Analysis of Shell And Tube Heat Exchanger(Epsilon-NTU Method) using MATLAB [INDEPENDENT PROJECT]

Aim  :- To compute the Performance parameter of Heat Exchanger using Epsilon-NTU method.

OBJECTIVE :

·       To calculate Effectiveness, based upon NTU(No. of transfer unit), and Capacity rate ratio(Crr).

·       To obtain exit temperature of hot and cold fluids.

·       To find out LMTD(Log mean Temperature difference ) and Net heat exchanged for future scope of study. (To vary the area of exposure so to get optimized design).

INTRODUCTION :

Heat exchanger is a device built for efficient heat transfer from one medium to another, whether the media are separated by a solid wall so that they never mix, or the media are in direct contact. They are widely used in space heating, refrigeration, air conditioning, power plants, chemical plants, petrochemical plants, petroleum refineries, and natural gas processing.

Economics plays a key role in the design and selection of heat-exchange equipment, and the engineer should bear this in mind when embarking on any new heat-transfer design problem. The weight and size of heat exchangers used in space or aeronautical applications are very important parameters, and in these cases cost considerations are frequently subordinated insofar as material and heat-exchanger construction costs are concerned.

The important parameters like inlet temperature of fluids, specific heat of fluid,overall heat transfer coefficient etc  of heat exchangers are collected and put a major consideration on it.
In this project, the software needed to configure all the parameters to put in. From there, the software runs and the main point is to create a new windows program that is similar to another existed software of calculating parameters of  heat transfer in market like Effectiveness,NTU,Capacity rate ratio , outlet temperature of fluid etc.

 The major purpose is to obtain a desired output by using this program.

THEORY : 

When a heat exchanger is placed into a thermal transfer system, a temperature drop is required to transfer the heat. The magnitude of this temperature drop can be decreased by utilizing a larger heat exchanger, but this will increase the cost of the heat exchanger. The role of heat exchangers has taken on increasing importance recently as engineers have become energy conscious and want to optimize designs not only in terms of a thermal analysis and economic return on the investment but also in terms of the energy payback of a system.

Basic Types of Heat Exchangers :

1.     Recuperators. In this type of heat exchanger the hot and cold fluids are separated by a wall and heat is transferred by a combination of convection to and from the wall and conduction through the wall.

2.     Regenerators. In a regenerator the hot and cold fluids alternately occupy the same space in the exchanger core. The exchanger core or “matrix” serves as a heat storage device that is periodically heated by the warmer of the two fluids and then transfers heat to the colder fluid.

3.     Direct Contact Heat Exchangers. In this type of heat exchanger the hot and cold fluids contact each other directly. An example of such a device is a cooling tower in which a spray of water falling from the top of the tower is directly contacted and cooled by a stream of air flowing upward.

v Overall Heat Transfer Coefficient

The thermal analysis and design of a heat exchanger fundamentally requires the application of the first law of thermodynamics in conjunction with the principles of heat transfer. The actual heat transfer may be computed by calculating either the energy lost by the hot fluid or the energy gained by the cold fluid.

 [Parallel – flow heat exchanger]

One of the first tasks in a thermal analysis of a heat exchanger is to evaluate the overall heat transfer coefficient between the two fluid streams.

The overall heat transfer coefficient between a hot fluid at temperature T_h  and a cold fluid at temperature T_c  separated by a solid plane wall is defined by

                                                q = UA(T_h – T_c )

Log Mean Temperature Difference :

The temperatures of fluids in a heat exchanger are generally not constant but vary from point to point as heat flows from the hotter to the colder fluid. Even for a constant thermal resistance, the rate of heat flow will therefore vary along the path of the exchangers because its value depends on the temperature difference between the hot and the cold fluid in that section.

EFFECTIVENESS-NTU METHOD :

When the inlet or exit temperatures are to be evaluated for a given heat exchanger, the analysis frequently involves an iterative procedure because of the logarithmic function in the LMTD. In these cases the analysis is performed more easily by utilizing a method based on the effectiveness of the heat exchanger in transferring a given amount of heat. The effectiveness method also offers many advantages for analysis of problems in which a comparison between various types of heat exchangers must be made for purposes of selecting the type best suited to accomplish a particular heat-transfer objective.

We define the heat-exchanger effectiveness as

To determine the maximum possible heat transfer for the exchanger, we first recognize that this maximum value could be attained if one of the fluids were to undergo a temperature change equal to the maximum temperature difference present in the exchanger, which is the difference in the entering temperatures for the hot and cold fluids. The fluid that might undergo this maximum temperature difference is the one having the minimum value of m_c because the energy balance requires that the energy received by one fluid be equal to that given up by the other fluid; if we let the fluid with the larger value of m_c go through the maximum temperature difference, this would require that the other fluid undergo a temperature difference greater than the maximum, and this is impossible. So, maximum possible heat transfer is expressed as

It may be shown that the same expression results for the effectiveness when the hot fluid

is the minimum fluid, except that “M_{c *}  C_c “and ˙ M_h*C_h are interchanged. As a consequence, the effectiveness is usually written

While the effectiveness-NTU charts can be of great practical utility in design problems,

there are applications where more precision is desired than can be obtained by reading the

graphs. In addition, more elaborate design procedures may be computer-based, requiring

analytical expressions for these curves.

