How to Solve Complex Temperature Distribution Problems Involving Heated Spheres?

[prathu41]

I don't know where to start and where and i do not understand the problem could you help me out please

In solving for the temperature distribution resulting from two spheres separated by distance and heated to maintain their temperatures equal to unity one derives the following set of infinite equations in coefficients

An + sigma [( Ap*(-1)^ n+p * (n+p)!/n!p! * (R)^-n-p-1] = Sn0

sigma is over the limit p=0 to p=infinity , n=0,1,2,..

where Sno is equal to unity if , and zero otherwise. This infinite set can be truncated to a set of finite equations (N) in the same number of unknowns by considering only the equations and unknowns with n<N . Write a computer program that will solve An for a given value of R and N . Take R=2 and vary N from 2 to 20 and plot the results for Ao. Next, take N=20 and plot Ao versus R as R is varied from 2 to 8. Show the prediction of the following approximate formula:
Ao= 1/(1+R^-1 + R^-4)

 

[willem2]

you need to copy the problem more accurately:

sigma is over the limit p=0 to p=infinity , n=0,1,2,..

THe usage of limit here is incorrect. I'd write: The summation is over the range p=0 to p=infinity.

the n=0,1,2,... isn't part of the summation. you get one equation with n=0, another with n=1 etc.

where Sno is equal to unity if , and zero otherwise.

What is this?


if you can't see what is going on, try to write out a few of the equations for n=0, 1,2

 

[Architeuthis Dux]

I would be happy to help you with solving this problem. First, it is important to understand the problem and what is being asked. From the given information, it seems that the problem involves calculating the temperature distribution between two heated spheres at a given distance. The equations provided involve coefficients and unknowns, and the goal is to create a computer program that can solve for the coefficients (An) for a given value of R and N.

To start, it may be helpful to review the equations provided and make sure you understand exactly what each term represents. Then, you can begin to break down the problem into smaller steps. For example, you could start by writing out the equations for a few different values of N and R to see if you can identify a pattern. This may also help you to understand how the equations change when N and R are varied.

Once you have a good understanding of the problem, you can begin to write the computer program. This may involve using a programming language such as Python or MATLAB. You will need to define the equations, set up a loop to vary N and R, and then plot the results. It may also be helpful to test your program with a few different values of N and R to make sure it is working correctly.

As you work on the problem, it may be helpful to consult with other scientists or professors for guidance and clarification. Additionally, there may be resources available online or in textbooks that can provide further explanation and assistance.

Remember, solving problems is a key part of being a scientist and it takes patience, persistence, and attention to detail. I am confident that with some effort and determination, you will be able to successfully solve this problem.