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