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$Date: 2008/12/03 17:02:19 $
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mat5_h_ave(T[1/K],Tinf_htgh[1/K],L_hin[1/m])[W/(m^2*K)]
mat8_h_ave(T[1/K],Tinf_htgh[1/K],W_work[1/m])[W/(m^2*K)]
mat8_h_ave(T[1/K],Tinf_htgh[1/K],W_safety[1/m])[W/(m^2*K)]
mat8_h_ave(T[1/K],Tinf_htgh[1/K],W_micro[1/m])[W/(m^2*K)]
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{"-d(-r*Dlogd_chns*logdr,vr)","-d(-r*Dlogd_chns*logdz,vr)","-d(-r*Dlogd_chns*logdr,vz)","-d(-r*Dlogd_chns*logdz,vz)"}
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{"-d(-r*(eta_chns+etaT_chns)*(vr+uz),logdr)","-d(r*(-2*(eta_chns+etaT_chns)*vz+p),logdr)","-d(-r*(eta_chns+etaT_chns)*(vr+uz),logdz)","-d(r*(-2*(eta_chns+etaT_chns)*vz+p),logdz)"}
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{"-d(-r*Dlogk_chns*logkr,logdr)","-d(-r*Dlogk_chns*logkz,logdr)","-d(-r*Dlogk_chns*logkr,logdz)","-d(-r*Dlogk_chns*logkz,logdz)"}
{"-d(-r*Dlogd_chns*logdr,logdr)","-d(-r*Dlogd_chns*logdz,logdr)","-d(-r*Dlogd_chns*logdr,logdz)","-d(-r*Dlogd_chns*logdz,logdz)"}
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
{"T","u","v","p","logk","logd"}
sqrt(abs(Tr)^2+abs(Tz)^2)
krr_htgh
k_htgh
r*rho_htgh*C_htgh
0
0
0
0
rho_htgh*u_htgh*(H_htgh+0.5*(u_htgh^2+v_htgh^2))
0
0
0
0
r*rho_htgh*C_htgh*u_htgh
-krr_htgh*TSr_htgh-krz_htgh*TSz_htgh
dflux_r_htgh+cflux_r_htgh
0
0
0
0
rho_htgh*v_htgh*(H_htgh+0.5*(u_htgh^2+v_htgh^2))
0
0
0
0
r*rho_htgh*C_htgh*v_htgh
-kzr_htgh*TSr_htgh-kzz_htgh*TSz_htgh
dflux_z_htgh+cflux_z_htgh
sqrt(dflux_r_htgh^2+dflux_z_htgh^2)
sqrt(cflux_r_htgh^2+cflux_z_htgh^2)
sqrt(tflux_r_htgh^2+tflux_z_htgh^2)
r*(krr_htgh*beta_r_htgh^2+krz_htgh*beta_r_htgh*beta_z_htgh+kzr_htgh*beta_z_htgh*beta_r_htgh+kzz_htgh*beta_z_htgh^2)/(beta_r_htgh^2+beta_z_htgh^2+eps)
0.5*h*sqrt(beta_r_htgh^2+beta_z_htgh^2)/(Dm_htgh+eps)
qs_htgh*T
beta_r_htgh*Tr+beta_z_htgh*Tz+r*(-krr_htgh*Trr-krz_htgh*Trz-kzr_htgh*Tzr-kzz_htgh*Tzz)
beta_r_htgh*Tr+beta_z_htgh*Tz+r*(-krr_htgh*Trr-krz_htgh*Trz-kzr_htgh*Tzr-kzz_htgh*Tzz)
beta_r_htgh*Tr+beta_z_htgh*Tz+r*(-krr_htgh*Trr-krz_htgh*Trz-kzr_htgh*Tzr-kzz_htgh*Tzz)
beta_r_htgh*Tr+beta_z_htgh*Tz+r*(-krr_htgh*Trr-krz_htgh*Trz-kzr_htgh*Tzr-kzz_htgh*Tzz)
beta_r_htgh*Tr+beta_z_htgh*Tz+r*(-krr_htgh*Trr-krz_htgh*Trz-kzr_htgh*Tzr-kzz_htgh*Tzz+rho_htgh*C_htgh*Tt)
0
0
0
0
nojac(1/max(2*C_htgh*rho_htgh*sqrt(emetric(u_htgh,v_htgh))/gamma_htgh,48*kmean_htgh/h^2))
h
C_htgh*T/gamma_htgh+pA_htgh/rho_htgh
r
0
0
z
0
0
Sr_htgh*detJ_htgh
Tr
Tz
sqrt(u^2+v^2)
uz-vr
ur+vz+u/r
etaT_chns/sigmad_chns+eta_chns
Cd1_chns*etaT_chns*exp(-logk)*pT_chns-Cd2_chns*rho_chns*exp(logd-logk)
