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Analytical Solution of 1D Convection Diffusion Eq.

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Old   July 10, 2003, 16:15
Default Analytical Solution of 1D Convection Diffusion Eq.
  #1
Suman Kumar
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Hi,

I am looking for reference on analytical solution for one dimensional steady-state convection-diffusion equation.

Regards,

SK.
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Old   July 11, 2003, 01:27
Default Re: Analytical Solution of 1D Convection Diffusion
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Markus Lummer
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Try

www.math.umn.edu/~olver/appl_/npd.pdf

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Markus
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Old   July 14, 2003, 04:55
Default Re: Analytical Solution of 1D Convection Diffusion
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K.M. BAZEETH AHAMED
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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)
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Old   July 14, 2003, 13:37
Default Re: Analytical Solution of 1D Convection Diffusion
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Suman Kumar
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Hi,

Thanks you very much for your response ! I am looking for the method of ananytical solution of STEADY ONE-DIMENSIONAL CONVECTION-DIFFUSION EQUATION. It is the Equation-5.4 Section-5.2 at Page-80 of " NUMERICAL HEAT TRANSFER AND FLUID FLOW" by PATANKAR. The exact analytical solution is given in the same reference in Section-5.2.3 at Page-85. I am looking for the reference book which describes the method for getting above mentioned solution.

Regards, SK.
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Old   July 14, 2003, 14:53
Default Re: Analytical Solution of 1D Convection Diffusion
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ag
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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 Cole-Hopf 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)
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Old   July 14, 2003, 20:21
Default Re: Analytical Solution of 1D Convection Diffusion
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ag
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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.
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Old   July 15, 2003, 04:11
Default Re: Analytical Solution of 1D Convection Diffusion
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K.M. BAZEETH AHAMED
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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
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Old   July 15, 2003, 15:05
Default Re: Analytical Solution of 1D Convection Diffusion
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MT
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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 convection-diffusion equation in this message thread

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