Heat Exchanger Notes

Heat Exchangers ME 430

ε

Heat Exchanger Performance The performance of heat exchangers operating under forced flow conditions is defined by the amount of heat transferred between the two fluid streams and is characterized by the UA value or the dimensionless factors: the effectiveness,ε, or number of transfer units (NTU’s), and the capacity ratio,Cr,

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Heat Exchangers

Plate Style

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Solar Water Heating

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Okotoks Solar Seasonal Storage and District Loop Simplified Schematic Glycol / Water Heat Exchanger

District Heating Loop Central Plant Outline Located on MR

Detached Garages with Solar Collector roofs

Underground Thermal Storage Located Beneath MR

Two Story Single Family Homes

District Heating Loop (Below Grade) Connects to Homes in Community

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Okotoks – Energy Delivery

Bore Hole Storage

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0

10

20

30

40

50

60 60 55

-10 50 45 -20

40 35 30

-30

25 20 -40

15 10

-50

5

-60

-70

-80

Energy Balance the rate of heat transfer between the two fluid streams in the heat exchanger, Q, is,

m& c

m& s

Tci

Tso

& p ) s (Tso − Tsi ) = (mc & p ) c (Tci − Tco ) Q = ( mc Q Q=0

Q=0 Q

& p is the heat where mc capacity rate of one of the fluid streams.

m& c

m& s

Tco

Tsi

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Simple Configurations

Heat transfer through a wall Q = qx A and Q = UA (∆T) U = (1/h1 + Rwall +1/h2)-1

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Simple Configurations for Tube & Shell

Q = UA (∆T) Need to determine ∆T. This is not straightforward as for the parallel flow case.

UA –Value & LMTD The unit’s overall conductance or UA value is defined as the product of the overall heat transfer coefficient and the heat transfer area. For counter-flow applications, the heat transfer rate is defined as the product of overall conductance and the log-mean temperature difference, LMTD, i.e.,

Q = UA ⋅ LMTD

where the log-mean temperature difference is equal to,

LMTD =

∆Tout − ∆Tin ⎛ ∆T ⎞ ln ⎜ out ⎟ ⎝ ∆Tin ⎠

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Parallel Flow Q = UA ⋅ LMTD LMTD =

∆Tout − ∆Tin ⎛ ∆T ⎞ ln ⎜ out ⎟ ⎝ ∆Tin ⎠

Counter Flow Q = UA ⋅ LMTD LMTD =

∆Tout − ∆Tin ⎛ ∆T ⎞ ln ⎜ out ⎟ ⎝ ∆Tin ⎠

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From “Heat Transfer”, By Y. Cengel

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Effectiveness The heat exchanger effectiveness, ε, is defined as the ratio of the rate of heat transfer in the exchanger, Q, to the maximum theoretical rate of heat transfer, Qmax , i.e.,

ε=

Q Qmax

The maximum theoretical rate of heat transfer is limited by the fluid stream with the smallest heat capacity rate, i.e.

ε=

& p ) s (Tso − Tsi ) (mc

& p ) min (Tci − Tsi ) (mc

m& c

m& s

Tci

Tso

Q Q=0

Q=0 Q

m& c

m& s

Tco

Tsi

& p ) min the is the smaller of (mc & p )c . & p ) s or (mc where (mc

NTU The number of transfer units (NTU) is an indicator of the actual heat-transfer area or physical size of the heat exchanger. The larger the value of NTU, the closer the unit is to its thermodynamic limit. It is defined as,

NTU =

UA & p ) min (mc

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Capacity Ratio The capacity ratio, Cr, is representative of the operational condition of a given heat exchanger and will vary depending on the geometry and flow configuration (parallel flow, counterflow, cross flow, etc.) of the exchanger. This value is defined as the minimum heat capacity rate divided by the maximum capacity rate, i.e.,

Cr =

& p ) min (mc & p ) max (mc

It is important to note that the capacity ratio will be directly proportional to the ratio of the mass flow rates if the specific heats of the flows are fairly constant.

Effects of Capacity Ratio and NTU on Effectiveness

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Effectiveness Relations

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NTU Relations

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Refrigeration

Examples Other Types Heat Pipe Rotary ILC Enthalpy Wheel

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Heat Pipe

Enthalpy Wheel The heart of the Energy Recovery Ventilator is the desiccant coated energy recovery wheel, which slowly rotates between its two sections. In one section, the stale, conditioned air is passed through the wheel, and exhausted in the atmosphere. During this process, the wheel absorbs sensible and latent energy from the conditioned air, which is used to condition (cool / heat) the incoming Fresh Air in the other section, during the second half of its rotation cycle.

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