exp(logd)
rho_chns*Cmu_chns*exp(2*logk-logd)
2*ur^2+2*vz^2+(uz+vr)^2+2*u^2/r^2
exp(logk)
etaT_chns/sigmak_chns+eta_chns
etaT_chns*exp(-logk)*pT_chns-rho_chns*exp(logd-logk)
-Dlogk_chns*(r*logkrr+r*logkzz+logkr)-r*(-rho_chns*(logkt+u*logkr+v*logkz)+Dlogk_chns*(logkr^2+logkz^2)+Slogk_chns)
-Dlogd_chns*(r*logdrr+r*logdzz+logdr)-r*(-rho_chns*(logdt+u*logdr+v*logdz)+Dlogd_chns*(logdr^2+logdz^2)+Slogd_chns)
rho_chns*U_chns*h/eta_chns
r*(rho_chns*(ut+u*ur+v*uz)+pr-F_r_chns)+2*(eta_chns+etaT_chns)*(u/r-ur)-(eta_chns+etaT_chns)*r*(2*urr+uzz+vrz)
r*(rho_chns*(vt+u*vr+v*vz)+pz-F_z_chns)-(eta_chns+etaT_chns)*(r*(vrr+uzr)+2*r*vzz+uz+vr)
r*rho_chns*u
r*rho_chns*v
r*(eta_chns+etaT_chns)
r*rho_chns
nojac(1/max(2*rho_chns*sqrt(emetric(u,v)),48*(eta_chns+etaT_chns)/h^2))
0.5*nojac(if(u^2+v^2<sqrt(eps),h*U_ref_chns,(u^2+v^2)/sqrt(emetric(u,v))))
rho_chns*r*divU_chns
nojac(0.5*h/max(rho_chns*U_chns,6*Dlogk_chns/h))
nojac(0.5*h/max(rho_chns*U_chns,6*Dlogd_chns/h))
0
0
0
0
1
1
mat4_rho
mat3_rho
mat2_rho
mat1_rho
mat9_rho((p+p_atm)[1/Pa],T[1/K])[kg/m^3]
mat4_C
mat3_C
mat2_C
mat1_C
mat9_Cp(T[1/K])[J/(kg*K)]
0
0
1
1
1
1
t` mat9_gamma
101325
101325
101325
101325
101325+p
0
0
1
1
1
1
mat9_eta(T[1/K])[Pa*s]
287
0
0
0
0
0
u
0
0
0
0
v
0
1
0.85
100000
Lag2
Lag2
0
0
0
0
1
0.5
1
gls
0.25
0
0
0
0
1
0.01[K]/helem_htgh
0
0
mat4_k
mat3_k
mat2_k
mat1_k
mat9_k(T[1/K])[W/(m*K)]
0
0
mat4_k
mat3_k
mat2_k
mat1_k
mat9_k(T[1/K])[W/(m*K)]
0
0
0
0
0
Sdr_guess_htgh
Sdz_guess_htgh
S0r_guess_htgh
S0z_guess_htgh
1
1
1
0
0
0
0
1
1
mat9_rho((p+p_atm)[1/Pa],T[1/K])[kg/m^3]
mat9_eta(T[1/K])[Pa*s]
0
-g*(rho_chns-rho_ref)
0
0
0
0
0.5
0.5
sc
0.35
1
0.1
0
Lagp2p1
Lagp2p1
-test(nojac(rho_chns)*(nojac(u)*ur+nojac(v)*uz)+pr+2*nojac(eta_chns+etaT_chns)*(u/r-ur)/r-nojac(eta_chns+etaT_chns)*(2*urr+uzz+vrz))*taum_chns*res_u_chns-test(nojac(rho_chns)*(nojac(u)*vr+nojac(v)*vz)+pz-nojac(eta_chns+etaT_chns)*(vrr+uzr+2*vzz+(uz+vr)/r))*taum_chns*res_v_chns-test(divU_chns)*tauc_chns*res_p_chns
0
(d(r,xi1)^2+d(r,xi2)^2)^2+2*(d(z,xi1)*d(r,xi1)+d(z,xi2)*d(r,xi2))^2+(d(z,xi1)^2+d(z,xi2)^2)^2
U_chns
d(r,xi1)^2+d(r,xi2)^2
d(z,xi1)*d(r,xi1)+d(z,xi2)*d(r,xi2)
d(z,xi1)^2+d(z,xi2)^2
-nojac(0.5*min(ck_chns*sqrt((tauc_chns*res_p_chns/(nojac(rhoint_g1_chns/vol_g1_chns)*nojac(sqrt(u2int_g1_chns/vol_g1_chns))))^2+(taum_chns*res_u_chns)^2+(taum_chns*res_v_chns)^2),U_ref_chns)*min(gijgij_chns^(-0.25),rho_chns*U_ref_chns/(48*(eta_chns+etaT_chns))))*rho_chns*r*(g11_chns*(ur*test(ur)+vr*test(vr))+g21_chns*(uz*test(ur)+vz*test(vr))+g21_chns*(ur*test(uz)+vr*test(vz))+g22_chns*(uz*test(uz)+vz*test(vz)))
{0,0,0,0,0}
{0,0,0,0,0}
