MATLAB: Heat transfer differential equation

heat transfer differential equationsMATLAB

Dear all,

I'm quite a new user of Matlab, I'm asking you somethiing that could be simple or obvious, but I've tried and no reasonable results came uot.

I've to calculate the Temperature evolution in time of a system affected by heat conduction and radiation, this is my equation:

and this is my attempt code:

function[yp] = f(t,y);
% defining constants
d = 0.00585;
l = 0.03325;
m = 0.009329;
v = 20;
cp = 0.5;
nu  = 16.24*10^-6;
sigma = 5.6704*10^-6;
eps = 0.8;
h = (0.26*((d/nu)*v)^0.6)*(0.7^0.37);
A = 7.926*10^-4;
k1 = (h*A)/(m*cp);
k2 = (sigma*eps*A)/(m*cp);
ya = 299;
% equation
yp = k1*(y-ya)+k2*(y^4);

Then, on the command window:

[t,y] = ode45('f',[0,5],1673)

What I am doing wrong (in the problem formulation, I don't care for instance to numbers)?

Thanks for any help!

Best Answer

I've solved my question using ode113:

[t,y] = ode113(@(t,y) -k1*(y-299)-k2*y^4,[0 100],1673)

, which eventually worked better and did not have any integration step tolerance warnings.

I'll try also your suggestion.

Thanks for your quick reply!

Related Solutions

MATLAB: Solving a ODE in matlab

ode = @(t,y) y.^2-y.*0.1*cos(2.*t)-0.2*cos(2.*t);
t=[0 8];
y0 = -1;
[t,y] = ode45(ode,t,y0);
plot(t,y)

MATLAB: How can get the value for each time step for a variable inside of a function

Hi,

you try this code (all in one file as nested function). The values you want to have in every iteration are now added to the solution and also saved in the results table. This should be what you want.

Result = main
function Result = main
%Initial conditions
Wads=0.045;
Tads=80;
Wdes=0.035;
Tdes=27;
Teva=7;
Tcond=27;
Mweva=0.65;         
Initial=[Wads Tads Wdes Tdes Mweva Teva Tcond 0 0 0 0];           
tspan=[1:1:800];
opts = odeset('RelTol',1e-6,'AbsTol',1e-6);
[t,Soln]=ode45(@(t,Soln)ODEdw(t,Soln),tspan,Initial,opts);
colNames = {'Time','Wads','Tads','Wdes','Tdes','Mweva', 'Teva','Tcond',...
    'Tcwaout', 'Thwdout', 'Tchwout', 'Tcwcout'};
Result = array2table([tspan',Soln],'VariableNames',colNames);
function [dYdt] =ODEdw(~,Soln)
Ea=4.2*10^4;         %Activation energy of surface diffusion, (J/mol)
R=8.314;             %Ideal gas constant, (j/mol.K)
Dso=2.54*10^-4;       %Pre-exponential constant, (m^2 S^-1)
Qs=2.8*10^6;         %Heat of adsorption, (J/kg)
%%%%%%%%%%%Operating conditions%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Thwdin=85;            %Inlet temperature of hot water in desorber, (oC)
Tcwain=27;            %Inlet temperature of cooling water in adsorber, (oC)
Tcwcin=27;            %Inlet temperature of cooling water in condenser, (oC)
Tchwin=14;            %Inlet temperature of chilling water in evaporator, (oC)
mcwa=8/60;            %Mass flow rate of cooling water in adsorber, (kg/s)
mcwc=20/60;           %Mass flow rate of cooling water in condenser, (kg/s)
mchw=1.6/60;          %Mass flow rate of chilling water in evaporator, (kg/s)
mhwd=7/60;            %Mass flow rate of hot water in desorber, (kg/s)
%%%%%%%%%Physical and thermal properties of adsorbent%%%%%%%%%%
Cps=924;              %Specific heat capacity of silica gel, (J/kg.K)
Ms=9;                 %Mass of silica, (kg)
Rp=5.6*10^-4;         %Radious of silica gel particle, (m)
ps=700;              %density of silica gel, (kg/m^3)
Por=0.3;              %Porosity of silica gel,
%%%%%%Physical and thermal properties of adsorbate%%%%%%%%%%%%%
Cpw=4200;             %Specific heat capcity of water, (J/kg.k)
Cpv=1900;             %Specific heat capacity of water vapor (J/kg.K)
M=18.02;              %Molar mass of water, (g/mol)
Lv=2500*10^3;         %Lantent heat of vaporization (J/kg) 
%%%%%%%%%Physical and thermal Properties of Condenser%%%%%%%%%%%%%
Acond=5.76;            %Surface area of condenser, (m^2)
Mhexcond=19.87;        %Mass of heat exchanger (Condenser), (kg)
Ucond=486.87;          %Heat transfer coefficient of condenser, (W/m^2.K)
UAcond=Acond*Ucond;
Mwcond=1.0;         %Mass of water in Condenser (kg)
%%%%%%%%%%Physical and thermal properties of adsorber/desorber   %%%%%%%
Mhex=65;             %Mass of heat exchanger (Adsorber/desorber), (kg)
Cphex=386;           %Heat capacity of heat excahgner, (J/kg.K)
Aad=2.11;            %Surface area of adsorber/desorber, (m^2)
Uads=189.60;         %Heat transfer coefficient of adsorber, (W/m^2.K)
Udes=203.99;         %Heat transfer coefficient of desorber, (W/m^2.K)
UAads=Aad*Uads;
UAdes=Aad*Udes;
Vt=0.5;              %volume of adsorber/desorber tank, (m^3)
%%%%%%%%%Physical and thermal Properties of Evaporator%%%%%%%%%%%%%%
Aeva=0.34;           %Surface area of evaporator, (m^2)
Mhexeva=16.1;        %Mass of heat exchanger (Evaporator), (kg)
Ueva=302.58;         %Heat transfer coefficient of evaporator, (W/m^2.K)
UAeva=Aeva*Ueva;
Wads=Soln(1);    
Tads=Soln(2);  
Wdes=Soln(3);    
Tdes=Soln(4);
Mweva=Soln(5);
Teva=Soln(6);
Tcond=Soln(7);
Kads=((15*Dso)/(Rp).^2)*exp(-Ea/(R*(Tads+273.16)));   %Overall mass tarsnfer coeffcient of adsorber

