# Normal Derivative values at boundary

**URL:** <https://community.freefem.org/t/normal-derivative-values-at-boundary/1249>\
**Category:** General Discussion\
**Created:** [October 7, 2021, 7:31am UTC](https://community.freefem.org/t/normal-derivative-values-at-boundary/1249 "2021-10-07T07:31:57Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![sumantkr](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/sumantkr/32/2681_2.png) [@sumantkr](https://community.freefem.org/u/sumantkr)\
**Post date:** [October 7, 2021, 7:31am UTC](https://community.freefem.org/t/normal-derivative-values-at-boundary/1249/1 "2021-10-07T07:31:57Z")

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Dear All

I am trying to get the normal derivative value at a specified boundary.

for this I have written code as:

```auto
real Nu = int1d(Th, hot)( dx(T)*N.x + dy(T)*N.y); 

for( int n1 = 0; n1<=20 ; n1++)
{ court<< Nu(20/n1, 0) << endl;
}

```

Am I right for Nu values at a boundary hot.

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<div class="post-metadata">

**Author:** ![Jamal](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/jamal/32/1527_2.png) [@Jamal](https://community.freefem.org/u/Jamal)\
**Post date:** [August 7, 2022, 11:24am UTC](https://community.freefem.org/t/normal-derivative-values-at-boundary/1249/3 "2022-08-07T11:24:36Z")

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```auto
varf vNeuman(used,v) = int1d(Th)(v*(dx(Uex)*N.x+dy(Uex)*N.y)/lenEdge);
Vh vn; // Finite element function to store the Normal derivative
vn[]= vNeuman(0,Vh);

plot(vn,wait=1);

```

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<div class="post-metadata">

**Author:** ![jna1g18](https://avatars.discourse-cdn.com/v4/letter/j/77aa72/32.png) [@jna1g18](https://community.freefem.org/u/jna1g18)\
**Post date:** [September 21, 2023, 10:52am UTC](https://community.freefem.org/t/normal-derivative-values-at-boundary/1249/4 "2023-09-21T10:52:14Z")

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Why do you integrate the normal derivative over the boundary?

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**Author:** ![cmd](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/cmd/32/67_2.png) [@cmd](https://community.freefem.org/u/cmd)\
**Post date:** [September 21, 2023, 12:10pm UTC](https://community.freefem.org/t/normal-derivative-values-at-boundary/1249/5 "2023-09-21T12:10:29Z")

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See my solution in [this post](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/7).