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July 10, 2003, 15:15 
Analytical Solution of 1D Convection Diffusion Eq.

#1 
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Hi,
I am looking for reference on analytical solution for one dimensional steadystate convectiondiffusion equation. Regards, SK. 

July 11, 2003, 00:27 
Re: Analytical Solution of 1D Convection Diffusion

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July 14, 2003, 03:55 
Re: Analytical Solution of 1D Convection Diffusion

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If i have understood ur question in right sense. It is available in most of the heat and mass transfer textbooks. (I understood that u need a solution for a 1D mass transfer problem by diffusion and by convection)


July 14, 2003, 12:37 
Re: Analytical Solution of 1D Convection Diffusion

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Hi,
Thanks you very much for your response ! I am looking for the method of ananytical solution of STEADY ONEDIMENSIONAL CONVECTIONDIFFUSION EQUATION. It is the Equation5.4 Section5.2 at Page80 of " NUMERICAL HEAT TRANSFER AND FLUID FLOW" by PATANKAR. The exact analytical solution is given in the same reference in Section5.2.3 at Page85. I am looking for the reference book which describes the method for getting above mentioned solution. Regards, SK. 

July 14, 2003, 13:53 
Re: Analytical Solution of 1D Convection Diffusion

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If it's the equation
dc/dt + c(dc/dx) = nu*d2c/dx2 then the solution can be found using the ColeHopf transformation as outlined in "Linear and Nonlinear Waves" by G. B. Whitham, chap. 4. The procedure is remarkably straightforward and consists of transforming the equation to remove the nonlinear term. (Sorry, I don't have Patankar's book on hand) 

July 14, 2003, 19:21 
Re: Analytical Solution of 1D Convection Diffusion

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I should have added that the steady state solution can be found by looking at the behavior of the full solution for large time.


July 15, 2003, 03:11 
Re: Analytical Solution of 1D Convection Diffusion

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hi as i dont have the book specified by u. i was not able to refer it. still i belive that i can help u in getting the solution if i know the nature of the problem exactly.Is it a heat transfer problem? or mass transfer problem? or mixed one? What is the equation and varaiables involved and the boundary conditions? u can mail me to kmbahamed@rediffmail.com


July 15, 2003, 14:05 
Re: Analytical Solution of 1D Convection Diffusion

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for the following equation U(d(phi)/dx) = nu*d2(phi)/dx2 Phi being any variable, you can use solution to second order ODE with constant coefficients (Ref: Kreyszig, Engineering Math.). It will have exp(+/) function as the basis solutions, constants will be determined from BC. If I recall correctly, that's what is described in Patankar's book. Note: ag gave a better (i.e. more general) answer to convectiondiffusion equation in this message thread


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