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MATHEMATICAL MODELING OF
HEAT EXCHANGER
by
Rahul Roy 2005B5A8654
Hari V Nair 2005B2A8528
Suraj S 2005B5A8602
in
Partial fulfillment of the course Industrial Instrumentation and Control (INSTR C312)
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI.
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INTRODUCTION
Heat exchangers are devices that transfer heat between two fluids. They can transfer
heat between a liquid and a gas (i.e., a liquid-to-air heat exchanger) or two gases (i.e.,
an air-to-air heat exchanger), or they can perform as liquid-to-liquid heat exchangers.
These devices are used in many applications, such as air conditioning, gas turbines,
automobiles and electronics cooling. For example, the radiator in a car is water-to-air
heat exchanger that cools the heated water returning from the engine.
The objective of this project is to do mathematical modeling of parallel flow heat exchanger and
cross flow heat exchanger. The inputs of the simulation will be the specific heat capacities of the
process fluids, mass flow rates, over all heat transfer coefficient of the system, pipe length and
radius, and input temperatures of process fluids.
Any overall energy balance starts with the following equations:
Q = heat transferred in thermal unit per time (Btu/h or kW)
M = mass flow rate
T = temperature
Cp = heat capacity or specific heat of fluid
Subscript H = hot fluid
Subscript C = cold fluid
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CLASSIFICATION
Heat exchangers may be classified according to their flow arrangement.
1. Parallel-flow heat exchangers
2. Counter-flow heat exchangers
3. Cross-flow heat exchanger
In parallel-flow heat exchangers, the two fluids enter the exchanger at the same end, and travel
in parallel to one another to the other side.
In counter-flow heat exchangers the fluids enter the exchanger from opposite ends.
In a cross-flow heat exchanger, the fluids travel roughly perpendicular to one another through
the exchanger.
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APPLICATIONS
1. Boilers and Steam Generators
2. Condensers
3. Radiators
4. Evaporators
5. Cooling towers (direct contact)
6. Regenerators
7. Recuperators
ASSUMPTIONS
We will use the following assumptions in our model:
1. Heat transfer is under steady-state conditions.
2. The overall heat-transfer coefficient is constant throughout the length of pipe.
3. There is no axial conduction of heat in the metal pipe.
4. The heat exchanger is well insulated. The heat exchange is between the two liquid
streams flowing in the heat exchanger. There is negligible heat loss to the
surroundings.
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WORKING EQUATION
Counter Flow
(
)
()
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Parallel Flow
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MATLAB CODE
parallelFlow.m
function parallelFlow
global Mh Mc r U l Ch Cc Th1 Tc1;
%Implements the mathematical modelling of a parallel Flow heat Exchanger
%Author: Rahul Roy | Hari V Nair | Suraj S Date:Feb 14, 2009
%written in Partial fulfillment of the course Industrial Instrumentation and Control (INSTR C312)
%Solution %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
a=((Mh*Ch)/(Mc*Cc));
b=(a+1);
d=(-2*pi*r*U*b)/(Mh*Ch);
x=0:0.01:l;% initialize an array of points for the length of the pipe
a_inv=1/a;
f=a_inv+1;
Th2=(((Tc1+(a*Th1)+((Th1-Tc1)*exp(d*x)))))/b;% Array stores the temperature of hot fluid along thelength of the tube
Tc2=(((Th1+(a_inv*Tc1)-((Th1-Tc1)*exp(d*x)))))/f;% Array stores the temperature of cold fluid along thelength of the tube
%Temperature Plotting%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure;
plot(x,Th2,'r');
hold on;
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plot(x,Tc2);
title('Heat Exchanger | Parallel Flow');
xlabel('distance(m)');
ylabel('temperature(degC)');
grid;
counterFlow.m
function counterFlow
global Mh Mc r U l Ch Cc Th1 Tc1;
%Implements the mathematical modelling of a counter Flow heat Exchanger
%Temperature versus distance along the length of the pipe.
%Author: Rahul Roy | Hari V Nair | Suraj S Date:Feb 14, 2009
%written in Partial fulfillment of the course Industrial Instrumentation and Control (INSTR C312)
%Solution %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
a=((Mh*Ch)/(Mc*Cc));
b=(1-a);
d=(2*pi*r*U*b)/(Mh*Ch);
x=0:0.01:l; % initialize an array of points for the length of the pipe
N=(100*l)+1; % number of elements in the array
h1=((Tc1*(exp(d*x)-1))+(Th1*b));
h2=exp(d*x)-a;
for (i=1:N)
Th2(i)=h1(i)/h2(i);% Array stores the temperature of hot fluid along the length of the tube
Tc2(i)=Tc1+(a*(Th1-Th2(i)));% Array stores the temperature of cold fluid along the length of the tube
end
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%Temperature Plotting%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure;
plot(x,Th2,'r');
hold on;
plot(x,Tc2);
title('Heat Exchanger | Counter Flow');
xlabel('distance(m)');
ylabel('temperature(degC)');
grid;
Finally a GUI application was written in matlab with the help of GUIDE (GUI Development Environment)
Guiv1.m and Guiv1.fig are the files required to run the GUI. The code in Guiv1.m makes callbacks to the
functions written in parallelFlow.m and counterFlow.m. For more information type help Guiv1.m in the
matlab command window.
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SIMULATION TRIAL 1
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SIMULATION TRIAL 2
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Simulation 1(Continued)
Increase pipe radius to 0.05m
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Reduce pipe length to 4m
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Increasing mass flow rate to 2.5 Kg/sec
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Using a coolant of specific heat 5500 J/Kg C (better coolant)
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REFERENCES
1. Holman, J.P Heat Transfer 8thedition
2. Bhanot Surekha Process Control- Principles and Applicatons
3. BV Babu et al, Chemical Engineering Laboratory Manual, EDD
Web links
http://heatexchangers.fopim.com/
http://en.wikipedia.org/wiki/Heat_exchanger
http://www.me.wustl.edu/ME/labs/thermal/me372b5.htm
http://www.mathworks.com/access/helpdesk/help/
http://heatexchangers.fopim.com/http://heatexchangers.fopim.com/http://en.wikipedia.org/wiki/Heat_exchangerhttp://en.wikipedia.org/wiki/Heat_exchangerhttp://www.me.wustl.edu/ME/labs/thermal/me372b5.htmhttp://www.me.wustl.edu/ME/labs/thermal/me372b5.htmhttp://www.mathworks.com/access/helpdesk/help/http://www.mathworks.com/access/helpdesk/help/http://www.mathworks.com/access/helpdesk/help/http://www.me.wustl.edu/ME/labs/thermal/me372b5.htmhttp://en.wikipedia.org/wiki/Heat_exchangerhttp://heatexchangers.fopim.com/