basic design methods of heat exchangers arrangement of

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Basic Design Methods of Heat Exchangers

Arrangement of Flow Paths in Heat Exchangers

Heat exchanger classification according to flow arrangements.

Multi-pass flow arrangements

Basic Equations in Design

heat transfer rate to the fluid

concerned associated

specific enthalpy

outlet inlet

1 and 2 designate the fluid inlet and outlet conditions

h and c refer to the hot and cold fluids 4

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.

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

Rw The wall resistance

overall Heat Transfer Coefficient

Finned wall.

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:

For the un-finned tubular heat exchangers:

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

which, when integrated with constant values of U, Ch, and Cc over the entire length of the heat

exchangers, results in

It can be shown that for a parallel-flow heat exchanger

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

ΔTm is the true (or effective)

mean temperature difference

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

Parallel and Counter flow Heat exchangers

Temperature variation for a counter flow heat exchanger.

LMTD correction factor F for a shell-and-tube heat exchanger with one shell pass and two or a

multiple of two tube passes.

LMTD correction factor F for a shell-and-tube heat exchanger with two shell passes and

four or a multiple of four tube passes

LMTD correction factor F for a shell-and-tube heat exchanger with three two-shell

passes and six or more even number tube passes.

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

LMTD correction factor F for a split-flow shell-type heat exchanger with one split-

flow shell pass and two-tube passes.

Temperature distribution in a crossflow heat exchanger

LMTD correction factor F for a crossflow heat exchanger

with both fluids unmixed

LMTD correction factor F for a single-pass crossflow heat exchanger with

one fluid mixed and the other unmixed.

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).

+ is for counter flow and the – is for parallel flow. 47

Effectiveness vs. NTU for various types of heat exchangers

Effectiveness vs. NTU for various types of heat exchangers.

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

Heat exchanger design

methodology.

basic design methods of heat exchangers arrangement of

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