# Rate of change in temperature at everypoint on a heated circle

**URL:** https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708
**Category:** General Discussion
**Created:** [September 15, 2023, 1:53am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708 "2023-09-15T01:53:52Z")
**Posts on this page:** 20
**Page:** 1

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 15, 2023, 1:53am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/1 "2023-09-15T01:53:52Z")

</div>

I solved a natural convection problem in a circle of radius r=0.1 with center (x0,y0)=(0.5,0.0.2\*sqrt(3)). Now I am trying to find the rate of heat transfer i.e.  
∂T/∂n  
where n is normal at a point on a circle where we have to compute the rate of heat transfer as mentioned in the following figure.

 ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/7/7c636c9435c82e1212ec40a429dc4428a2cb3185.png)  
Could you please guide me to find the rate of heat transfer on every point of a circle using a loop?  
Thanks

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<div class="post-metadata">

### 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 16, 2023, 4:58am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/2 "2023-09-16T04:58:55Z")

</div>

Something like this?

```auto
mesh Th; // mesh
int BoundaryLabel = 1; // boundary label
real k = 1.0; // thermal conductivity 
int1d(Th,BoundaryLabel)(k*(N.x*dx(T) + N.y*dy(T)));

```

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 16, 2023, 7:04am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/3 "2023-09-16T07:04:46Z")

</div>

> [@cmd](#):
>
> ```auto
> mesh Th; // mesh
> int BoundaryLabel = 1; // boundary label
> real k = 1.0; // thermal conductivity 
> int1d(Th,BoundaryLabel)(k*(N.x*dx(T) + N.y*dy(T)));
> 
> ```

Thanks, Chris for your response.  
Why you take int1d??? I think it is like grad(T)'_[N.x, N.y] at some point on the circle. But the problem is how I can compute grad(T)'_[N.x, N.y] at some specific point of the circle such as (x1,y1), where N.x and N.y should be the x and y compute of the normal “n” on the circle at point (x1,y1). Could you please guide me in this direction or any other which is appropriate?

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 16, 2023, 7:13am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/4 "2023-09-16T07:13:25Z")

</div>

![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/2/225eb2f950be28f257a02ff12ded81d27771f152.jpeg)

@cmd May be this will help you to elaborate on my point.

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<div class="post-metadata">

### 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 16, 2023, 8:33am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/5 "2023-09-16T08:33:44Z")

</div>

Just create a vector like:

```auto
Vh Tx = dx(T);
Vh Ty = dy(T);

```

And then you can evaluate this at any point and compute the heat flux.

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 16, 2023, 8:56am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/6 "2023-09-16T08:56:44Z")

</div>

Thanks @cmd. What about the normal vector “n” at any point? It will be the same and just the change in dx(T) and dy(T)? if not then how I can evaluate N.x and N.y at any point on the circle?

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<div class="post-metadata">

### 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 16, 2023, 11:46am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/7 "2023-09-16T11:46:00Z")

</div>

You can compute it yourself using the known geometry of your mesh. Or you can do something like:

```auto
varf vHF(p,q) = on(BoundaryLabel, p = N.x*dx(T) + N.y*dy(T));
Vh HF;
HF[] = vHF(0,Vh,tgv=1);

```

---

<div class="post-metadata">

### Author: ![marchywka](https://avatars.discourse-cdn.com/v4/letter/m/ee59a6/32.png) [@marchywka](https://community.freefem.org/u/marchywka)
#### Post date: [September 16, 2023, 2:03pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/8 "2023-09-16T14:03:00Z")

</div>

I think the earlier point about trying to do a point wise result is well taken but  
extending on your idea I guess you also flag the dofs that make up the boundary,  
The IND result appears to select the boundary dofs, fwiw.

```auto
load "msh3"
load "medit"
load "isoline"
 load "mjm_dscope_freefem"
real szx=100;
real szy=100;
int nx=50;
int ny=50;
int nc=30;
real r=20;
real[int,int] cp(2,nc);
for(int i=0; i<nc; ++i) 
	{ real t=1.0*i/nc; cp(0,i)=r*cos(t*2.0*pi); cp(1,i)=r*sin(t*2.0*pi); }
border left(t=0, 1){x=-szx/2; y=szy*(t-.5);label=1; }
border top(t=0, 1){x=szx*(t-.5);y=szy/2; label=2; }
border right(t=0, 1){x=szx/2; y=-szy*(t-.5);label=3; }
border bottom(t=0, 1){x=-szx*(t-.5);y=-szy/2; label=4; }
border mycircle(t=0, 1){
P=Curve(cp, 0, nc-1, t);
label=5;
}// EOM

mesh Th = buildmesh(left(-ny)+top(-nx)+right(-nx)+bottom(-ny)+mycircle(nc));
//plot(Th);
//medit("mesh",Th);
fespace Vh(Th,P1);
Vh p,q,ind;
Vh T=x*x;
// https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/6

varf vIND(ind,q) = on(5, ind = 5 );
varf vHF(p,q) = on(5, p = N.x*dx(T) + N.y*dy(T));
Vh HF,IND;
IND[] = vIND(0,Vh,tgv=1);
HF[] = vHF(0,Vh,tgv=1);
cout << " n = "<<HF[].n<<endl;
cout << " ind = "<<IND[]<<endl;
//medit("ind",Th,IND);

/*
meshL Th1=Sline(1024,[x]);
fespace Mh(Th1,P1);
Mh asol=uh(x,x);
Mh anex=uex(x,x);
Mh diff=anex-asol; // =uex(x,x);
//mjmdscopeL(Th1,"names asol anex diff "+nn,asol,anex,diff,"asdf"); // warning do not forget () 
mjmdscopeL(Th1,"names asol anex diff "+nn,asol,anex,diff,"asdf"); // warning do not forget () 

*/
//mjmdscopeL(Th1,"names asol anex diff "+nn,asol,anex,diff); // warning do not forget () 

