## Introduction

The chief thought of the paper is to give the thorough cognition of the chief issues without the elaborate survey of the literature. The basic design of this type of heat money changer involves many design parametric quantities as described below:

The comprehensive study that I have presented has been a apogee of a assortment of undertakings mentioned below I have done over a period of 6 months:

Collection of informations from the industry. A visit to Mazda Heat Exchanger and Patel Air-Temp was a of import portion of it and we took existent practical readings from these companies.

Choice of heat exchanger- Shell and Tube type.

This was followed by the basic design of the Heat money changer utilizing LMTD- Log Mean Temperature Difference method.

After the basic design I did the modern design by Kern ‘s method and Bell Delaware method.

Simulation utilizing numerical method by using Euler ‘s theorem in a C plan.

Thereafter for optimisation I did the comparing of both the designs followed by the alterations in natural design by altering the variables.

Finally I compared my complete design with the existent heat money changer in the industry and derived decisions.

## Abbreviation, Notations and Nomenclature

B- baffle spacing ( pitch )

PT- tubing pitch

C -clearance

Do- tubing outside diameter

D -inside diameter of shell

Re- Reynold ‘s figure based on the maximal flow speed

Vmax – utilizing the expression of this reynold ‘s figure is calculated

a, m- correlativity invariables

F1, F2 – Correction factors for the surface

U – overall heat transportation co-efficient

H is the convective heat transportation coefficient

Roentgen is the co-relation factor

hafnium is the fouling factor

Re is Reynold ‘s figure

Pr is the Prandtl figure

## Basic theory

## Fundamentalss

The cardinal equation for heat transportation across a surface is given by:

The log average temperature difference a?†Tlm ( LMTD ) for rip flow is given by

The rectification factor is a map of the fluid temperatures and the figure of tubing and shell base on ballss and is correlated as a map of two dimensionless temperature ratios

Kern developed a relationship applicable to any heat money changer with an even figure of base on ballss and generated temperature rectification factor secret plans ; secret plans for other agreements are available in the TEMA criterions.

The overall heat transportation coefficient U is the amount of several single oppositions as follows:

The combined fouling coefficient hafnium can be defined as follows:

Nature of the heat transportation procedure, the watercourse belongingss and the heat transportation surface agreements affects the single heat transportation coefficient as it depends on them. Under the stratifying conditions Nusset method is used for the horizontal condensation where the liquid movie is run outing under the gravitation with minimal influence due to vapor shear. This is the CCTHERM method.

## Determination of shell diameter and figure of tubings:

## Number of tubings

Nt = 0.875* ( CTP/CL ) * ( ( Ds*Ds ) / ( Pr*Pr*Do*Do ) )

Where ;

CTP= Tube count computation changeless = 0.93 for one tubing base on balls

= 0.90 for two tubing base on balls

= 0.85 for three tubing base on balls

CL= Tube layout changeless = 1 for 90 grades and 45 grades

= 0.87 for 30 grades and 60 grades

PR= Pitch ratio = ( Pt ) / ( Do ) = 1.25

Where ;

Pt= pitch

## The Kern ‘s Method

## Introduction to Kern ‘s Method

Kern adapted the Nusselt equation to let rating of unstable conditions at the movie temperature. This method requires the movie to be in streamline flow with a Reynolds Numbers scope 1800 to 2100.

## Parameters included

## 2.2.1. Tube Diameter

The most common sizes used are 3/4 ” Doctor of Optometry and 1 ” Doctor of Optometry Use smallest diameter for greater heat transportation country with a normal lower limit of 3/4 ” Doctor of Optometry tubing due to cleaning considerations and vibration.1/2 ” od tubings can be used on shorter tubing lengths say & lt ; 4ft. The wall thickness is defined by the Birmingham wire pot ( BWG ) inside informations are given in Kern Table 10

## 2.2.2. Tube Number and Length

Choose the figure of tubings per tubing side base on balls to give optimal speed 3-5 ft/s ( 0.9-1.52 m/s ) for liquids and sensible gas speeds are 50-100 ft/s ( 15-30 m/s )

If the speed can non be achieved in a individual base on balls consider increasing the figure of base on ballss. Tube length is determined by heat transportation required capable to works layout and force per unit area bead restraints. To run into the design force per unit area bead restraints may necessitate an addition in the figure of tubings and/or a decrease in tubing length. Long tube lengths with few tubings may give rise to blast side distribution jobs.

