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December 27th, 2011, 04:13 AM  #1 
Newbie Joined: Jun 2010 Posts: 3 Thanks: 0  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. thanks 
December 27th, 2011, 11:47 AM  #2 
Senior Member Joined: Nov 2011 Posts: 595 Thanks: 16  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 twodimensional 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!

December 29th, 2011, 01:35 AM  #3 
Newbie Joined: Jun 2010 Posts: 3 Thanks: 0  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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dimensional, equation, heat, laplace, transform 
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