Formulation {

// Required for temperature initialization from other results
 { Name getdpThermalInitialization; Type FemEquation ;
    Quantity {
      { Name T  ; Type Local  ; NameOfSpace Hgrad_T ; }

    }
    Equation {
      Galerkin { [  Dof{T}, {T} ] ;
        In Region[Vol_The] ; Jacobian JVol ; Integration I1 ; }
      Galerkin { [ -ScalarField[XYZ[]]{0}, {T} ] ;
        In Region[Vol_The] ; Jacobian JVol ; Integration I1 ; }

      Galerkin { [ +ScalarField[XYZ[]]{0}, {T} ] ;
        In Region[moved_domains] ; Jacobian JVol ; Integration I1 ; }
      Galerkin { [ -ScalarField[new_xyz[]]{0}, {T} ] ;
        In Region[moved_domains] ; Jacobian JVol ; Integration I1 ; }
    }
  }

  { Name cFormulation ; Type FemEquation;
    Quantity {
      { Name T;  Type Local; NameOfSpace Hgrad_T; }
	  { Name hflux;  Type Local; NameOfSpace Hgrad_flux; }	 
	  { Name U_h;  Type Global; NameOfSpace Hgrad_flux [U_hflux]; }	 
	  { Name hrflux;  Type Local; NameOfSpace Hrgrad_flux; }	 
	  { Name U_hr;  Type Global; NameOfSpace Hrgrad_flux [U_hrflux]; }	
	 
     If (#Sur_RESISTANCE_T_List())
		{ Name Tresistance ; Type Local ; NameOfSpace Hgrad_T[Tresistance] ; }
	  EndIf
	  If(Flag_MagTherm==2)
	  { Name a ; Type Local ; NameOfSpace Hcurl_a_Mag_2D; }
      { Name ur; Type Local ; NameOfSpace Hregion_u_Mag_2D; }
      { Name istr ; Type Local ; NameOfSpace Hregion_i_Mag_2D ; }
	  EndIf
	  If(Flag_MagTherm==3)
	  { Name a ; Type Local ; NameOfSpace Hcurl_a_3D; }
      { Name e; Type Local ; NameOfSpace Hregion_u_3D; }
      { Name e0  ; Type Local ; NameOfSpace Hregion_u0_3D ; }
	  EndIf

    }
    Equation {
      Galerkin { [ lambda[{T}] * Dof{d T} , {d T} ];
                 In Vol_The; Integration I1; Jacobian JVol;  }
  	  If (#Sur_RESISTANCE_T_List())
		Galerkin { [ ( 1/resistance_thermal[] ) * Dof{Tresistance} , {Tresistance} ] ;
			In Sur_RESISTANCE_T; Integration I1 ; Jacobian JSur ; }
	  EndIf
		
      Galerkin { DtDof [ rho[{T}] * cp[{T}] * Dof{T} , {T} ];
                 In Vol_The; Integration I1; Jacobian JVol;  }	  
      Galerkin { [ -qVol[{T}, $Time] , {T} ];
                 In Vol_The; Integration I1; Jacobian JVol;  }
	  Galerkin { [ rho[{T}] * cp[{T}] * _velocityEffects[]*Vector[Velocity_x[$Time], Velocity_y[$Time], Velocity_z[$Time]] * Dof{Grad T} ,{T}];
				 In Vol_The; Integration I1; Jacobian JVol;}
	  Galerkin { [ rho[{T}] * cp[{T}] * _velocityEffects[]*Omega_Z[]*Vector[-Y[], X[], 0] * Dof{Grad T},{T}];
				 In Vol_The; Integration I1; Jacobian JVol;}

	  If(Flag_MagTherm==2)
      Galerkin { [ -steinmetz_k[]*1e6* (Freq*1e-3)^steinmetz_a[] * <a>[Norm[{d a}] ]^steinmetz_b[], {T} ];
                 In non_conducting_domain; Integration I1; Jacobian JVol;  }
	  Galerkin { [ -0.5 * sigma[{T}[1]] * <a>[SquNorm[Dt[{a}]+{ur}/GeomCoeff[]]], {T} ];
				 In conducting_domain; Integration I1; Jacobian JVol;  }	
	  Galerkin { [ -0.5 * sigma[{T}[1]] * <a>[SquNorm[Dt[{a}]+{ur}/GeomCoeff[]]], {T} ];
				 In source_domain; Integration I1; Jacobian JVol;  }
	  Galerkin { [ -0.5*SquNorm[Nc[]*{istr}/area[]]/(FillFactor[]*sigma[{T}[1]]), {T} ];
				 In stranded_source_domain; Integration I1; Jacobian JVol;  }		 
      Galerkin { [ -0.5 * Re[(1+Complex[0,1])* Sqrt[3.14*Freq/(nu[{d a}, {T}[1]]*sigma[{T}[1]])]] * SquNorm[1/((1+Complex[0,1])* Sqrt[3.14*Freq/(nu[]*sigma[{T}[1]])]) *  <a>[(Dt[{a}]+{ur})] ] , {T} ];
                 In Sur_SIBC_B; Integration I1; Jacobian JSur;  }
	  EndIf

