Define function for transient transient boundary condition

As shown below in yellow highlight, I have a polynomial expression for a refrigerant time-varying thermal boundary condition. I want to define this as a function that I can call later in a thermalBC statement. My code won’t run. I need help in defining the function properly and calling it properly. Thanks

F1= 3.843e-8
F2= -3.482e-5
F3= 1.179e-2
F4= -1.95
F5= 23.69

tlistmin= 0;                                                                   % Minimum time (s)
tlistmax= 300;                                                              % Maximum time (s)
tlistdelta= (tlistmax-tlistmin)/100                       % time step

tlist=tlistmin:tlistdelta:tlistmax

Trefrig= F1*tlist.^4 + F2*tlist.^3 + F3*tlist.^2 + F4*tlist + F5

function Trefrig = Trefrig(state.time)

thermalBC(thermalmodel,"Edge",7,...
    "ConvectionCoefficient",hrefrig,...
    "AmbientTemperature", @Trefrig)

[John McGrath]

Hi Walter

Thanks for your suggestion. MatLab is coming back with "Invalid use of operator" for the line:

functtion Trefrig = Trefrig(state.time)

[Walter Roberson]

I did not make any suggestions.

I might possibly have reformatted the code.

Answer 1

[Torsten]

F1= 3.843e-8;
F2= -3.482e-5;
F3= 1.179e-2;
F4= -1.95;
F5= 23.69;
Trefrig = @(location,state)F1*state.time^4 + F2*state.time^3 + F3*state.time^2 + F4*state.time + F5;
thermalBC(thermalmodel,"Edge",7,...
                       "ConvectionCoefficient",hrefrig,...
                       "AmbientTemperature",Trefrig)

For further information, I recommend

https://uk.mathworks.com/help/pdf_doc/pde/pde.pdf

[John McGrath]

Thanks for pointing out the pde document

john

[Torsten]

And the code fragment does not work ?

[John McGrath]

To test it I just tried to plot the transient Trefrig with code below. MatLab comes back with

Error using plot

Invalid data argument.

Error in untitled55 (line 16)

plot(tlist, Trefrig);

tlistmin= 0;                                                                   % Minimum time (s)
tlistmax= 300;                                                              % Maximum time (s)
tlistdelta= (tlistmax-tlistmin)/100                       % time step

tlist=tlistmin:tlistdelta:tlistmax

F1= 3.843e-8
F2= -3.482e-5
F3= 1.179e-2
F4= -1.95
F5= 23.69

Trefrig = @(location,state)F1*state.time^4 + F2*state.time^3 + F3*state.time^2 + F4*state.time + F5;

figure
plot(tlist, Trefrig); 

grid on
title("Trefrig")
xlabel("Time, seconds")
ylabel("Temperature, degrees-Celsius")

[Walter Roberson]

Trefrig = @(location,state)F1*state.time^4 + F2*state.time^3 + F3*state.time^2 + F4*state.time + F5;

Okay, Trefrig is the handle to an anonymous function.

plot(tlist, Trefrig); 

You are trying to plot passing in a numeric vector, and a function handle. plot() is not able to process function handles.

Your Trefrig function handle ignores the first parameter, and instead uses state.time from the second parameter. However, you have not defined any structure or "object" at all, let alone one with a time field.

[Torsten]

The function handle "Trefrig" is constructed to be used by the PDE Toolbox, not for plotting.

If you want to plot, use

tlistmin= 0;                                                                   % Minimum time (s)
tlistmax= 300;                                                              % Maximum time (s)
tlistdelta= (tlistmax-tlistmin)/100;                       % time step
tlist=tlistmin:tlistdelta:tlistmax;
F1= 3.843e-8;
F2= -3.482e-5;
F3= 1.179e-2;
F4= -1.95;
F5= 23.69;
Trefrig = @(t)F1*t.^4 + F2*t.^3 + F3*t.^2 + F4*t + F5;
plot(tlist,Trefrig(tlist))

[John McGrath]

This plotting code worked. Thanks Torsten

I'd like to return to your original suggested code to produce the transient thermal boundary condition that I seek.

I ran into a problem when I copied and pasted your code into the Command Window.

F1= 3.843e-8;

F2= -3.482e-5;

F3= 1.179e-2;

F4= -1.95;

F5= 23.69;

Trefrig = @(location,state)F1*state.time^4 + F2*state.time^3 + F3*state.time^2 + F4*state.time + F5;

thermalBC(thermalmodel,"Edge",7,...

