Fdtxjr

Picking the different solutions to the time independent Schrodinger eqaution

Biological Blimps: Propulsion

Unexpected behavior of the procedure `Area` on the object 'Polygon'

Why "had" in "[something] we would have made had we used [something]"?

Can a College of Swords bard use a Blade Flourish option on an opportunity attack provoked by their own Dissonant Whispers spell?

Does the UK parliament need to pass secondary legislation to accept the Article 50 extension

How can I write humor as character trait?

Did arcade monitors have same pixel aspect ratio as TV sets?

Do the primes contain an infinite almost arithmetic progression?

Keeping a ball lost forever

How does the math work for Perception checks?

Hero deduces identity of a killer

Can disgust be a key component of horror?

Are Captain Marvel's powers affected by Thanos' actions in Infinity War

Why does the Sun have different day lengths, but not the gas giants?

Why would a new[] expression ever invoke a destructor?

How do you respond to a colleague from another team when they're wrongly expecting that you'll help them?

Angel of Condemnation - Exile creature with second ability

Add big quotation marks inside my colorbox

Why does a simple loop result in ASYNC_NETWORK_IO waits?

putting logo on same line but after title, latex

Plot of a tornado-shaped surface

How to hide some fields of struct in C?

How much character growth crosses the line into breaking the character

Laplace equation problem with numerous non-homogeneous BC(s) [Linear Superposition]

RObin problem (Laplace equation)Laplace Equation with Tangential Derivative Prescribed on the BoundaryGreen Solution to Laplace Equation with Robin Boundary ConditionsLaplace equation with non-homogeneous boundary conditions3D Homogenous Laplace equation with integral boundary conditionsLaplacian with Integral BC(s)Evaluating Fourier coefficients to complete a Laplace equation solutionTwo fluids flowing perpendicular in thermal contact with a Wall [Help to mathematically model]Evaluating Coefficients for a Fourier Series when Exponential terms are present [Approach needed]Two-dimensional Laplace equation with weird Robin BC

0

$begingroup$

I need to solve the three-dimensional Laplace equation ($nabla^2T = 0$) where $nabla^2=fracpartial^2partial x^2 +fracpartial^2partial y^2+fracpartial^2partial z^2$ in the domain where $xin[0,L];yin[0,l]$ and $zin[0,w]$. The boundary conditions are
$$Tvert_0,y,z = T_hi, fracpartial Tpartial xvert_L,y,z = 0$$
$$Tvert_x,0,z = T_ci, fracpartial Tpartial yvert_x,l,z = 0$$
$$fracpartial Tpartial zvert_x,y,0 = k_c(Tvert_x,y,0-T_c,av )$$
$$fracpartial Tpartial zvert_x,y,w = k_h(T_h,av - Tvert_x,y,w)$$
Here, $T_c,av = frac12Bigg(T_ci+e^-b_cBigg[T_ci+fracb_clint_0^l e^b_c s/lT(x,s,z)mathrmdsBigg]Bigg)$

and, $T_h,av = frac12Bigg(T_hi+e^-b_hBigg[T_hi+fracb_hLint_0^L e^b_h s/LT(s,y,z)mathrmdsBigg]Bigg)$
As can be seen there are two non-homogeneous Dirichlet conditions and two non-homogeneous Robin conditions. Using, the linear nature of the Laplace operator I am supposed to divide the problem into sub-problems and finally add up all the solutions.

I need help on segregating this problem into smaller ones. I have encountered examples where each problem must have a single non-homogeneous BC.

Secondly, what could be a good guess initial solution form for such problems ?.

