# [Getdp] trouble with Heat Equation

trophime christophe trophime at labs.polycnrs-gre.fr
Thu Jun 7 12:02:30 CEST 2001

```Hi, I'm back with some stupid questions...

I am trying to set a transient Heat Equation
and I end up with some problems:

1/ which is the default orientation of the normal
on line (or surface)?

My initial formulation expect the normal to be exterior
is this right?

FunctionSpace {
{ Name Hgrad_v_Th ; Type Form0 ;
BasisFunction {
// T = T  s   ,  for all nodes
//      n  n
{ Name sn ; NameOfCoef tn ; Function BF_Node ;
Support Region[ {Domain_Th, SurfaceConvection,
SurfaceHeatFlux} ] ; Entity NodesOf[ All ] ; }
}
Constraint {
{ NameOfCoef tn ; EntityType NodesOf ;
NameOfConstraint FixedTemperature ; }
}
}

// Source heat (fully fixed space)
{ Name Hregion_qth_Heat_Axi ; Type Scalar ;
BasisFunction {
{ Name sr ; NameOfCoef qthsr ; Function BF_Node ;
Support DomainS_Th ; Entity NodesOf[ All ] ; }
}
Constraint {
{ NameOfCoef qthsr ; EntityType NodesOf ;
NameOfConstraint SourceHeatDensity ; }
}
}

}

Formulation {
{ Name Heat_Axi ; Type FemEquation ;
Quantity {
{ Name T ; Type Local ; NameOfSpace Hgrad_v_Th ; }
{ Name Qth ; Type Local ; NameOfSpace Hregion_qth_Heat_Axi ; }
}
Equation {
Galerkin { [ k[] * Dof{d T} , {d T} ] ; In Domain_Th ;
Galerkin { [ -Dof{Qth} , {T} ]; In DomainS_Th ;
Galerkin { [ -h[] * Dof{T} , {T} ]; In SurfaceConvection;
Jacobian SurAxi ; Integration I1; }
Galerkin { [ h[] * T_ambiant[] , {T} ]; In SurfaceConvection;
Jacobian SurAxi ; Integration I1; }
Galerkin { [ -Flux[] , {T} ]; In SurfaceHeatFlux;
Jacobian SurAxi ; Integration I1; }
}
}

2/ how to set both initial and boundary conditions?
I have tried the following:

{ Name FixedTemperature; Type Assign;
Case {
{ Region Region[{Domain_Th, SurfaceConvection,
SurfaceHeatFlux}]; Type Init; Value T_ref;}
{ Region BottomSurfaceInd1; Type Assign; Value T_Bottom;}
{ Region TopSurfaceInd1; Type Assign; Value T_Top;}
{ Region BottomSurfaceInd; Type Assign; Value T_Bottom;}
{ Region TopSurfaceInd; Type Assign; Value T_Top;}
}
}

But I get Neuman BC on the lines where I want to set a Dirichlet BC.

```