"ConvectionCoefficient",hrefrig,...

"AmbientTemperature",Trefrig)

The errors returned are these:

Error using pde.ThermalBC (line 87)

The value of 'AmbientTemperature' is invalid. Must be specified as a numeric value.

Error in pde.ThermalModel/thermalBC (line 154)

bc = pde.ThermalBC(self.BoundaryConditions,argsToPass{:});

Error in untitled205 (line 7)

thermalBC(thermalmodel,"Edge",7,...

My understanding is that you have defined an anonymous function [Trefrig] and use its handle to specify the time-varying boundary condition in the thermalBC line of code. I don’t understand why the error occurs.

I have some related questions. When you use “@location,state)”, is it understood that location refers to “Edge”,7 and state refers to state.time? In my original code I defined a time variable tlist as well as the minimum time, the maximum time and the time increment. How are those values defined for your code using state.time?

[Torsten]

I don’t understand why the error occurs.

@Walter Roberson wrote that the ambient temperature can only be specified as a constant value, not as a time-varying function handle. You will have to check the documentation of the PDE Toolbox.

I have some related questions. When you use “@location,state)”, is it understood that location refers to “Edge”,7 and state refers to state.time? In my original code I defined a time variable tlist as well as the minimum time, the maximum time and the time increment. How are those values defined for your code using state.time?

If the ambient temperature could be specified as a time-varying function handle (see above), the function is called by the PDE Toolbox solver during the integration and returns your ambient temperature, evaluated at the time "state.time" when the solver needs it to know. It's not possible to set it in the way you did.

Answer 2

[Walter Roberson]

function Trefrig = Trefrig(state.time)
thermalBC(thermalmodel,"Edge",7,...
    "ConvectionCoefficient",hrefrig,...
    "AmbientTemperature", @Trefrig)

First of all: when you define a function then the list of parameters must be strictly unindexed variables. You cannot designate the field of a structure to receive data.

Second of all, attempting to assign the output to the same name as the function would be an attempt to convert between the name representing a function and the name representing a variable, and is no longer permitted.

Thirdly: neither thermalmodel nor hrefrig are defined inside the function.

Fourthly: you are passing @Trefrig as the AmbientTemperature parameter. That is a handle to the exact same function you are defining. The intent is almost certainly that the function handle would be invoked -- but invoking it would cause termalBC to be called again, which would pass in @Trefrig which would lead to @Trefrig being called again, which would call termalBC again which... If you are going to deliberately construct recursive code, you need to ensure that you have an escape condition before blindly calling the function again.

Fifthly: the AmbientTemperature parameter accepts scalar numeric values only, not a function handle.

[John McGrath]

Thank you for your help. I understand that I did many things incorrectly but I am not sure how best to rectify them. I have tried to modify my code based on your comments but I confess that I don't understand all of them well enough to correct what I did wrong. I understand from MatLab PFDE Users Guide and online info that I can use an anonymous function to deal with time varying boundary conditions. I believe that means that I could replace line 1 of the code above with soemthing like:

Trefrig=@(location,state)F1*state.time^4+F2*state.time^3+F3*state.time^2+F4*state.time+F5

and then modfiy the thermalBC code by invoking Trefrig rather than using @Trefrig.

I think that this approach would address many of your comments but it doesn't seem that it addresses all of them since I have been trying variations of this but have not been successful achieving a solution that works. Another question I have with this approach is how to define the time limits and increment for state.time

I'm getting errors

Error using pde.ThermalBC (line 87)

The value of 'AmbientTemperature' is invalid. Must be specified as a numeric value.

Error in pde.ThermalModel/thermalBC (line 154)

bc = pde.ThermalBC(self.BoundaryConditions,argsToPass{:});

Error in untitled208 (line 18)

thermalBC(thermalmodel,"Edge",7,...

[Walter Roberson]

AmbientTemperature cannot be set to a function handle. This is unlike most of the other parameters, which mostly can be set to function handles.

[John McGrath]

So what is the proper way to model a time-varying Ambient Temperature? The error message indicates that it must be a numeric value but the Ambient Temperature is not a single value, it's a vector of numeric values, one for each time.

thanks

[Torsten]

You will have to define your problem as a general PDE, not as a heat transfer problem.

Look at page 2-127 of the linked User Guide for the PDE Toolbox on how to define a general Neumann boundary condition on edge 7 for a general PDE.