eout = Rate of E Accumulation
WortH2O
0,,,, 22222 outOHinOHOHpOHOHin TTcmQ
0,,,, outwortinwortwortpwortwortout TTcmQ
0,,,,,, 2222 outOHinOHOHpOHoutwortinwortwortpwort TTcmTTcm
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Heat TransferRate of Ein – Rate of Eout = Rate of E Accumulation
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 3.5 and 4.2 kJ/kg.K Determine the exit temperature of the chilled water.
WortH2O
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ConductionTransfer of microscopic kinetic energy from one
molecule to another1-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 20C. Calculate the rate of heat transfer through the plate.
xTkAQ
RTQ
kAxR
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ConductionSame equations apply for multi-layer systems1-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.
TotalRTQ
...3
3
2
2
1
1 Akx
Akx
Akx
RTotal
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ConductionHollow cylinders (pipes)
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.
mTotal kA
xR
r2
r1
1
2
12
ln2
rrrr
LAm
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ConvectionTransfer of heat due to a moving fluidNatural convection – buoyant forces drive flowForced convection – mechanical forces drive flow
Tem
pera
ture
Tfluid
Twall
Fluid Wall
wallfluidconvection TThAQ
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Heat TransferOverall Heat Transfer Coefficient
For “thin walled” heat exchangers, Ai = Ao
totaltotal R
TTAUQ
kAxRconduction hA
Rconvection1
€
1Uo
= 1houtside
+ xkw
+ 1hinside
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ConvectionA 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.
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ConvectionCondensation
Constant temperature processOccurs when a saturated comes in contact with a surface with temperature below Tsat
for the vaporFilm coefficients: 5,000-20,000 W/m2.K
BoilingConstant temperature processSome surface roughness promotes boilingBubbles rise – significant natural convectionFraction of surface “wetted” effects QFig 9, page 114 in Kunze.
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RadiationVibrating atoms within substance give off photons
Emissivity of common substancesPolished aluminum: 0.04Stainless steel: 0.60Brick: 0.93Water: 0.95Snow: 1.00
Radiation between surface and surroundings:
4T RadiatedEnergy
4surr
4surf TT Q surfsurf A
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RadiationSometimes, we’ll make an analogy to convection
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.
surrsurfrad TT Q surfrad Ah
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Log Mean Temperature DifferenceParallel Flow Counter Flow
Length
Tem
pera
ture
T1 T T2
Length
Tem
pera
ture T1
TT2
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Log Mean Temperature Difference
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.
2
1
21
lnTTTT
Tm
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FoulingLayers of dirt, particles, biological growth, etc. effect resistance to heat transfer
We cannot predict fouling factors analyticallyAllow for fouling factors when sizing heat transfer
equipmentHistorical information from similar applicationsLittle fouling in water side, more on productTypical values for film coefficient, p. 122
ioodirtyo
RRUU
11
,
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Heat Exchanger SizingBeer, 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 rateb. Determine the LMTDc. Determine the overall heat transfer coefficientd. Determine the outside area requirede. Determine the length of tube required
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Heat LossesTotal Heat Loss = Convection + RadiationPreventing heat loss, insulation
Air – low thermal conductivityAir, goodWater – relatively high thermal conductivityWater, badVessels/pipes above ambient temperature – open pore structure to allow water vapor outVessels/pipes below ambient temperature - closed pore structure to avoid condensation