{1,2,3,4,5}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","-u","0","0","0","0"}
{"0","0","nr_chns*u+nz_chns*v","0","0","0","-logd+0.75*log(Cmu_chns)+1.5*logk-log(kappa_chns)-log(dw_chns)"}
{"0","0","0","0","0","0","0"}
{"0","0","nr_chns*u+nz_chns*v","0","0","0","-logd+0.75*log(Cmu_chns)+1.5*logk-log(kappa_chns)-log(dw_chns)"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","test(-u)","0","0","0","0"}
{"0","0","test(nr_chns*u+nz_chns*v)","0","0","0","test(-logd)"}
{"0","0","0","0","0","0","0"}
{"0","0","test(nr_chns*u+nz_chns*v)","0","0","0","test(-logd)"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
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{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"dVolbnd_htgh*h_htgh*(-T+Tinf_htgh)","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","r*(-rho_chns*Cmu_chns^0.25*exp(0.5*logk)*u/(log(abs(dwplus_chns))/kappa_chns+Cplus_chns)-nr_chns*p)","r*(-rho_chns*Cmu_chns^0.25*exp(0.5*logk)*v/(log(abs(dwplus_chns))/kappa_chns+Cplus_chns)-nz_chns*p)","0","0","0"}
{"dVolbnd_htgh*h_htgh*(-T+Tinf_htgh)","0","0","0","0","0","0"}
{"0","0","r*(-rho_chns*Cmu_chns^0.25*exp(0.5*logk)*u/(log(abs(dwplus_chns))/kappa_chns+Cplus_chns)-nr_chns*p)","r*(-rho_chns*Cmu_chns^0.25*exp(0.5*logk)*v/(log(abs(dwplus_chns))/kappa_chns+Cplus_chns)-nz_chns*p)","0","0","0"}
{"dVolbnd_htgh*h_htgh*(-T+Tinf_htgh)","0","0","0","0","0","0"}
{"dVolbnd_htgh*h_htgh*(-T+Tinf_htgh)","0","0","0","0","0","0"}
{"dVolbnd_htgh*h_htgh*(-T+Tinf_htgh)","0","0","0","0","0","0"}
{"dVolbnd_htgh*h_htgh*(-T+Tinf_htgh)","0","0","0","0","0","0"}
{"dVolbnd_htgh*h_htgh*(-T+Tinf_htgh)","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
1
1
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
3
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","0","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"T","J","u","v","p","logk","logd"}
nr_htgh*dflux_r_htgh+nz_htgh*dflux_z_htgh
rho_htgh*C_htgh*T*(nr_htgh*u_htgh+nz_htgh*v_htgh)
ndflux_htgh+ncflux_htgh
1
1
1
1
1
1
1
1
1
1
1
1
1
1
s
s
s
s
s
s
s
Sr_htgh
(eta_chns+etaT_chns)*(2*nr_chns*ur+nz_chns*(uz+vr))
(eta_chns+etaT_chns)*(2*nr_chns*ur+nz_chns*(uz+vr))
(eta_chns+etaT_chns)*(2*nr_chns*ur+nz_chns*(uz+vr))
(eta_chns+etaT_chns)*(2*nr_chns*ur+nz_chns*(uz+vr))
-nr_chns*p+2*nr_chns*(eta_chns+etaT_chns)*ur+nz_chns*(eta_chns+etaT_chns)*(uz+vr)
-nr_chns*p+2*nr_chns*(eta_chns+etaT_chns)*ur+nz_chns*(eta_chns+etaT_chns)*(uz+vr)
-nr_chns*p+2*nr_chns*(eta_chns+etaT_chns)*ur+nz_chns*(eta_chns+etaT_chns)*(uz+vr)
-nr_chns*p+2*nr_chns*(eta_chns+etaT_chns)*ur+nz_chns*(eta_chns+etaT_chns)*(uz+vr)
(eta_chns+etaT_chns)*(nr_chns*(vr+uz)+2*nz_chns*vz)
