MATLAB: How to plot quiver with an input of Temperature data

quivertemperature

I have temperature data of a sample (V=(28,30,4997)). Each V(:,:,i) is a matrix with temperature values. I want to plot a quiver of temperature dissipation/accumulation and temperature image at the same time but i am a bit confused with inputs for u and v vectors. What u and v should be if i have only matrices of temperature?

My code:

[x,y]=meshgrid(1:1:30,1:1:28);
k=4997;
cnt=0;
for i=1:k
    u(:,:,i)=V(:,:,i);
    v(:,:,i)=V(:,:,i);
    %figure
    imagesc(V(:,:,i));
    hold on
    axis tight
    q=quiver(x,y,u(:,:,i),v(:,:,i))
    q.AutoScale='on';
    q.AutoScaleFactor=0.8;
    
    colormap jet
   
    cnt=i;
    title(cnt);
    
    pause (0.1)
  
end

Best Answer

Presumably your heat-flux is just proportional to the temperature gradient (assuming constant and isotropic heat conductivity), for that I would start with:

[dTdx,tTdy] = gradient(V(:,:,i));
u(:,:,i) = -heat_conductivity*dTdx;
v(:,:,i) = -heat_conductivity*dTdy;

If you want total change in thermal energy per pixel you'll have to add local heating and subtract local cooling, for this the contribution of heat condution will be proportional to the divergence of the heat-flux. If you image a fluid that moves you'll also have to take the effect of convection into account. If the above suggestion doesn't work you have to clarify your question.

HTH

Related Solutions

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

MATLAB: Time dependent external heat flux in PDE Toolbox

Hi Pascal,

You are on the right track, refer to the externalHeatFlux in the example:

https://www.mathworks.com/help/pde/ug/heat-conduction-in-multidomain-geometry-with-nonuniform-heat-flux.html

Thought the example is for spatial variaion, you can make your heat flux funciton of time using state.time, state is available to you as second argument.

function Qflux = timeDepHeatFlux(region,state)
    if isnan(state.time)
    Qflux = nan(size(region.x));
    return;
    end
    % Write you time dependent function here....
end

Regards,

Ravi

Best Answer

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

MATLAB: Time dependent external heat flux in PDE Toolbox

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