multiple summation of series (3 variables)

Hello all,

I am trying to solve the triple sum of a series attached but don't seem to be able to do that and cannot do so even having looked at previous threads to similar issues.

The formula should give 3D temperature distribution in a brick but that does not really change the task much :)

h,t,K are constants. x,y,z are the coordinates, a,b,c are the dimensions of the brick and m,n,p are the variables to be summed up.

I have tried to solve it with symsum but do not get a value as the result. This might well be that this is a user mistake as I am not familiar with symbolic variables.

x=0.0575;
y=0.0575;
z=0.045;
t=20;
syms m n p;
T_xyz=h*t-(64*h/(Dc*pi^3))*symsum(symsum(symsum((sin((2*m-1)*pi*x/X))*(sin((2*n-1)*pi*y/Y))*(sin((2*p-1)*pi*z/Thick))*(1-exp(-Dc*t*pi^2*(((2*m-1)^2/X^2)+((2*n-1)^2/Y^2)+((2*p-1)^2/Thick^2))))/(pi^2*(((2*m-1)^2/X^2)+((2*n-1)^2/Y^2)+((2*p-1)^2/Thick^2))*(2*m-1)*(2*n-1)*(2*p-1)),p,1,3),n,1,3),m,1,3);

Please note that I am using X instead of 2a, Y instead of 2b, Thick instead of 2c and Dc instead of K but yet again this should not hamper the functionality.

Any help to move forward would be greatly appreciated.

Many thanks in advance, Valentin

[Basil Saeed]

What are you getting instead? And what do you mean "do not get a value as a result"? Are you trying to get a numerical value? or an expression involving functions (such as exp, log, ...) and constants.

Also, are the variables "Thick", "X", "Y", "Dc" meant to be left undefined or do you assign a numerical value to them before you do the summation?

[Valentin Buchinger]

Dear Basil,

thank you for getting back to me so quickly. What I am getting is sort of an expression which Matlab does not want to solve for me in a second step either. It follows roughly my input expression but with values. It seems though as if some of the parentheses are set differently. Anyhow, I am looking to get a single numerical value to cut the long story short.

Yes I would like to get a numerical value and no function/expression. "Thick", "X", "Y", "Dc" are defined/calculated earlier in the script and are constants.

Cheers

[Basil Saeed]

Hi Valentin,

If your expression does not contain any undefined symbols, then try adding the line:

eval(T_xyz)

to your code (after you preform the summation)

[Valentin Buchinger]

Hi Basil,

thank you for the hint. Now I indeed get a numerical value as the result :) Thanks for the swift support on this.

Cheers

[Stephen23]

@Valentin Buchinger: do NOT use eval for this, it is the wrong tool for the job (not matter how much other beginners will tell you to use it). Use double, just like the symbolic toolbox documentation advises.

https://www.mathworks.com/help/symbolic/functionlist.html

Answer 1

[Stephen23]

The correct tool to use is double.

[Valentin Buchinger]

Thank you very much for the help.

Answer 2

[Basil Saeed]

If your expression does not contain any undefined symbols, then try adding the line:

    eval(T_xyz)

to your code (after you preform the summation)

[Steven Lord]

DON'T use eval. Since T_xyz is a symbolic expression, use the double function instead as recommended in the Release Notes.

[Valentin Buchinger]

Thank you for the help.