Mixing
Example/Reference needed for Laplace equation coupled with another equation
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I have been trying to solve a heat-exchanger problem where two fluids are separated by a conducting wall between them and the fluids flow perpendicular to each other. So i need to consider two dimensional conduction in this separating wall while heat gets exchanged between the two fluids through this wall.
Are there any examples of analytic solution to a Laplace equation coupled with another ODE ? I have failed to find any such example. Most texts deal with variants of the Laplace operator with different bc(s).
ordinary-differential-equations pde problem-solving laplacian coupling
asked Feb 1 at 17:04
Indrasis MitraIndrasis Mitra
50111
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add a comment |
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I have been trying to solve a heat-exchanger problem where two fluids are separated by a conducting wall between them and the fluids flow perpendicular to each other. So i need to consider two dimensional conduction in this separating wall while heat gets exchanged between the two fluids through this wall.
Are there any examples of analytic solution to a Laplace equation coupled with another ODE ? I have failed to find any such example. Most texts deal with variants of the Laplace operator with different bc(s).
ordinary-differential-equations pde problem-solving laplacian coupling
asked Feb 1 at 17:04
Indrasis MitraIndrasis Mitra
50111
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I don't think you can get closed form solutions for coupled problems like the one you describe. Just for testing purposes you can choose a function satisfying the boundary conditions and add source terms to the pde's so that this function is the actual solution. The problems will be coupled through the boundary conditions.
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– PierreCarre
Feb 1 at 17:11
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@PierreCarre Have a look math.stackexchange.com/questions/3093821/…
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– Indrasis Mitra
Feb 1 at 18:00
add a comment |
$begingroup$
I have been trying to solve a heat-exchanger problem where two fluids are separated by a conducting wall between them and the fluids flow perpendicular to each other. So i need to consider two dimensional conduction in this separating wall while heat gets exchanged between the two fluids through this wall.
Are there any examples of analytic solution to a Laplace equation coupled with another ODE ? I have failed to find any such example. Most texts deal with variants of the Laplace operator with different bc(s).
ordinary-differential-equations pde problem-solving laplacian coupling
asked Feb 1 at 17:04
Indrasis MitraIndrasis Mitra
50111
$endgroup$
I have been trying to solve a heat-exchanger problem where two fluids are separated by a conducting wall between them and the fluids flow perpendicular to each other. So i need to consider two dimensional conduction in this separating wall while heat gets exchanged between the two fluids through this wall.
Are there any examples of analytic solution to a Laplace equation coupled with another ODE ? I have failed to find any such example. Most texts deal with variants of the Laplace operator with different bc(s).
ordinary-differential-equations pde problem-solving laplacian coupling
ordinary-differential-equations pde problem-solving laplacian coupling
asked Feb 1 at 17:04
Indrasis MitraIndrasis Mitra
50111
asked Feb 1 at 17:04
Indrasis MitraIndrasis Mitra
50111
asked Feb 1 at 17:04
Indrasis MitraIndrasis Mitra
50111
asked Feb 1 at 17:04
Indrasis MitraIndrasis Mitra
50111
asked Feb 1 at 17:04
Indrasis MitraIndrasis Mitra
50111
50111
$begingroup$
I don't think you can get closed form solutions for coupled problems like the one you describe. Just for testing purposes you can choose a function satisfying the boundary conditions and add source terms to the pde's so that this function is the actual solution. The problems will be coupled through the boundary conditions.
$endgroup$
– PierreCarre
Feb 1 at 17:11
$begingroup$
@PierreCarre Have a look math.stackexchange.com/questions/3093821/…
$endgroup$
– Indrasis Mitra
Feb 1 at 18:00
add a comment |
$begingroup$
I don't think you can get closed form solutions for coupled problems like the one you describe. Just for testing purposes you can choose a function satisfying the boundary conditions and add source terms to the pde's so that this function is the actual solution. The problems will be coupled through the boundary conditions.
$endgroup$
– PierreCarre
Feb 1 at 17:11
$begingroup$
@PierreCarre Have a look math.stackexchange.com/questions/3093821/…
$endgroup$
– Indrasis Mitra
Feb 1 at 18:00
$begingroup$
I don't think you can get closed form solutions for coupled problems like the one you describe. Just for testing purposes you can choose a function satisfying the boundary conditions and add source terms to the pde's so that this function is the actual solution. The problems will be coupled through the boundary conditions.
$endgroup$
– PierreCarre
Feb 1 at 17:11
$begingroup$
I don't think you can get closed form solutions for coupled problems like the one you describe. Just for testing purposes you can choose a function satisfying the boundary conditions and add source terms to the pde's so that this function is the actual solution. The problems will be coupled through the boundary conditions.
$endgroup$
– PierreCarre
Feb 1 at 17:11
$begingroup$
@PierreCarre Have a look math.stackexchange.com/questions/3093821/…
$endgroup$
– Indrasis Mitra
Feb 1 at 18:00
$begingroup$
@PierreCarre Have a look math.stackexchange.com/questions/3093821/…
$endgroup$
– Indrasis Mitra
Feb 1 at 18:00
add a comment |
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I don't think you can get closed form solutions for coupled problems like the one you describe. Just for testing purposes you can choose a function satisfying the boundary conditions and add source terms to the pde's so that this function is the actual solution. The problems will be coupled through the boundary conditions.
$endgroup$
– PierreCarre
Feb 1 at 17:11
$begingroup$
@PierreCarre Have a look math.stackexchange.com/questions/3093821/…
$endgroup$
– Indrasis Mitra
Feb 1 at 18:00