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Integrating volumetric heat generation in COMSOL
Posted 12 ago 2014, 19:22 GMT-4 1 Reply
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Hi all,
I solved four first order non-linear differential equations of the form
d(y1)/dx=-A*y1+B*y2
d(y2)/dx=A*y2-B*y1
d(y3)/dx=-C*y3+D*(y1+Y2)-E*(y3-y4)
d(y4)/dx=C*y4-D*(y1+y2)-E*(y3-y4)
with four Dirichlet boundary conditions using coefficient form PDE solver (using the itarative solver). The constants A through E are known.
The volumetric heat generation term E_th is related to the above variables with the following differential equation,
d(E_th)/dx=F*(y1+y2)+G*(y3+y4) where F and G are known constants.
I am thinking of coupling the above stated heat generation term after integration to the heat transfer module as a source term.
What is the most efficient way to integrate and couple the volumetric heat generation term to the heat transfer module?
thank you,
Indika.
I solved four first order non-linear differential equations of the form
d(y1)/dx=-A*y1+B*y2
d(y2)/dx=A*y2-B*y1
d(y3)/dx=-C*y3+D*(y1+Y2)-E*(y3-y4)
d(y4)/dx=C*y4-D*(y1+y2)-E*(y3-y4)
with four Dirichlet boundary conditions using coefficient form PDE solver (using the itarative solver). The constants A through E are known.
The volumetric heat generation term E_th is related to the above variables with the following differential equation,
d(E_th)/dx=F*(y1+y2)+G*(y3+y4) where F and G are known constants.
I am thinking of coupling the above stated heat generation term after integration to the heat transfer module as a source term.
What is the most efficient way to integrate and couple the volumetric heat generation term to the heat transfer module?
thank you,
Indika.
1 Reply Last Post 13 ago 2014, 18:26 GMT-4
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Posted:
10 years ago
Hello,
First, I don't see why the system is non-linear, unless parameters A, ..., E were functions of y1, ..., y4.
You can integrate the expression to get E_th in several ways:
1. Defining an integration operator (in 'Definitions/Component couplings/Integration') .You have to define the domain (for you in x) where to apply the integration, and then just use the operator with the variable or expression to integrate as an argument, like intop1(F*(y1+y2)+G*(y3+y4)).
2. With the 'integrate' operator (syntax: integrate(expr, var, lower, upper)).
3. There are other ways, like adding PDE's or ODE's ...
Finally, you could just add a fifth equation, the heat equation, and in it add a 'Heat Source' node for the domain, and in the value 'General Source' write just E_th if you defined it as an expression, or directly the value of the integral if you use an operator.
I think you don't need more.
Jesus.
First, I don't see why the system is non-linear, unless parameters A, ..., E were functions of y1, ..., y4.
You can integrate the expression to get E_th in several ways:
1. Defining an integration operator (in 'Definitions/Component couplings/Integration') .You have to define the domain (for you in x) where to apply the integration, and then just use the operator with the variable or expression to integrate as an argument, like intop1(F*(y1+y2)+G*(y3+y4)).
2. With the 'integrate' operator (syntax: integrate(expr, var, lower, upper)).
3. There are other ways, like adding PDE's or ODE's ...
Finally, you could just add a fifth equation, the heat equation, and in it add a 'Heat Source' node for the domain, and in the value 'General Source' write just E_th if you defined it as an expression, or directly the value of the integral if you use an operator.
I think you don't need more.
Jesus.