```

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 17, 2023, 5:32am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/9 "2023-09-17T05:32:48Z")

</div>

Thank you @cmd and @marchywka for your response. I have seen the normal on a curved body can be computed as:  
 ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/d/db17491c91b4a02ac95e405de60ac719aa230742.png)  
where n\_x and n\_y are the x and y components respectively. Since the x and y component of a circle at any point is -cos(theta) and sin(theta) respectively. May, I compute the rate of heat transfer at any point (x\_i,y\_i) on the circle such x\_i=0.5+r_cos(theta), y\_i=0.5+r_sin(theta), where (0.5,0.5) is center of circle and r is radius, using the following expression:  
-cos(theta)_dx(T)(x\_i,y\_i)+sin(theta)dy(T)(x\_i,y\_i), for 0\<theta\<2pi_r

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<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 17, 2023, 5:46am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/10 "2023-09-17T05:46:18Z")

</div>

This gives the following error:  
Compile error :  
line number :19, Curve

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 17, 2023, 7:00am UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/11 "2023-09-17T07:00:06Z")

</div>

Hi @cmd @marchywka the following is the Poisson equation solved in a circle of radius 0.1 and center (0.5, ):

real Mesh=60;  
real ra=0.1;  
border C(t=0,1){x=0.5+ra_cos(2_pi_t);y=0.2_sqrt(3)+ra_sin(2_pi_t);}  
mesh Th=buildmesh(C(Mesh));  
plot(Th,wait=1);  
fespace Vh(Th,P2);  
func f= x_y;  
Vh U,V;  
problem Poisson(U,V,solver=LU)=  
int2d(Th)(dx(U)\*dx(V) + dy(U)\*dy(V))

- int2d(Th)( f\*V )

- 

on(C,U=1) ;  
Poisson;  
real n=11;  
real[int] xx(n),flux(n);  
for(int i=0;i\<n;i++)  
{  
xx[i] = (2_pi_i)/(n-1);  
flux[i]=-cos(xx[i])_dx(U)(0.5+ra_cos(xx[i]),0.2_sqrt(3)+ra_sin(xx[i]))  
-sin(xx[i])_dy(U)(0.5+ra_cos(xx[i]),0.2_sqrt(3)+ra_sin(xx[i]));  
cout\<\<ra_xx[i]\<\<" "\<\<flux[i]\<\<endl;  
}  
macro grad(u) [dx(u),dy(u)]//  
cout\<\<"flux1 = "\<\<((grad(U))'_[N.x,N.y])\<\<endl;  
plot(U);

Now I have computed ∂U/∂n on 500 points on the circle. My way is correct? If yes then how can get the same values on every 500 points using (grad(U))'\*[N.x,N.y] command?

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 18, 2023, 12:45pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/12 "2023-09-18T12:45:38Z")

</div>

@cmd @marchywka could you please give your valuable suggestions on the above posts please. Thanks!

---

<div class="post-metadata">

### Author: ![marchywka](https://avatars.discourse-cdn.com/v4/letter/m/ee59a6/32.png) [@marchywka](https://community.freefem.org/u/marchywka)
#### Post date: [September 18, 2023, 1:07pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/13 "2023-09-18T13:07:03Z")

</div>

Can you upload the code? Did it run? I guess you can do it pointwise  
uising u(x,y) and FF should give you the value at that arbitrary point  
with interpolation If you want to calculate the normal yourself  
its easy for a circle but difficult in general.

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 18, 2023, 1:12pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/14 "2023-09-18T13:12:34Z")

</div>

Yes, @marchywka you are right this is easy for the circle that is why I mentioned this code and computed the required expression using some mathematics, now I want to know how I can get the same results using ((grad(U))'\* [N.x, N.y]) command or some other way which is appropriate for every shape not only circle.