In a thermodynamic sense, higher effectiveness values correspond to reduced values of thermodynamic irreversibility and smaller entropy generation. To achieve both high heat transfer and high effectiveness one must increase the value of the UA product, either by increasing the size (and cost) of the exchanger or by forcing the fluid(s) through the heat exchanger at higher velocities to produce increased convection coefficients. Or, one may employ so-called heat-transfer augmentation techniques to increase the value of UA.

 Q . Water at a rate of 7500 Kg/h enters a counter-flow exchanger at 15 deg Celcius to coll 8000Kg/h of air at 105 deg Celcius .
        The overall heat transfer coefficient is 145 W/m2k, and the exchanger area is 20 m2. Find all the performance parameter               and Exit temperature of water and air.

 MATLAB CODE :

%% Program Heat exhanger 
% program to test Epsilon - NTU method.
% assuming a counterflow heat exhanger with known properties, known inlet
% temperatures and mass flowrates.
clc;
clear all;
close all;
format longg;
%% Input Variable
c_p_hot = 1.2; % KJ/kg-K
m_rate_hot =2.222; % kg/s
T_hot_in = 378; % K
c_p_cold = 4.18; % KJ/kg-K 
m_rate_cold = 2.08333; %kg/s
T_cold_in = 288;
U=0.145; %kW/m2.K (Overall heat transfer coefficient)
A=20;  %m2 
HE_Type = 'Counter Flow'
%% calculation related to Heat Exchanger
C_hot = m_rate_hot*c_p_hot; %{heat capacity of hot fluid}
C_cold = m_rate_cold*c_p_cold; %{heat capacity of cold fluid}
C_min = min(C_hot,C_cold); % finds the flow with lower heat capacity and higher temperature change.
C_max = max(C_hot,C_cold); % finds the flow with higher heat capacity and lower temperature change. 
C_r=C_min/C_max; %[capacity rate ratio of the heat exchanger]
NTU = U*A/C_min
%% Effectiveness calculation
% Special case of boiling or condensing:
if C_r == 0
    epsilon = 1-exp(-NTU);
    return;
end
%general cases please refer the TABLE from NTU method 
switch HE_Type
    case 'Parallel Flow'
        epsilon = (1-exp(-NTU*(1+C_r)))/(1+C_r);
    case 'Counter Flow'
        if C_r==1
            epsilon = NTU/(1+NTU);
        else
            epsilon = (1-exp(-NTU*(1-C_r)))/(1-C_r*exp(-NTU*(1-C_r)));
        end
    case 'One Shell Pass'
        epsilon = 2/(1+C_r+sqrt(1+C_r^2)*(1+exp(-NTU*sqrt(1+C_r^2)))/(1+exp(-NTU*sqrt(1+C_r^2))));
    case 'N Shell Pass'
        NTUN = NTU/N;
        epsilon1 = 2/(1+C_r+sqrt(1+C_r^2)*(1+exp(-NTUN*sqrt(1+C_r^2)))/(1+exp(-NTUN*sqrt(1+C_r^2))));
        epsilon = (((1-epsilon1*C_r)/(1-epsilon1))^N-1) / (((1-epsilon1*C_r)/(1-epsilon1))^N-C_r);
    case 'Cross Both Unmixed'
        epsilon = 1-exp(1/C_r * NTU^0.22 * (exp(-C_r*NTU^0.78)-1));
    case 'Cross Cmax Mixed'
        epsilon = 1/C_r*(1-exp(-C_r*(1-exp(-NTU))));
    case 'Cross Cmin Mixed'
        epsilon = 1 - epx(-1/C_r*(1-exp(-C_r*NTU)));
    otherwise % the type is not in the list, therefore we assume there's no heat exchanger.
        epsilon = 0; 
end
%% Final output of the results 
Q_max = C_min*(T_hot_in-T_cold_in);
Q = epsilon * Q_max ;
T_hot_out = T_hot_in - Q/C_hot 
T_cold_out = T_cold_in + Q/C_cold 
Q_hot=m_rate_hot*c_p_hot*(T_hot_in-T_hot_out)
Q_cold=m_rate_cold*c_p_cold*(T_cold_in-T_cold_out)
LMTD = ((T_hot_in-T_cold_out)-(T_hot_out-T_cold_in))/log((T_hot_in-T_cold_out)/(T_hot_out-T_cold_in))
Q_exchange = U*A*LMTD
Effectiveness_Heat_exchanger = epsilon

RESULTS : 

Respective User have to provide some INPUT VARIABLE in the above code, with desired Type of Heat Exchanger . Results are shown below for the standard problem taken by reference[2] book and all the results will be calculated in the command window.

• With the help of the programme we have received out Outlet temperature for hot and cold fluids
• Performance characteristics of the heat exchanger have also been determined like Capacity rate ratio, NTU, Effectiveness.
• Finally, we determined the Net heat transfer, LMTD of the Heat exchanger.

Applications:- 

• Heat Exchanger are used in Condenser of stream power plant
• Heat Exchanger are also used widely is Chemical Industry
• Widely used in Food processing Opeartions
• Widely used in Automotive sector

References :- 

1. Heat Transfer by J.P Holman(10th  edition)
2. Frank P. Incropera : Introduction to heat transfer : Wiley
3. Principle of Heat transfer by Frank kreith;Manglik;Bohn
4. Description on E-NTU Heat Transfer by MATLAB
5. Study of NTU method
6. Epsilon-NTU relationships in parallel-series arrangements
7. Steady State Thermal Analysis of Shell and Tube Type Heat Exchanger
8. Design of Shell and Tube Heat Exchanger Using MATLAB and Finding the Steady State Time Using Energy Balance Equation