(eta_chns+etaT_chns)*(nr_chns*(vr+uz)+2*nz_chns*vz)
(eta_chns+etaT_chns)*(nr_chns*(vr+uz)+2*nz_chns*vz)
(eta_chns+etaT_chns)*(nr_chns*(vr+uz)+2*nz_chns*vz)
-nz_chns*p+nr_chns*(eta_chns+etaT_chns)*(vr+uz)+2*nz_chns*(eta_chns+etaT_chns)*vz
-nz_chns*p+nr_chns*(eta_chns+etaT_chns)*(vr+uz)+2*nz_chns*(eta_chns+etaT_chns)*vz
-nz_chns*p+nr_chns*(eta_chns+etaT_chns)*(vr+uz)+2*nz_chns*(eta_chns+etaT_chns)*vz
-nz_chns*p+nr_chns*(eta_chns+etaT_chns)*(vr+uz)+2*nz_chns*(eta_chns+etaT_chns)*vz
0
0
0
mat6_h_ave(T[1/K],Tinf_htgh[1/K],L_wout[1/m])[W/(m^2*K)]
0
mat8_h_ave(T[1/K],Tinf_htgh[1/K],L_win[1/m])[W/(m^2*K)]
mat8_h_ave(T[1/K],Tinf_htgh[1/K],L_win*2[1/m])[W/(m^2*K)]
mat5_h_ave(T[1/K],Tinf_htgh[1/K],L_hin[1/m])[W/(m^2*K)]
mat8_h_ave(T[1/K],Tinf_htgh[1/K],W_work[1/m])[W/(m^2*K)]
mat8_h_ave(T[1/K],Tinf_htgh[1/K],W_safety[1/m])[W/(m^2*K)]
mat8_h_ave(T[1/K],Tinf_htgh[1/K],W_micro[1/m])[W/(m^2*K)]
mat8_h_ave(T[1/K],Tinf_htgh[1/K],W_mantel[1/m])[W/(m^2*K)]
mat5_h_ave(T[1/K],Tinf_htgh[1/K],L_hout[1/m])[W/(m^2*K)]
273.15
T_amb
273.15
T_inneramb
T_amb
T_inneramb
T_amb
T_amb
T_amb
T_amb
T_amb
273.15
T_outer
273.15
T_inner
273.15
T_inner
273.15
273.15
273.15
273.15
T_outer
0
0
none
epsilon_htgh*sigma_htgh*T^4
J
0
1
273.15
1
0.5*h
100
0
0
0
nr
nz
400
0
0
400
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
exp(logk)
exp(logk)
exp(logk)
exp(logk)
0.005
0.005
0.005
0.005
10
10
10
10
1
1
1
1
0.01
0.01
0.01
0.01
0.05
0.05
0.05
0.05
0.5*h
0.5*h
0.5*h
0.5*h
rho_chns*dw_chns*Cmu_chns^0.25*exp(0.5*logk)/eta_chns
rho_chns*dw_chns*Cmu_chns^0.25*exp(0.5*logk)/eta_chns
rho_chns*dw_chns*Cmu_chns^0.25*exp(0.5*logk)/eta_chns
rho_chns*dw_chns*Cmu_chns^0.25*exp(0.5*logk)/eta_chns
0
0
0
0
t^
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
nr
unr
nr
unr
nz
unz
nz
unz
0
0
0
0
0
0
0
0
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
{1,2,1,1,1,1,1,1,3,4,5,6,7,1,8,1,9,1,10,11}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
{"0","0","0","0","0","0","0"}
1
1
2
3
4
5
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"","","","","","",""}
{"T","J","u","v","p","logk","logd"}
0
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
{1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1}
5.67e-08
8.31451
10
1.44
1.92
1
1.3
0.09
5.5
0.42
mat9_rho(p_atm[1/Pa],T_inneramb[1/K])[kg/m^3]
elirradiation
{"1"}
hemicube
256
4
auto
128
elcplscalar
{"1"}
nojac(rho_chns)
nojac(1)
nojac(max((+(u)^2+(v)^2),(eta_chns/rho_chns/h)^2))
nojac(-1/max(emetric(u,v),(visc_vel_fact_chns*eta_chns/rho_chns)^2*emetric2))
ref
ref
ref
ref
ref
ref
ref
ref
0
0
0
0
0
0
0
0
{"1","2","3","4"}
{"5"}
