Mathematical Modelling of Heat Exchanger(Mini Report)
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Transcript of Mathematical Modelling of Heat Exchanger(Mini Report)
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;