# Circuler grid need to be solved by Finite difference method pls help me

• nafiz27me
In summary, the problem at hand is to solve a heat conduction problem for a circular grid using the finite difference method. The two-dimensional equation for this problem is given by 1/r * δ/δr (r * δT/δr) + 1/r^2 * ((δ^2 T)/(δΦ^2 )) = 0. The discretized values for this equation are given by (T_((i,j,k)-T_((i+1,j,k) ) )/Δr)+((T_((i+1.j.k) )+T_((i-1,j,k) )-2T_((i,j,k) ))/(Δr^2 )) +
nafiz27me
Circuler grid need to be solved by Finite difference method! pls help me...

hi this is the picture of the problem.. i have studied the rectangular grid but not the circular grid... now pls someone help me to find out the way to solve a heat conduction problem for circle using finite difference method.

1/r δ/δr (r δT/δr)+ 1/r^2 ((δ^2 T)/(δΦ^2 ))=0
this is the two dimensional equation and the discritise values are below...

1) 1/r δ/δr (r δT/δr)= 1/r (δT/δr)+(δ^2 T)/(δr^2 )=1/r (T_((i,j,k)-T_((i+1,j,k) ) )/Δr)+((T_((i+1.j.k) )+T_((i-1,j,k) )-2T_((i,j,k) ))/(Δr^2 ))

2) 1/r^2 ((δ^2 T)/(δΦ^2 ))= 1/r^2 ((T_((i.j+1.k) )+T_((i,j-1,k) )-2T_((i,j,k) ))/(ΔΦ^2 ))

#### Attachments

• circuler grid.png
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so the final discretized form is: (T_((i,j,k)-T_((i+1,j,k) ) )/Δr)+((T_((i+1.j.k) )+T_((i-1,j,k) )-2T_((i,j,k) ))/(Δr^2 )) + (T_((i.j+1.k) )+T_((i,j-1,k) )-2T_((i,j,k) ))/(ΔΦ^2 )) =0or rearranging the terms, you get:T_((i,j,k)) = (T_((i+1,j,k) ) + (T_((i-1,j,k) )/(Δr^2 )) + (T_((i.j+1.k) )+T_((i,j-1,k) )/(ΔΦ^2 )) / (1/Δr + 1/Δr^2 + 1/ΔΦ^2 )Hope this helps!

## 1. What is a circular grid?

A circular grid is a type of grid used in computational methods, such as the Finite Difference Method, to solve problems involving circular or cylindrical geometries.

## 2. Why is the Finite Difference Method used to solve problems involving circular grids?

The Finite Difference Method is used because it is a numerical method that can handle complex geometries, such as circular grids, and can provide accurate solutions to differential equations.

## 3. How does the Finite Difference Method work?

The Finite Difference Method works by dividing the circular grid into a finite number of smaller cells and approximating the partial derivatives in the differential equations using the values at the neighboring grid points.

## 4. What are the advantages of using the Finite Difference Method to solve problems involving circular grids?

The Finite Difference Method is relatively easy to implement and can handle a wide range of complex geometries. It also provides accurate solutions and can be easily adapted to different boundary conditions.

## 5. Are there any limitations to using the Finite Difference Method for circular grids?

The Finite Difference Method may not be suitable for problems with irregular boundaries or highly non-linear equations. It also requires a fine grid resolution to accurately capture the behavior of the solution, which can be computationally expensive.

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