Pwa=133.32*exp(18.3-(3820/((Teva+273.16)-46.1))); % Saturated vapour pressure of waterm (vapour) at adsorbent temperature, (Pa)

Psga=133.32*exp(18.3-(3820/((Tads+273.16)-46.1))); % Saturated vapour pressure of water at adsorbent temperature, (Pa)

Weqa=0.346*(Pwa/Psga)^0.625;
Aads=(Kads*(Weqa-Wads));
TLads=(Ms*(Cpw+Cpw*Wads)+Mhex*Cphex); %Left hand side of adsorber equation
Tcwaout=Tads+(Tcwain-Tads)*exp((-UAads)/(mcwa*Cpw));
   
Kdes=((15*Dso)/(Rp).^2)*exp(-Ea/(R*(Tdes+273.16)));   %Overall mass tarsnfer coeffcient of adsorber
Pwd=133.32*exp(18.3-(3820/((Tcond+273.16)-46.1))); % Saturated vapour pressure of waterm (vapour) at adsorbent temperature, (Pa)
Psgd=133.32*exp(18.3-(3820/((Tdes+273.16)-46.1))); % Saturated vapour pressure of water at adsorbent temperature, (Pa)
Weqd=0.346*(Pwd/Psgd)^0.625;
Ades=(Kdes*(Weqd-Wdes));
TLdes=(Ms*(Cps+Cpw*Wdes)+Mhex*Cphex); %Left hand side of desorber equation
Thwdout=Tdes+(Thwdin-Tdes)*exp((-UAdes)/(mhwd*Cpw));
  
TLeva=(Mweva*Cpw+Mhexeva*Cphex); %Left hand side of evaporator equation

Tchwout=Teva+(Tchwin-Teva)*exp((-UAeva)/(mchw*Cpw));
  
TLcond=(Mwcond*Cpw+Mhexcond*Cphex); %Left hand side of evaporator equation
Tcwcout=Tcond+(Tcwcin-Tcond)*exp((-UAcond)/(mcwc*Cpw));
dYdt=[Kads*(Weqa-Wads);((Qs*Ms*Aads)+(Ms*Cpv*Aads*(Teva-Tads))+mcwa*Cpw*(Tcwain-Tcwaout))/TLads;
    Kdes*(Weqd-Wdes); ((Qs*Ms*Ades)+(mcwa*Cpw*(Thwdin-Thwdout)))/TLdes; 
    -Ms*((Kads*(Weqa-Wads))+(Kdes*(Weqd-Wdes)));((-Lv*Ms*Aads)+Ades*Ms*Cpw*(Tcond-Teva)+mchw*Cpw*(Tchwin-Tchwout))/TLeva;
    (Ades*Ms*Cpv*(Tdes-Tcond)+(Lv*Ms*Ades)+mcwc*Cpw*(Tcwcin-Tcwcout))/TLcond; Tcwaout; Thwdout; Tchwout; Tcwcout];
end
end

Best regards

Stephan

Best Answer

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