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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:Heat Transfer
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?
Heat Transfer EquipmentMash 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 TransferTransfer of energy from a high temperature to low temperature
Conservation of Energy
Ein – Eout = Esystem
Qin = m(u2 – u1) = mc(T2-T1)
WortQin
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
Heat TransferRate of Ein – Rate of Eout = Rate of E Accumulation
Wort
H2O
0,,,, 22222 outOHinOHOHpOHOHin TTcmQ
0,,,, outwortinwortwortpwortwortout TTcmQ
0,,,,,, 2222 outOHinOHOHpOHoutwortinwortwortpwort TTcmTTcm
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 4.0 and 4.2 kJ/kg.K Determine the exit temperature of the chilled water.
Wort
H2O
ConductionTransfer 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 20C. Calculate the rate of heat transfer through the plate.
x
TkAQ
R
TQ
kA
xR
ConductionSame 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.
TotalR
TQ
...
3
3
2
2
1
1 Ak
x
Ak
x
Ak
xRTotal
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
r
rrr
LAm
ConvectionTransfer of heat due to a moving fluid
Natural convection – buoyant forces drive flow
Forced convection – mechanical forces drive flowTe
mpe
ratu
re
Tfluid
Twall
Fluid Wall
wallfluidconvection TThAQ
Heat TransferOverall Heat Transfer Coefficient
For “thin walled” heat exchangers, Ai = Ao€
˙ Q = UoAΔT =ΔT
Rtotal
kA
xRconduction
hARconvection
1
€
1
Uo
=1
houtside
+x
kw
+1
hinside
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.
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.
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
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
Log Mean Temperature Difference
Parallel Flow Counter Flow
Length
Tem
pera
ture
T1 T T2
Length
Tem
pera
ture T1
TT2
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
lnT
TTT
Tm
FoulingLayers 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
ioodirtyo
RRUU
11
,
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 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 LossesTotal 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