{"rhoint_g1_chns","vol_g1_chns","u2int_g1_chns","mdt2_cfl_g1_chns"}
{"1","2","3","4"}
{"4"}
elconst
nojac(sqrt(-mdt2_cfl_g1_chns))
{"Air","Mantel","Microfiber","Safety","Working"}
1600[degC]
40[degC]
5.340 [m]
1.795[m]
5.051[m]
1.506[m]
400[degC]
1420[degC]
1220[degC]
850[degC]
300[degC]
0.152[m]
0.08[m]
0.007[m]
0.05[m]
1[atm]
9.82[kg/m^2]
W_mantel
Thickness of the safety lining
T_init_safety
Initialvalue of the safety lining
T_inneramb
Temperature of the air inside ladle
T_inner
Temperature inside the ladle
p_atm
Air pressure
L_hin
Length of the inner boundery of the ladle wall
T_init_mantel
Initialvalue of the mantel
T_init_work
Initialvalue of the working lining
g
Earth gravity
L_hout
Length of the outer boundery of the ladle wall
T_init_micro
Initialvalue of the micro fiber
L_wout
Length of the outer boundery under the ladle
W_work
Thickness of the working lining
W_safety
Thickness of the safety lining
T_amb
Ambient temperature
W_micro
Thickness of the micro fiber
L_win
Length of the inner boundery of the ladle bottom
{0}
{0}
htgh
weak
Working Lining
mat1
1365[J/(kg*K)]
8[W/(m*K)]
3010[kg/(m^3)]
Safety Lining
mat2
1000[J/(kg*K)]
1.7[W/(m*K)]
2100[kg/(m^3)]
Micro Fiber
mat3
1046.7[J/(kg*K)]
0.025[W/(m*K)]
300[kg/(m^3)]
Mantel
mat4
470[J/(kg*K)]
53[W/(m*K)]
7850[kg/(m^3)]
Nat. Vertical wall, L=height
mat5
h_ave(T[1/K],Tinf_htgh[1/K],L_htgh[1/m])[W/(m^2*K)]
h_ave(T,Tinf,L)
inline
flc2hs(1e9-abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058),0.2e9)*0.56*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25+flc2hs(abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058)-1e9,0.2e9)*0.12*(10.255*(log10((T+Tinf)/2))^2-69.518*log10((T+Tinf)/2)+121.9)*abs(T-Tinf)^0.33
{"d(flc2hs(1e9-abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058),0.2e9)*0.56*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25+flc2hs(abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058)-1e9,0.2e9)*0.12*(10.255*(log10((T+Tinf)/2))^2-69.518*log10((T+Tinf)/2)+121.9)*abs(T-Tinf)^0.33,T)","d(flc2hs(1e9-abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058),0.2e9)*0.56*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25+flc2hs(abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058)-1e9,0.2e9)*0.12*(10.255*(log10((T+Tinf)/2))^2-69.518*log10((T+Tinf)/2)+121.9)*abs(T-Tinf)^0.33,Tinf)","d(flc2hs(1e9-abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058),0.2e9)*0.56*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25+flc2hs(abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058)-1e9,0.2e9)*0.12*(10.255*(log10((T+Tinf)/2))^2-69.518*log10((T+Tinf)/2)+121.9)*abs(T-Tinf)^0.33,L)"}