pde problem-solving boundary-value-problem heat-equation laplacian

share|cite|improve this question

edited Mar 15 at 2:34

Ethan Bolker

45.1k553120

asked Mar 13 at 5:25

Indrasis MitraIndrasis Mitra

80111

$endgroup$

add a comment | 

0

$begingroup$

I need to solve the three-dimensional Laplace equation ($nabla^2T = 0$) where $nabla^2=fracpartial^2partial x^2 +fracpartial^2partial y^2+fracpartial^2partial z^2$ in the domain where $xin[0,L];yin[0,l]$ and $zin[0,w]$. The boundary conditions are
$$Tvert_0,y,z = T_hi, fracpartial Tpartial xvert_L,y,z = 0$$
$$Tvert_x,0,z = T_ci, fracpartial Tpartial yvert_x,l,z = 0$$
$$fracpartial Tpartial zvert_x,y,0 = k_c(Tvert_x,y,0-T_c,av )$$
$$fracpartial Tpartial zvert_x,y,w = k_h(T_h,av - Tvert_x,y,w)$$
Here, $T_c,av = frac12Bigg(T_ci+e^-b_cBigg[T_ci+fracb_clint_0^l e^b_c s/lT(x,s,z)mathrmdsBigg]Bigg)$

and, $T_h,av = frac12Bigg(T_hi+e^-b_hBigg[T_hi+fracb_hLint_0^L e^b_h s/LT(s,y,z)mathrmdsBigg]Bigg)$
As can be seen there are two non-homogeneous Dirichlet conditions and two non-homogeneous Robin conditions. Using, the linear nature of the Laplace operator I am supposed to divide the problem into sub-problems and finally add up all the solutions.

I need help on segregating this problem into smaller ones. I have encountered examples where each problem must have a single non-homogeneous BC.

Secondly, what could be a good guess initial solution form for such problems ?.

pde problem-solving boundary-value-problem heat-equation laplacian

share|cite|improve this question

edited Mar 15 at 2:34

Ethan Bolker

45.1k553120

asked Mar 13 at 5:25

Indrasis MitraIndrasis Mitra

80111

$endgroup$

add a comment | 

$begingroup$

I need to solve the three-dimensional Laplace equation ($nabla^2T = 0$) where $nabla^2=fracpartial^2partial x^2 +fracpartial^2partial y^2+fracpartial^2partial z^2$ in the domain where $xin[0,L];yin[0,l]$ and $zin[0,w]$. The boundary conditions are
$$Tvert_0,y,z = T_hi, fracpartial Tpartial xvert_L,y,z = 0$$
$$Tvert_x,0,z = T_ci, fracpartial Tpartial yvert_x,l,z = 0$$
$$fracpartial Tpartial zvert_x,y,0 = k_c(Tvert_x,y,0-T_c,av )$$
$$fracpartial Tpartial zvert_x,y,w = k_h(T_h,av - Tvert_x,y,w)$$
Here, $T_c,av = frac12Bigg(T_ci+e^-b_cBigg[T_ci+fracb_clint_0^l e^b_c s/lT(x,s,z)mathrmdsBigg]Bigg)$

and, $T_h,av = frac12Bigg(T_hi+e^-b_hBigg[T_hi+fracb_hLint_0^L e^b_h s/LT(s,y,z)mathrmdsBigg]Bigg)$
As can be seen there are two non-homogeneous Dirichlet conditions and two non-homogeneous Robin conditions. Using, the linear nature of the Laplace operator I am supposed to divide the problem into sub-problems and finally add up all the solutions.

I need help on segregating this problem into smaller ones. I have encountered examples where each problem must have a single non-homogeneous BC.

Secondly, what could be a good guess initial solution form for such problems ?.

pde problem-solving boundary-value-problem heat-equation laplacian

share|cite|improve this question

edited Mar 15 at 2:34

Ethan Bolker

45.1k553120

asked Mar 13 at 5:25

Indrasis MitraIndrasis Mitra

80111

$endgroup$

share|cite|improve this question

edited Mar 15 at 2:34

Ethan Bolker

45.1k553120

asked Mar 13 at 5:25

Indrasis MitraIndrasis Mitra

80111

share|cite|improve this question

edited Mar 15 at 2:34

Ethan Bolker

45.1k553120

asked Mar 13 at 5:25

Indrasis MitraIndrasis Mitra

80111

edited Mar 15 at 2:34

Ethan Bolker

45.1k553120

edited Mar 15 at 2:34

Ethan Bolker

45.1k553120

asked Mar 13 at 5:25

Indrasis MitraIndrasis Mitra

80111

asked Mar 13 at 5:25

Indrasis MitraIndrasis Mitra

80111