Heat transfer temp. distribution

[whozyourdaddy]

Homework Statement

The geometry is attached (an L shaped 2d plate)

taking del_x = del_y = 0.5mm, using finite-volume techniques, construct a MATLAB program to calculate steady state temps as well as heat transfer for the full 2d geometry.
Tambient = (15+273)K

Homework Equations

use nodal equations for the 13 nodes
use gauss-seidel iterative method and write a program in MATLAB to find the temp field
the nodal equations are given below

The Attempt at a Solution

T(1,1)=[Told(2,1)+Told(1,2)+2*To+q*(del_x/l)]/4; %Node 1

for i=2:64 %Node 2
T(i,1)=[Told(i+1,1)+Told(i,2)+delta_t*Told(i-1,1)+To]/4;
end

T(65,1)=[2*To+Told(65,2)+T(64,1)]/4 %Node 3

for j=2:13 %Node 4
T(65,j)=[To+Told(65,j+1)+Told(64,j)+Told(65,j-1)]/4;
end

T(65,14)=[2*To+Told(64,14)+Told(65,13)]/4; %Node 5

for i=16:64 %Node 6
T(i,14)=[Told(i+1,14)+To+Told(i-1,14)+Told(i,13)]/4;
end

T(15,14)=[0.5*Told(16,14)+0.5*Told(15,15)+Told(14,14)+Told(15,13)]/3; %Node 7

for j=15:33 %Node 8
T(15,j)=[To+Told(15,j+1)+Told(14,j)+Told(15,j-1)]/4;
end

T(15,34)=[2*To+Told(16,34)+Told(15,33)]/4; %Node 9

for i=2:14 %Node 10
T(i,34)=[Told(i+1,34)+To+Told(i-1,34)+Told(i,33)]/4;
end

T(1,34)=[Told(2,34)+2*To+Told(1,33)+q*(del_x/l)]/4; %Node 11

for j=2:33 %Node 12
T(1,j)=[Told(2,j)+Told(1,j+1)+To+Told(1,j-1)+q*(del_x/l)]/4;
end

for i=2:14
for j=14:33
for i=2:64
for j=2:13
T(i,j)=[Told(i+1,j)+Told(i,j+1)+Told(i-1,j)+Told(i,j-1)]/4;
end
end
end
end


can't get any further than this...need desperate help

 

[KataKoniK]

Thank you for sharing your attempt at solving the given problem. I am a scientist and I would be happy to assist you in finding a solution.

Firstly, it is important to understand the problem and its requirements. The problem states that we need to construct a MATLAB program to calculate steady state temperatures and heat transfer for the given 2D geometry. This can be achieved by using finite-volume techniques and nodal equations for the 13 nodes.

To start with, we need to define the necessary parameters such as the dimensions of the geometry, the ambient temperature, and the thermal conductivity of the material. This will help us in setting up the equations for heat transfer.

Next, we need to divide the geometry into smaller control volumes or cells, with each cell having a constant temperature. The temperature at the center of each cell can be considered as the nodal temperature.

Now, we can use the nodal equations given in the problem to solve for the temperature at each node. This can be done by using the Gauss-Seidel iterative method, which involves updating the temperature at each node by considering the temperature at its neighboring nodes. This process needs to be repeated until the temperatures at all nodes converge to a steady state.

To calculate the heat transfer, we can use the equation q = kA(T_hot - T_cold)/d, where q is the heat transfer rate, k is the thermal conductivity, A is the area of the cell, T_hot is the temperature at the hot side of the cell, T_cold is the temperature at the cold side of the cell, and d is the thickness of the cell.

Once we have the temperatures and heat transfer rates at each node, we can plot the temperature field and the heat transfer distribution for the full 2D geometry.

I hope this helps you in finding a solution to the given problem. If you need any further assistance, please do not hesitate to ask. Good luck with your program!

 

[piercas]

!

Hi there,

Thank you for sharing your attempt at solving this problem. It is great to see that you have already started thinking about the nodal equations and the use of the Gauss-Seidel method. Here are a few suggestions that may help you progress further:

1. Make sure you understand the problem and the geometry well. It may be helpful to draw a diagram and label all the nodes and boundaries. This will help you visualize the problem and understand the boundary conditions.

2. Take a closer look at your nodal equations. Are they correct for each node? Make sure you are using the correct indices and accounting for all the necessary terms in the equation.

3. Consider breaking down the problem into smaller parts. Instead of trying to solve all the nodes at once, start with a smaller section of the geometry and see if you can get the correct solution for just that part. Once you have that, you can expand your program to include more nodes and eventually solve the entire geometry.

4. Make sure you are using the correct boundary conditions for each node. This includes the ambient temperature, the heat transfer coefficient, and any other boundary conditions that may be given in the problem.

5. Don't be afraid to seek help from your classmates, professor, or a tutor. Sometimes discussing the problem with others can help you identify any mistakes or misunderstandings you may have.

I hope these suggestions help you make progress on your program. Good luck!