MATHEMATICAL MODELING OF HEAT EXCHANGER

by

M.SAI CHANDU 2009A8PS219P

SHARDOOL RASTOGI 2009A8PS222P

NIMISH TRIPATHI 2008B5A8691P

in

Partial fulfillment of the course Industrial Instrumentation and Control (INSTR C312)

BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI.

ACKNOWLEDGEMENTS

We sincerely thank Prof. Surekha Bhanot, instructor-in-charge,

INSTR C312 (Industrial Instrumentation and Control), for her guidance and

support in the completion of this project.

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

counter 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

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.

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.

WORKING EQUATION

Counter Flow

a=MhChMcCc

b=1−a=1−MhChMcCc

d=2 πrUbMhCh

Th ( x )=Tc 1(edx−1 )+Th1 (1−a )

edx−a

Tc ( x )=Tc 1+a (Th1−Th ( x ) )

Mh=mass flowrateof hot fluid

Mc=mass flowrate of cold fluid

Ch ,Cc−specific heat capacity of hot∧cold fluid

Th1=input temperature of hot fluid

Tc 1=input temperature of cold fluid

U=overall Heat Transfer Coeff .

r=radiusof the pipe

Parallel Flow

Th ( x )=(Tc 1+(MhChMcCc )Th1)+ (Th1−Tc1 ) e

−2πrUbMhCh

¿

(MhChMcCc )+1¿

Tc ( x )=(Th1+(McCcMhCh )Tc 1)−(Th1−Tc 1 ) e

−2πrUbMhCh

¿

( McCcMhCh )+1¿

Mh=mass flowrateof hot fluid

Mc=mass flowrate of cold fluid

Ch ,Cc−specific heat capacity of hot∧cold fluid

Th1=input temperature of hot fluid

Tc 1=input temperature of cold fluid

U=overall Heat Transfer Coeff .

r=radiusof the pipe

SIMULINK BLOCK DIAGRAM(COUNTER FLOW HEAT EXCHANGER

SIMULATION RESULTS

1)TEMPERATURE OF HOT LIQUID

2)TEMPERATURE OF COLD LIQUID

MATLAB CODE

CounterFlow

clear allclose all disp('########################################################');disp(' ####### Counter Flow Heat Exchanger Simulation #########');disp(' ########################################################'); %Simulates a Counter FLow Heat Exchanger%User Input CodeTc1=input('Enter entry temperature[COLD FLUID](deg C):');Mc=input( 'Enter mass flow rate [COLD FLUID](kg/s) :');Cc=input( 'Enter specific heat [COLD FLUID](J/kgC):');Th1=input('Enter entry temperature [HOT FLUID](deg C):');Mh=input( 'Enter mass flow rate [HOT FLUID](kg/s) :');Ch=input( 'Enter specific heat [HOT FLUID](J/kgC):');r=input( 'Enter radius of pipe (m):');U=input( 'Enter heat transfer coefficient (w/m2C):');l=input( 'Enter tube length (m):'); %Solution

p=((Mh*Ch)/(Mc*Cc));b=(1-p);d=(2*pi*r*U*b)/(Mh*Ch);x=0:0.01:l; % initialize an array of points for the length of the pipeN=(100*l)+1; % number of elements in the arrayh1=((Tc1*(exp(d*x)-1))+(Th1*b));h2=exp(d*x)-p;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+(p*(Th1-Th2(i)));% Array stores the temperature of cold fluid along the length of the tubeend %Temperature Plottingfigure;plot(x,Th2,'r');hold on;plot(x,Tc2);title('Heat Exchanger | Counter Flow');xlabel('distance');ylabel('temperature');grid; ParallelFlow

clear allclose all disp('#########################################################');disp(' ####### Parallel Flow Heat Exchanger Simulation #########');disp(' #########################################################'); %Simulates a Parallel Flow Heat Exchanger%User Input CodeTc1=input('Enter entry temperature[COLD FLUID](deg C):');Mc=input( 'Enter mass flow rate [COLD FLUID](kg/s) :');Cc=input( 'Enter specific heat [COLD FLUID](J/kgC):');Th1=input('Enter entry temperature [HOT FLUID](deg C):');Mh=input( 'Enter mass flow rate [HOT FLUID](kg/s) :');Ch=input( 'Enter specific heat [HOT FLUID](J/kgC):');r=input( 'Enter radius of pipe (m):');U=input( 'Enter heat transfer coefficient (w/m2C):');l=input( 'Enter tube length (m):');

%Solution p=((Mh*Ch)/(Mc*Cc));b=(p+1);d=(-2*pi*r*U*b)/(Mh*Ch);x=0:0.01:l;% initialize an array of points for the length of the pipep_inv=1/p;f=p_inv+1;Th2=(((Tc1+(p*Th1)+((Th1-Tc1)*exp(d*x)))))/b;% Array stores the temperature of hot fluid along the length of the tubeTc2=(((Th1+(p_inv*Tc1)-((Th1-Tc1)*exp(d*x)))))/f;% Array stores the temperature of cold fluid along the length of the tube %Temperature Plottingfigure;plot(x,Th2,'r');hold on;plot(x,Tc2);title('Heat Exchanger | Parallel Flow');xlabel('distance');ylabel('temperature');grid;