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December 27th, 2011, 04:13 AM   #1
Joined: Jun 2010

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Two dimensional heat Equation Laplace Transform

Anybody can help me solving the attached problem..
It is an emergency..
Give me a tip or introduce references for solving the problem..
---------------it is about solving 1d heat transfer pde using laplace trans. and then solving the 2d heat transfer pde using the solution of the 12 pde.

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morteza08 is offline  
December 27th, 2011, 11:47 AM   #2
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Re: Two dimensional heat Equation Laplace Transform

First write your solution as a product of time and space function. Then you will obtain a simple equation for time with a frequency omega and another equation of diffusion relating a and omega in the spatial form. Apply the Laplace transform on this equation, second derivative becomes a product by p^2. Then solve your equation for this new function (in p space) and rewrite the function in the cartesian space by integration. Then write you global function as a sum of the prodcut (space part) X (time part) with coefficient in front, which you choose to respect your boundary conditions (already only some solution of the inital equation should respect part of it). For the two-dimensional problem, same thing by product of functions of different variables which will give you three equations (one for x, one for y and one for t). this is called separation of variable if you are not familiar with it. Good luck!
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December 29th, 2011, 01:35 AM   #3
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Re: Two dimensional heat Equation Laplace Transform

Thank you Dougy.
I am familiar with it.
But I wrote I need the solution using Laplace transformation for both 1d and 2d problems
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