---

<div class="post-metadata">

### 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 18, 2023, 1:33pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/15 "2023-09-18T13:33:36Z")

</div>

The code I gave [here](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/7) should do what you’re asking. If not, please explain why it doesn’t do what you need.

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 18, 2023, 1:39pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/16 "2023-09-18T13:39:15Z")

</div>

How I can extract flux[1], flux[2],…,flux[500] (as I obtained in above), where flux[i] are the rate of change on the circle for 500 different points.

---

<div class="post-metadata">

### 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 18, 2023, 1:43pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/17 "2023-09-18T13:43:59Z")

</div>

The code I provided should give you the flux at each point on the boundary in the array `HF[]`

---

<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 18, 2023, 2:02pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/18 "2023-09-18T14:02:37Z")

</div>

Yes sir @cmd , I got an array for this circle problem (posted by me) as bellow.  
0.009976449806 0.01022786813 0 0.01017127374 0  
0 0.01036609768 0.01010309073 0 0.009996923058  
0 0 0.01026848656 0 0  
0.01005449145 0.01028976586 0 0 0  
0 0 0 0.00988521446 0.00983777796  
0 0.009760014285 0 0 0.009681407371  
0.009626978686 0.009370266281 0 0.009495604429 0  
0 0.00950908328 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0.01026828858 0 0 0  
0.01023723867 0 0.0100778128 0 0.01049083483  
0.01028432381 0.01026328347 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0.009178976079 0 0.008948200174  
0.009317974872 0 0 0 0  
0.009620942578 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0.01017972185  
0.009804091975 0 0.01008043608 0.0103381028 0  
0.01020221113 0 0 0 0.01025413732  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0.01003440996  
0.008979116319 0 0 0.009211466015 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0.01014617075 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0.01015735372 0.009878638772 0 0.009768710773 0  
0 0.009638180034 0 0 0  
0 0 0.009850216655 0 0  
0.009638531588 0.009303229429 0 0.009486680878 0  
0 0.008808276496 0.00892237405 0 0  
0.008736047786 0.008641869733 0 0.008553388845 0.008482261106  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0.009640006896 0 0.009363356954 0 0  
0 0 0 0 0  
0 0.008381280385 0 0 0.008352637005  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0.008178891123 0 0 0.008094416784  
0.007921689614 0 0.008035840762 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0.009187034163 0 0.009467530159  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0.008906538187  
0 0.009034063396 0 0 0  
0 0 0.007920278564 0.0081499919 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0.008781110423 0 0.008897509133 0  
0 0 0 0.008030449285 0  
0.007771554442 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0.008762036982 0 0.008709343918 0.007504656477 0.00766564131  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0.008616690592 0 0.008551253631  
0.00772690838 0 0.007563498948 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0.008481464341 0.008401306223 0  
0.007601874843 0 0.007479486991 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0.008348593026 0 0.008253466641 0.007498606579 0  
0.007430781148 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0.008178010639 0  
0.008169095043 0.007451143256 0 0.007342576625 0  
0 0 0 0 0  
0 0 0 0 0.007081512038  
0.00731168822 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0.008008827717  
0 0.008000198325 0 0 0  
0 0 0 0 0  
0 0 0 0 0.0072574087  
0.007384942941 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0.008004415351 0 0.00789793697 0  
0 0 0 0 0  
0 0.00725077262 0 0.007265244413 0  
0.00709932628 0.007246035103 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0.007883428924 0 0.007768981524 0 0  
0 0 0 0.007245020798 0.007392743923  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0.007796203849 0 0.007662102185  
0 0 0 0 0.007232847062  
0.007291578599 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0 0.00772438426 0 0.00756676888  
0 0 0 0.007308923286 0  
0.007145375743 0 0 0 0  
0 0 0 0 0  
0 0 0 0 0  
0 0.007654159697 0.007484197262 0 0.007355853744  
0.00716194191 0 0 0 0  
0 0 0 0 0  
0 0 0.007611156238 0 0  
0.007549765583 0 0.007423663465

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<div class="post-metadata">

### Author: ![M\_Usman](https://avatars.discourse-cdn.com/v4/letter/m/e5b9ba/32.png) [@M\_Usman](https://community.freefem.org/u/M_Usman)
#### Post date: [September 18, 2023, 2:04pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/19 "2023-09-18T14:04:53Z")

</div>

@cmd I want to plot in 2D on the x-axis surface length means 0 to 2_pi_ra and on the y-axis value of flux. How can I get appropriate data in a .dat file so that I can plot in tecplot.?

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<div class="post-metadata">

### 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 18, 2023, 3:16pm UTC](https://community.freefem.org/t/rate-of-change-in-temperature-at-everypoint-on-a-heated-circle/2708/20 "2023-09-18T15:16:11Z")

</div>

It looks like the data is there. You will have to post-process it to plot it.  
[https://doc.freefem.org/documentation/visualization.html](https://doc.freefem.org/documentation/visualization.html)

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