CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Analytical solution to this integral?

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   July 28, 2010, 11:00
Default Analytical solution to this integral?
  #1
New Member
 
Anon
Join Date: Apr 2009
Posts: 13
Blog Entries: 1
Rep Power: 16
technophobe is on a distinguished road
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
technophobe is offline   Reply With Quote

Old   July 28, 2010, 11:41
Default solution for the integral
  #2
Member
 
Ramesh K
Join Date: Dec 2009
Location: Bangalore
Posts: 73
Rep Power: 16
RameshK is on a distinguished road
Send a message via Yahoo to RameshK
(-log(cos(alpha)b+a) - log(cos(alpha)))/3
RameshK is offline   Reply With Quote

Old   July 28, 2010, 12:21
Default
  #3
New Member
 
Anon
Join Date: Apr 2009
Posts: 13
Blog Entries: 1
Rep Power: 16
technophobe is on a distinguished road
That was quick!

Thank you very much ramesh - that worked a treat.
technophobe is offline   Reply With Quote

Old   July 28, 2010, 12:48
Default
  #4
Super Moderator
 
Praveen. C
Join Date: Mar 2009
Location: Bangalore
Posts: 342
Blog Entries: 6
Rep Power: 18
praveen is on a distinguished road
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.
praveen is offline   Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
analytical solution of 1D shock tube problem ma Main CFD Forum 10 May 11, 2015 06:20
Oscillating Cylinder in Parallel Flow: Analytical Solution startingcfd Main CFD Forum 7 March 23, 2012 06:49
Analytical solution of poisson equation kostaspan Main CFD Forum 1 April 22, 2010 13:24
IcoFoam parallel woes msrinath80 OpenFOAM Running, Solving & CFD 9 July 22, 2007 03:58
Could anybody help me see this error and give help liugx212 OpenFOAM Running, Solving & CFD 3 January 4, 2006 19:07


All times are GMT -4. The time now is 10:18.