## 2.2.3. Tube Layout, Pitch and Clearance

Choose the figure of tubings per tubing side base on balls to give optimal speed 3-5 ft/s ( 0.9-1.52 m/s ) for liquids and sensible gas speeds are 50-100 ft/s ( 15-30 m/s )

If the speed can non be achieved in a individual base on balls consider increasing the figure of base on ballss. Tube length is determined by heat transportation required capable to works layout and force per unit area bead restraints. To run into the design force per unit area bead restraints may necessitate an addition in the figure of tubings and/or a decrease in tubing length.

Long tube lengths with few tubings may give rise to blast side distribution job

Tube pitch is defined as:

Triangular form provides a more robust tubing sheet building. Square pattern simplifies cleaning and has a lower shell side force per unit area bead Typical dimensional agreements are shown below, all dimensions in inches.

## 2.2.4. Heat Transfer Area

Using the maximal figure of tubings, capable to adequate proviso for recess nose, for a given shell size will guarantee optimal shell side heat transportation in minimising tubing package bypassing. The heat reassign country required design border is so achieved by seting the tubing length topic to economic considerations. On low cost tubing stuffs it may be more economical to utilize standard lengths and accept the increased design border.

It is a common pattern to cut down the figure of tubings to below the maximal allowed peculiarly with expensive tubing stuff.In these state of affairss the mechanical design must guarantee suited proviso of rods, saloon baffles, spacers, baffles to minimise bypassing and to guarantee mechanical strength. [ 1 ]

## Baffle Design

## Definitions

Shell side cross flow country is given by:

## Minimal spacing ( pitch )

Segmental baffles usually should non be closer than 1/5th of shell diameter ( ID ) or 50.8mm ( 2in ) whichever is greater.

## Maximal spacing ( pitch )

Spacing does non usually exceed the shell diameter. Tube support home base spacing determined by mechanical considerations e.g. strength and quiver. [ 3 ]

Maximal spacing is given by:

[ 4 ]Most failures occur when unsupported tubing length greater than 80 % TEMA upper limit due to designer seeking to restrict shell side force per unit area bead. [ 6 ]

## Baffle cut.

Baffle cuts can change between 15 % and 45 % and are expressed as ratio of section opening tallness to blast indoors diameter. The upper bound ensures every brace of baffles will back up each tubing. Kern shell side force per unit area bead correlativities are based on 25 % cut which is standard for liquid on shell side When steam or vapour is on the shell side 33 % cut is used. Baffle pitch and non the baffle cut determines the effectual speed of the shell side fluid and hence has the greatest influence on shell side force per unit area bead. Horizontal shell side condensation require segmental baffles with cut to make side to side flow to accomplish good vapour distribution the vapour speed should be every bit high as possible consistent with hearty force per unit area bead restraints and to infinite the baffles consequently. [ 3 ]

## Fouling Considerations

It can be shown that the design border achieved by using the combined fouling movie coefficient is given by:

[ 4 ]Where AC is the clean HTA, Af is the dirty or design HTA and UC is the clean OHTC.

Using typical fouling coefficients gives the undermentioned consequences in British units

[ 4 ]## Bell-Delaware Method

This method incorporates rectification factors for the undermentioned elements:

1. Leakage through the spreads between the tubings and the baffles and the baffles and the shell.

2. Bypassing of the flow around the spread between the tubing package and the shell

3. Consequence of the baffle constellation acknowledging that merely a fraction of the tubings are in pure cross flow.

4. Consequence of inauspicious temperature gradient on heat transportation in laminar flow ( Re & lt ; 100 ) but is considered of dubious cogency.

