Heat Transfer Equations

For “thin walled” tubes, Ai = Ao

€

˙ Q = UoAΔTm

€

1

Uo

=1

houtside

+x

kw

+1

hinside

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

ioodirtyo

RRUU

11

,

Log Mean Temperature Difference

For Round, Thin-Walled Tubes

2

1

21

lnT

TTT

Tm

1

2

12

ln2

r

rrr

LAm

Log Mean Temperature Difference

Parallel Flow Counter Flow

Length

Tem

pera

ture

T1 T T2

Length

Tem

pera

ture T1

TT2

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

Heat Transfer – Continued

Hot wort at 95C is transferred from one tank to another through a 2.5 cm diameter stainless steel pipe (k = 120 W/m.K, wall thickness 0.1 mm). The pipework is 150 m long and the wort has specific heat capacity of 4.0 kJ/kg.K and density of 975 kg/m3. The heat transfer coefficients on the inside and outside of the pipe are 4000 W/m2K and 125 W/m2K and the temperature of the surroundings is 10C. Assume that the pipe’s wall is “thin.” Approximate the rate of heat loss from the pipe and the exit temperature at the end of the pipe. The velocity in the pipe is 1.0 m/s.

Heat Transfer – ContinuedPrevious Problem continued…

How would adding a 1 cm thick layer of insulation (k = 0.05 W/m.K) to the outer surface of the pipe effect the exit temperature of the wort.

Our pipe has an external emissivity of 0.7. Calculate the heat loss by radiation (without insulation) and compare it to the heat loss by convection.

Refrigeration Terms

• Cooling Load, Cooling Capacity – Qin

• Compressor Load – Win

• Condenser Load – Qout

• Tons of Refrigeration – Rate of Heat Input

• Refrigerant – The Fluid

• Vapor-Compression Refrigeration

• Heat Pump – Same Cycle, Use Qout

Refrigeration

Efficiency = desired output / required input

Desired output = Heat removal from refrigerated space (Qin)

Required input = Work input to compressor

Conservation of Energy: Qin + Win = Qout

COP can be > 1.0

= Cooling Capacity

in

in

W

QCOP

inQ

Refrigeration

• Used when no other method of cooling is available

• Very expensive (40-60% of a brewery’s utility bill)

• Removal of heat from low T source to high T sink

Primary RefrigerantsAmmonia (R-717), R-12, R-134aSaturation temp < Desired application temp

2 to 8C Maturation tanks0 to 1C Beer Chillers-15 to -20C CO2 liquefaction

Typically confined to small region of brewery

Secondary RefrigerantsWater with alcohol or salt solutionsMethanol/glycol, potassium carbonate, NaClLower freezing temperature of waterLow-toxicity (heat exchange with product)Pumped long distances across brewery

Theory and the Cycle

Condenser

Evaporator

Compressor

Qout

Qin

Win

1

23

4

Refrigeration

Applying Conservation of Energy…

12

41

21

32

14

0)(

0)(

0)(

hh

hhCOP

hhmW

hhmQ

hhmQ

in

out

in

Refrigeration1-2: Constant entropy compression (s1 = s2)2-3: Constant pressure heat rejection (3 = sat liq.)3-4: Constant enthalpy throttling4-1: Constant pressure heat addition (1 = sat vap.)

Coefficient of Performance

• Describes how well a refrigeration plant is running

• Heat removed divided by energy input• COP increase with temperature

difference between source and sink

€

COP =Qe

Wc

=h1 − h4

h2 − h1

Typical Manufacturers Performance Curves

Chemical structure of refrigerants

Refrigerant R12, CF2Cl2

Dry Air Fin Condensers• Fluid in condenser does not contact

cooling fluid• High electricity costs for fans

Wet Evaporative Condensers• Fluid in condenser does not contact

cooling fluid• Water sprayed onto tubes to evaporate

and cool

Cooling Tower Condensers• A secondary fluid (water) sprayed• Air passes across water droplets, cools• Forced or induced draft, counter or cross• Cool water to heat exchange condenser

Condenser Selection Considerations• Ambient temperature (Air-fin?)• Ambient humidity (evaporation?)• Space, accessibility, maintenance• Electricity costs (air-fin)• Chemical costs (evaporative, tower)

Legionellosis or L. pneumophila• Major source cooling towers and

evaporative coolers• Name from 1976 meeting of American

Legion – killed 36 people• Kill by heating to 60oC or chlorine

Evaporators and Expansion Devices• Direct expansion with thermostat valve• Regulates flow of liquid being throttled

into evaporator• Diaphragm to balance pressure between

liquid in condenser and sum of evaporator and spring pressure

Evaporators and Expansion Devices• Flooded with level control• Level of liquid in reservoir (typically shell

and tube heat exchanger) controlled with variable throttle valve.

Refrigeration Example

An ideal vapor-compression refrigeration cycle using ammonia operates between the pressures of 2 and 14 bar. The system cools a secondary refrigerant at a rate of 25 kW. Determine:

• The evaporator and condenser temperatures

• The mass flow rate of refrigerant.

• The COP of the system.

• The power consumed by the compressor, in kW