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Basic Design Methods of Heat Exchangers
Arrangement of Flow Paths in Heat Exchangers
Heat exchanger classification according to flow arrangements.
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Multi-pass flow arrangements
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Basic Equations in Design
heat transfer rate to the fluid
concerned associated
specific enthalpy
outlet inlet
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1 and 2 designate the fluid inlet and outlet conditions
h and c refer to the hot and cold fluids 4
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Basic Equations in Design
Fluid temperature variation in parallel-
flow, counter flow, evaporator, and
condenser heat exchangers:
(a) counter flow;
(b) parallel flow;
(c) cold fluid evaporating at constant
temperature;
(d) hot fluid condensing at constant
temperature.
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A is the total hot-side or cold-side heat transfer area
ΔTm is a function of Th1, Th2, Tc1, and Tc2
U is the average overall heat transfer coefficient based on that area
Rt is the total thermal resistance t is the thickness of the wall
hi and ho are heat transfer coefficients for inside and outside flows
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Rw The wall resistance
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overall Heat Transfer Coefficient
Finned wall.
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Ao and Ai represent the total
surface area of the outer and
inner surfaces
δ is the fin thickness and L is the fin length
If a straight or pin fin of length L and uniform cross section is used and an adiabatic tip is
assumed, then the fin efficiency is given by:
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For the un-finned tubular heat exchangers:
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for adiabatic, steady-state, steady flow, the energy balance yields
Ch and Cc are the hot- and cold-fluid heat capacity rates
+ and – signs correspond to parallel- and counter flow
Heat transfer area dA may also be expressed as:
for counter flow
LMTD Method for Heat Exchanger Analysis
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which, when integrated with constant values of U, Ch, and Cc over the entire length of the heat
exchangers, results in
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It can be shown that for a parallel-flow heat exchanger
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ΔT1 is the temperature difference between the two fluids at one end of the heat exchanger
and ΔT2 is the temperature difference of the fluids at the other end of the heat exchanger.
Parallel flow Counter flow 17
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ΔTm is the true (or effective)
mean temperature difference
and
ΔTlm,cf is the LMTD for a
counter flow arrangement
P is the temperature effectiveness of the heat
exchanger on the cold-fluid side.
R is the ratio of the (mcp) value of the cold
fluid to that of the hot fluid
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Parallel and Counter flow Heat exchangers
Temperature variation for a counter flow heat exchanger.
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LMTD correction factor F for a shell-and-tube heat exchanger with one shell pass and two or a
multiple of two tube passes.
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LMTD correction factor F for a shell-and-tube heat exchanger with two shell passes and
four or a multiple of four tube passes
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LMTD correction factor F for a shell-and-tube heat exchanger with three two-shell
passes and six or more even number tube passes.
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LMTD correction factor F for a divided-flow shell-type heat exchanger with one divided
flow shell pass and an even number of tube passes
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LMTD correction factor F for a split-flow shell-type heat exchanger with one split-
flow shell pass and two-tube passes.
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Temperature distribution in a crossflow heat exchanger
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LMTD correction factor F for a crossflow heat exchanger
with both fluids unmixed
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LMTD correction factor F for a single-pass crossflow heat exchanger with
one fluid mixed and the other unmixed.
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Slide 25
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Slide 26
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Slide 31
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Slide 25
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Slide 26
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The ε-NTU Method for Heat Exchanger Analysis
where Cmin and Cmax are the smaller and larger of the two
magnitudes of Ch and Cc, respectively, and C* ≤ 1. C* = 0
corresponds to a finite Cmin and Cmax approaching ∞ (a
condensing or evaporating fluid).
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The ε-NTU Method for Heat Exchanger Analysis
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The ε-NTU Method for Heat Exchanger Analysis
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The ε-NTU Method for Heat Exchanger Analysis
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+ is for counter flow and the – is for parallel flow. 47
The ε-NTU Method for Heat Exchanger Analysis
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The ε-NTU Method for Heat Exchanger Analysis
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The ε-NTU Method for Heat Exchanger Analysis
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The ε-NTU Method for Heat Exchanger Analysis
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The ε-NTU Method for Heat Exchanger Analysis
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Effectiveness vs. NTU for various types of heat exchangers
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Effectiveness vs. NTU for various types of heat exchangers.
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Slide 25
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Now calculate NTU either from the formula of Slide 51 or 52-54 with a proper
interpretation for ε, NTU, and C*. From slide 51 for a 1 to 2 shell-and-tube heat
exchanger, we have
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Heat exchanger design
methodology.
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