[IIC_assignment] Mathematical Modelling of Heat Exchanger

8/12/2019 [IIC_assignment] Mathematical Modelling of Heat Exchanger

1/18

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.


2/18


3/18

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


4/18

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.


5/18

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.


6/18

WORKING EQUATION

Counter Flow

(

)

()


7/18

Parallel Flow


8/18

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;


9/18

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


10/18

%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.


11/18

SIMULATION TRIAL 1


12/18

SIMULATION TRIAL 2


13/18


14/18

Simulation 1(Continued)

Increase pipe radius to 0.05m


15/18

Reduce pipe length to 4m


16/18

Increasing mass flow rate to 2.5 Kg/sec


17/18

Using a coolant of specific heat 5500 J/Kg C (better coolant)


18/18

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/

Documents

[IIC_assignment] Mathematical Modelling of Heat Exchanger