Nat. Horiz. plane, Downside, L=width
mat6
h_ave(T[1/K],Tinf_htgh[1/K],L_htgh[1/m])[W/(m^2*K)]
h_ave(T,Tinf,L)
inline
(0.25*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25)
{"d((0.25*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25),T)","d((0.25*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25),Tinf)","d((0.25*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25),L)"}
Nat. Horiz. plane, Upside, L=width
mat8
h_ave(T[1/K],Tinf_htgh[1/K],L_htgh[1/m])[W/(m^2*K)]
h_ave(T,Tinf,L)
inline
flc2hs(1e9-abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058),0.2e9)*0.54*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25+flc2hs(abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058)-1e9,0.2e9)*0.14*(10.255*(log10((T+Tinf)/2))^2-69.518*log10((T+Tinf)/2)+121.9)*abs(T-Tinf)^0.33
{"d(flc2hs(1e9-abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058),0.2e9)*0.54*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25+flc2hs(abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058)-1e9,0.2e9)*0.14*(10.255*(log10((T+Tinf)/2))^2-69.518*log10((T+Tinf)/2)+121.9)*abs(T-Tinf)^0.33,T)","d(flc2hs(1e9-abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058),0.2e9)*0.54*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25+flc2hs(abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058)-1e9,0.2e9)*0.14*(10.255*(log10((T+Tinf)/2))^2-69.518*log10((T+Tinf)/2)+121.9)*abs(T-Tinf)^0.33,Tinf)","d(flc2hs(1e9-abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058),0.2e9)*0.54*(-1.4322*log10((T+Tinf)/2)+6.3126)*(abs(T-Tinf)/L)^0.25+flc2hs(abs(T-Tinf)*L^3*10^(-4.4449*log10((T+Tinf)/2)+19.058)-1e9,0.2e9)*0.14*(10.255*(log10((T+Tinf)/2))^2-69.518*log10((T+Tinf)/2)+121.9)*abs(T-Tinf)^0.33,L)"}
Air
mat9
Cp(T[1/K])[J/(kg*K)]
cs(T[1/K])[m/s]
eta(T[1/K])[Pa*s]
1.4
k(T[1/K])[W/(m*K)]
nu0(T[1/K])[m^2/s]
rho(p[1/Pa],T[1/K])[kg/m^3]
0[S/m]
rho(p,T)
inline
p*0.02897/8.314/T
{"d(p*0.02897/8.314/T,p)","d(p*0.02897/8.314/T,T)"}
cs(T)
inline
sqrt(1.4*287*T)
{"d(sqrt(1.4*287*T),T)"}
Cp(T)
piecewise
const
poly
{"0","1.04763657E+03","1","-3.72589265E-01","2","9.45304214E-04","3","-6.02409443E-07","4","1.28589610E-10"}
{"200","1600"}
eta(T)
piecewise
const
poly
{"0","-8.38278000E-07","1","8.35717342E-08","2","-7.69429583E-11","3","4.64372660E-14","4","-1.06585607E-17"}
{"200","1600"}
nu0(T)
piecewise
const
poly
{"0","-5.86912450E-06","1","5.01274491E-08","2","7.50108343E-11","3","1.80336823E-15","4","-2.91688030E-18"}
{"200","1600"}
k(T)
piecewise
const
poly
{"0","-2.27583562E-03","1","1.15480022E-04","2","-7.90252856E-08","3","4.11702505E-11","4","-7.43864331E-15"}
{"200","1600"}
