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-   -   Analytical solution to this integral? (http://www.cfd-online.com/Forums/main/78623-analytical-solution-integral.html)

technophobe July 28, 2010 10:00

Analytical solution to this integral?
 
Dear All,

I am currently seeking an analytical model for condensation upon various geometries. I am updating a legacy code, which needs an analytical expression to be entered.

My work on this has led me to the point where I need to evaluate the following integral:
\int\frac{(a+2b\cos{\alpha})\sin{\alpha}}{3(a+b\cos{\alpha})\cos{\alpha}}.d\alpha

Can anyone think of a suitable technique to evaluate this integral analytically? I cannot think of a suitable substitution or transformation.

Many thanks,
T

RameshK July 28, 2010 10:41

solution for the integral
 
(-log(cos(alpha)b+a) - log(cos(alpha)))/3

technophobe July 28, 2010 11:21

That was quick!

Thank you very much ramesh - that worked a treat.

praveen July 28, 2010 11:48

Since a technique was asked in the original question, I would add the following. Since \sin\alpha d \alpha = -d(\cos\alpha) the integral becomes an integral of a rational polynomial. You rewrite integrand as A/(a + b\cos\alpha) + B/\cos\alpha which can then be integrated.


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