The first measure is to cipher the ideal cross flow heat transportation coefficient utilizing the VDI-Mean Nusselt

The maximal speed is calculated utilizing flow country computations depending on tubing layout and pitch, baffle spacing, shell diameter and tubing package diameter. Correction factors are applied to the deliberate heat transportation coefficient for baffle constellation, for escape related to blast to perplex and tube to perplex, and for beltway in the package to blast spread. [ 2 ]

As per this method:

ho’=ho* ( Jc*J*Jb*Js*Jr )

Correction factors ;

Jc= Baffle cut and spacing

Ji= Tube to perplex and blast to perplex escape 0.7 to 0.8

Jb= Bundle by go throughing effects, clearance is 0.7 to 0.9

Js= Variable baffle spacing at recess and mercantile establishment is 0.85 to 0.95

Jr= Shell side Re figure

Entire consequence = { Jc*Ji*Jb*Jg*Jr = 0.6 }

## Thermal Design

## Calculation of inside convective heat transportation Co-efficient ( hello )

Assuming v=2m/sec in the tubing

Re=

=2.0*18.84/0.672*10^-6

=56071.42

## Nusselt Number

X=0.4, if fluid is being heated

X=0.3, if fluid is being cooled

=0.023* ( 56071 ) ^0.8* ( 4.25 ) ^0,4

=258.27

Nu= hi*di/k

= hi*18.84*10^-3/0.626

hello = 8581.58W/m^2k

Assuming ho=5000W/m^2k

=15.21

Q=m*cp*del T

=1.389*4.186*2

=116.27

Q=U A lmtd

116.27 = 3.159*A*15.21 ;

A=2.420m^2

U= 2662.14W/m2k

Q=U A lmtd

116.27 = 4.352*A*15.21 ;

A1=2.87m^2

## Kern ‘s Method Calculations

Assuming PR = 1.25 ;

De = 0.021m

6.04* 10^-4

Ho =2900.93 W/m2*k

Therefore,

Therefore we get,

And,

W/m2k

Q=U A lmtd

116.27 = 2.670*A*15.21 ;

A2=2.8624m^2 vitamin D.

## Simulation

## Modeling the Heat Exchanger:

aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦ … ( 1 )

aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦ ( 2 )

aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦ … ( 1 )

## Euler ‘s Theorm:

Y2 = Y1 + Yaˆ?h

From Euler ‘s theorm we get

## Determination of

From Equation no ( 1 ) we get,

## For hello:

X=0.4, if fluid is being heated

X=0.3, if fluid is being cooled

Re = Reynolds ‘s Number

Re=

Here, , Pr value vary with temperature.

## For Tt1:

## =

Rf= Fouling Factor.

## Simulation Consequences

DESIGN ( A°C )

SIMULATION ( A°C )

Tc1

35

35

Tc2

43

42

Th2

45

45

Th1

65

62

## Decision

From the simulation consequences, the fluctuation between design and simulation was found to be less than 5 per centum and which is in the allowable scope. Now to optimise the design following parametric quantities can be varied utilizing our package to further cut down the fluctuation.

Length

Standard internal and external tubing diameters

Baffle spacing

Fluid Velocity

Number of tubings

Base on ballss

Tube layout

Pitch

## Recognition

I am highly grateful to Dr. Zheng Li, senior Professor at the Department of Mechanical Engineering at University of Bridgeport and my undertaking usher for his valuable inputs into my undertaking and without whose counsel this comprehensive survey would n’t hold been possible.

I am besides to a great extent indebted to our Head of Department Dr. Jani Pallis who gave me of import tips on a good paper presentation.