Resistivity
{"alphares","T0","res0"}
{"Temperature coefficient","Reference temperature","Resistivity at reference temperature"}
SI
uq ~
t
off
time
stationary
auto
1.0E-6
25
tol
100
1
off
on
off
1.0
1.0E-4
10.0
off
on
0.0010
25
lumped
automatic
auto
on
1
4
tol
10
1
off
const
1.0
minimal
1.0
1.0E-2
10.0
0.0010
0.01
range(0,1,590)
0
1
0.1
11
step
none
tlist
free
bdf_ida
0.01
off
15
off
on
on
on
on
on
on
off
on
on
0.0010
5
1
0.1
0.75
linear
off
off
maybe
bweuler
1
off
6
0
300
0.0
0
lambda
0
T_inner
800 900 1000 1100 1200 1300
step
none
off
1
off
0.0
0.0
0.0
on
auto
off
nonsym
eliminate
auto
1000
on
none
on
off
off
on
off
currgeom
l2
10000000
longest
weak
on
0
1
2
1
fltpft
2
1.7
0.5
0.5
on
off
off
sensitivity
adjoint
on
cholesky
analytic
500
10
1.0e-6
1.0e-6
1.0e-6
1.0e-6
0
off
u,logk,T,logd,p,v
u,logk,logd,T,p,v
on
init_expr_radio
Automatic
0
u_init_radio
Automatic
0
off
off
off
off
umfpack
linsolver
0.0
0.1
0.7
nd
on
off
nd
on
1.0E-8
on
off
tol
2
1.0E-6
400.0
10000
left
right
1
50
1
1.0
3
6
v
5000
512.0
off
2.0
on
droptol
gmres
0.02
100
0.8
on
on
shape
regular
on
2
2
off
Geom1
on
on
J T
1e-3
1
umfpack
linsolver
0.0
0.1
0.7
nd
on
off
nd
on
1.0E-8
on
off
tol
2
1.0E-6
400.0
10000
left
right
1
50
1
1.0
3
6
v
5000
512.0
off
2.0
on
droptol
gmres
0.02
100
0.8
on
on
shape
regular
on
2
2
off
Geom1
on
on
u v p
1e-3
1
umfpack
linsolver
0.0
0.1
0.7
nd
on
off
nd
on
1.0E-8
on
off
tol
2
1.0E-6
400.0
10000
left
right
1
50
1
1.0
3
6
v
5000
512.0
off
2.0
on
droptol
gmres
0.02
100
0.8
on
on
shape
regular
on
2
2
off
Geom1
on
on
logd logk
1e-3
1
umfpack
linsolver
0.0
0.1
0.7
nd
on
off
nd
on
1.0E-8
on
off
tol
2
1.0E-6
400.0
10000
left
right
1
50
1
1.0
3
6
v
5000
512.0
off
2.0
on
droptol
gmres
0.02
100
0.8
on
on
shape
regular
on
2
2
off
Geom1
on
on
1
iter
0.5
1
1
20
10
1.0E-2
1
const
off
1.0
1.0E-4
1.0E-2
10.0
minimal
onevery
2
iter
0.5
1
1
20
10
1.0E-2
1
const
off
1.0
1.0E-4
1.0E-2
10.0
minimal
onevery
3
iter
0.5
1
1
20
10
1.0E-2
1
const
off
1.0
1.0E-4
1.0E-2
10.0
minimal
onevery
off
off
off
umfpack
1
1
umfpack
auto
auto
Geom1
0
off
off
off
1011790
COMSOL 3.5.0.603
1267658515433
1265808563422
off
html
off
a4
off
full
off
Geom1
draw
1
-2.6539960043237865
4.448995961408443
-0.2670000076293945
5.607000160217285
-1.0
1.0
1.0
1.0
1.0
-0.8431174046517993
0.8431174046517993
-0.8305126593995298
0.8305126593995298
1.3540172197673421
4.920000076293941
8.431174046517993
1.3540172197673421
4.920000076293941
0.0
0.0
1.0
0.0
point
headlight
on
255
255
255
1.3540173
4.92
8.431174
directional
light 1
on
255
255
255
1.0
-1.0
1.0
directional
light 2
on
255
255
255
-1.0
1.0
-1.0
directional
light 3
on
255