	  If(Flag_MagTherm==3)
      Galerkin { [ -steinmetz_k[]*1e6* (Freq*1e-3)^steinmetz_a[] * <a>[Norm[{d a}] ]^steinmetz_b[], {T} ];
                 In non_conducting_domain; Integration I1; Jacobian JVol;  }
      Galerkin { [ -0.5 * sigma[{T}[1]] * <a>[SquNorm[Dt[{a}]+{e}]], {T} ];
                 In conducting_domain ; Integration I1; Jacobian JVol;  }
      Galerkin { [ -0.5 * sigma[{T}[1]] * <a>[SquNorm[Dt[{a}]+{e}]], {T} ];
                 In source_domain ; Integration I1; Jacobian JVol;  }
      Galerkin { [ -0.5*FillFactor[]/Fs[Sqrt[cross_section_area[]*4/3.14]*Sqrt[3.14*Freq*sigma[{T}[1]]/(2*nu[{d a}, {T}[1]])]]*SquNorm[1.0/cross_section_area[]/(Norm[{e0}])*({e})]/sigma[{T}[1]], {T} ];
                 In stranded_source_domain ; Integration I1; Jacobian JVol;  }
      Galerkin { [ -0.5 * Re[(1+Complex[0,1])* Sqrt[3.14*Freq/(nu[]*sigma[{T}[1]])]] * SquNorm[1/((1+Complex[0,1])* Sqrt[3.14*Freq/(nu[]*sigma[{T}[1]])]) *  <a>[(Dt[{a}]+{e})] ] , {T} ];
                 In Sur_SIBC_B; Integration I1; Jacobian JSur;  }
	  EndIf


      Galerkin { [ -qSurf[{T}, $Time] , {T} ];
                 In Region[{Sur_HEATFLUX_T, Sur_COMBINED_T}]; Integration I1; Jacobian JSur;  }
				 				 
      Galerkin { [ h[{T}, $Time] * Dof{T} , {T} ] ;
                 In Region[{Sur_CONVECTIVE_T, Sur_COMBINED_T}] ; Integration I1; Jacobian JSur;  }
      Galerkin { [ -h[{T}, $Time] * tref[] , {T} ] ;
                 In Region[{Sur_CONVECTIVE_T, Sur_COMBINED_T}] ; Integration I1; Jacobian JSur;  }

	  If(radiationNLFlag==1)
		  Galerkin { [ hr[{T}] * sb_constant * (({T}+273.)^4) , {T} ] ;
					 In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ; Integration I1; Jacobian JSur;  }

		  Galerkin { [ - hr[{T}] * sb_constant * ((tref[]+273.)^4) , {T} ] ;
					 In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ; Integration I1; Jacobian JSur;  }

		  Galerkin { JacNL[ hr[{T}] * sb_constant * 4 * (({T}+273.)^3) * Dof{T} , {T} ] ;
					 In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ; Integration I1; Jacobian JSur;  }
					 
		  Galerkin { JacNL[ - hr[{T}] * sb_constant * 4 * (({T}+273.)^3) * {T} , {T} ] ;
					 In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ; Integration I1; Jacobian JSur;  }
	  EndIf
				 

      Galerkin { [ -qSurfInt[{T}, $Time]/SurfaceArea[], {T} ];
                 In Region[{Sur_HEATFLOW_T}]; Integration I1; Jacobian JSur;  }
				 
      Galerkin { [ -qSurfInt[{T}, $Time]/SurfaceArea[] , {T} ];
                 In Region[{Sur_COMBINED_T}]; Integration I1; Jacobian JSur;  }

// Thermal loss calculation
      GlobalTerm { [ Dof{U_h} , {U_h} ]  ; In Region[{Sur_CONVECTIVE_T, Sur_COMBINED_T}] ;  }
      Galerkin { [ -h[{T}, $Time] *( tref[])/SurfaceArea[], {hflux} ]  ; 
				  In Region[{Sur_CONVECTIVE_T, Sur_COMBINED_T}] ; Jacobian JSur; Integration I1; }	
      Galerkin { [ h[{T}, $Time] *( Dof{T})/SurfaceArea[], {hflux} ]  ; 
	             In Region[{Sur_CONVECTIVE_T, Sur_COMBINED_T}] ; Jacobian JSur; Integration I1; }

      GlobalTerm { [ Dof{U_hr} , {U_hr} ]  ; In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ;  }
      Galerkin { [ - hr[{T}, $Time] * sb_constant*((tref[]+273.)^4)/SurfaceArea[] , {hrflux} ]  ; 
	             In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ; Jacobian JSur; Integration I1; }
      Galerkin { [ hr[{T}, $Time] * sb_constant*(({T}+273.)^4)/SurfaceArea[] , {hrflux} ]  ; 
	             In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ; Jacobian JSur; Integration I1; }
				 
	  Galerkin { [ -hr[{T}] * sb_constant * 4 * (({T}+273.)^3)/SurfaceArea[] * {T} , {hrflux} ] ;
				 In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ; Integration I1; Jacobian JSur;  }					 
	  Galerkin { [  hr[{T}] * sb_constant * 4 * (({T}+273.)^3)/SurfaceArea[] * Dof{T} , {hrflux} ] ;
     			 In Region[{Sur_RADIATION_T, Sur_COMBINED_T}] ; Integration I1; Jacobian JSur;  }	

    }
  }
}