so far: conservation of mass and energy pressure drop in pipes flow measurement instruments

So Far:Conservation of Mass and EnergyPressure Drop in PipesFlow Measurement InstrumentsFlow Control (Valves) Types of Pumps and Pump Sizing

This Week:Energy Balance and Heat TransferConduction, Convection, RadiationHeat Exchangers

500 kg of grain (25C) is mixed with hot (80C) and cold (10C) 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 38C, how much hot and cold water should be added?

(Continued) A three step mashing process, with 20 minute-long rests at 50, 62 and 72C, is desired. The mash should be heated quickly, but not too quickly between rests; with an optimal rate of 1C 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.

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 energy required for the electric heaters, in kW-hr?

(f) If steam is used, what is the total mass of steam required, in kg?

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?

Heat Transfer EquipmentMash 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

Heat Transfer Equipment

Mash Mixer – External heating jacket

Steam in

Steam out

Wort


Mash Mixer – External heating jacket


Wort kettle – Internal calandria

Steam


Wort kettle – Internal calandria


Wort kettle – External calandria

Steam


Plate Heat Exchanger


Shell and tube heat exchanger

Heat TransferTransfer of energy from a high temperature to low temperature

Conservation of Energy

Ein – Eout = Esystem

Qin = m(u2 – u1) = mcv(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


Wort

H2O

0,,,, 22222 outOHinOHOHpOHOHin TTcmQ

0,,,, outwortinwortwortpwortwortout TTcmQ

0,,,,,, 2222 outOHinOHOHpOHoutwortinwortwortpwort TTcmTTcm


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

ConvectionOverall Heat Transfer Coefficient

For “thin walled” heat exchangers, Ai = Ao

totaltotal R

TTAUQ

kA

xRconduction

hARconvection

1

€

1

Ro=

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 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

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

so far: conservation of mass and energy pressure drop in pipes flow measurement instruments

Documents