# Numerical integration of 'T' across a 3D surface

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 March 22, 2006, 17:49 Numerical integration of 'T' across a 3D surface #1 ACFD-student Guest   Posts: n/a Hi folks, Strictly speaking, this is not CFD but it's cloely related. I would be really grateful if anyone could help me out here: I have a three-dimensional surface with approximately 50,000 nodes and a carpet-like distribution of temperature on it. I now need to compute the averaged value of temperature on this surface. Note that the nodes are non-uniformly spaced so that a simple statistical averaging is out of the question. For each node I have the x, y and z-coordinates and the value of the dependent variable T. There is no way that anyone could know the equation of the function T=f(x,y,z) so I need to perform a numerical integration (SIMPSON, TRAPEZOIDAL, etc.) in order to solve the triple integral . The question is: How? Do I start with the integration in x, then extend it to x-y and then finally perform the same thing in x-y-z or do I better start with the whole thing by computing each node with respect to its surrounding nodes? The last point is really a question of what is easier to do unless there are math-packages such as MATHCAD or MATLAB that have a build-in procedure implemented. Thanks a lot for your help. ACFD-student

 March 23, 2006, 02:33 Re: Numerical integration of 'T' across a 3D surfa #2 Harish Guest   Posts: n/a The simplest possibility you can try is T_avg=sum(i=1,n)t_ids_i/S . http://mathworld.wolfram.com/search/...al+integration+ points to the different kinds of integration you can try.But most of the integrations are done on a uniform mesh size in packages so it might be difficult to use matlab or mathcad. -H

 March 23, 2006, 04:19 Re: Numerical integration of 'T' across a 3D surfa #3 Yves Guest   Posts: n/a One way of making the average would be to 1) make a triangulation of your surface 2) compute for each triangle the average temperature by taking the (non-weighted) average of the values in the 3 nodes 3) making the global average by weighting the values on each triangle by its surface

 March 23, 2006, 16:06 Re: Numerical integration of 'T' across a 3D surfa #4 ACFD-student Guest   Posts: n/a Thanks Harish. One question : What is T_ids and how do I compute this? Do you perhaps mean to sub-divide the surface into a number of small faces (sub-areas 'S') where for each face the mean temperature t_ids is computed? I would really appreciate you coming back. Thanks. ACFD-student

 March 23, 2006, 16:16 Re: Numerical integration of 'T' across a 3D surfa #5 ACFD-student Guest   Posts: n/a Yves, thanks for your advise. I think I'll try this. Should you or anyone else have any more thoughts on this, please post a note on this forum. Thanks guys. ACFD-student

 March 23, 2006, 16:51 Re: Numerical integration of 'T' across a 3D surfa #6 Harish Guest   Posts: n/a What I meant was assuming all the small faces are square you can use the four corner points to calculate a mean average for that cell.There are many ways in doing this and is used extensively in Finite volumes.then use that approximation to for that small area as a constant and use it to average. -H

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