255
255
-1.0
-1.0
1.0
directional
light 4
on
255
255
255
1.0
-1.0
-1.0
on
on
on
on
off
on
on
on
on
on
on
on
off
off
off
off
1.0
1.0
1.0
size
cycle
off
off
0.5
orbit
none
none
off
off
off
off
on
off
off
on
on
on
on
on
on
1.0E-6
intersection
1.0
normal
off
2
1.0
off
on
off
on
off
off
on
on
4
on
0.8
0.3
1.3
0.001
1
10
1.0
1.0
on
0
regular
{"","","","","","","","","","","","","","","",""}
{"","","","","","","","","","","","","","","",""}
{"","","","","","","","","","","","","","","","","","","",""}
{"","","","","","","","","","","","","","","","","","","",""}
{"","","","","","","","","","","","","","","","","","","",""}
{"","","","","","","","","","","","","","","","","","","",""}
{"","","","",""}
{"triaf","triaf","triaf","triaf","triaf"}
{"","","","","0.07"}
on
{"T"}
on
231.48407994246702
1408.7013639869258
on
off
degC
{"T"}
off
K
Rainbow
off
on
on
255,0,0
interp
fill
off
{"T"}
on
off
K
{"T"}
off
K
{"T"}
on
off
K
Rainbow
off
on
on
255,0,0
20
off
off
step
none
off
off
{"T"}
on
on
off
K
{"T"}
off
K
Rainbow
off
on
on
255,0,0
interp
on
sub
{"u","v"}
off
m/s
{"",""}
off
{"T"}
off
K
15
off
15
off
step
none
step
none
arrow
proportional
255,0,0
on
1
off
{"","","","","","","","","","","",""}
off
{"T"}
off
K
8
off
8
off
step
none
step
none
arrow
proportional
0,153,0
on
1
off
{"u","v"}
m/s
off
255,0,0
{"T"}
K
Rainbow
off
on
{"T"}
off
K
5
sub
off
step
none
step
none
0.001
0.01
0.01
Inf
5000
on
off
0.05
20
off
1
0.5
1.3
0.5
none
off
mass
lines
radius,partr,1e-4
4*pi/3*1e-9
{"","",""}
{"tflux_r_htgh","tflux_z_htgh"}
W/m^2
on
{"0","0","0"}
partstart_explicit
10
off
step
none
{"0","0"}
step
none
step
none
off
255,0,0
{"T"}
K
Rainbow
off
on
255,0,0
on
1
once
step
none
stick
0.001
off
{""}
{""}
off
on
on
0.001
partt
off
5
0.001
off
{"",""}
{"",""}
off
on
on
0.001
{"partu","partv","partw"}
partt
off
5
off
{"T"}
off
on
K
{"T"}
off
off
K
on
off
on
2
{"Geom1"}
0
0
stored
step
none
on
on
off
all
on
off
off
on
on
{"tflux_r_htgh","tflux_z_htgh"}
W/m^2
{"",""}
on
1
0
stored
step
none
moviefile
AVI
640
480
10
full
11
off
off
off
{"T"}
off
K
0
0
stored
step
none
off
auto
4
on
{"ntflux_htgh"}
off
W/m
0
0
stored
step
none
off
auto
4
on
{"C_htgh*T*rho_htgh"}
off
N
0
0
stored
step
none
{"T"}
on
on
off
K
Rainbow
off
on
on
255,0,0
interp
fill
off
{"ntflux_htgh"}
on
off
W/m^2
arc
off
{"T"}
K
solid
cyclecolor
none
off
off
255,0,0
Rainbow
off
on
on
255,0,0
interp
fill
{"T"}
off
K
off
{"T"}
K
solid
cyclecolor
none
off
off
255,0,0
255,0,0
0
0
stored
step
none
on
on
on
{"lin","lin"}
on
on
4
1
off
{"T"}
off
degC
arc
off
{"T"}
K
solid
cyclecolor
none
off
off
255,0,0
Rainbow
off
on
on
255,0,0
interp
fill
200
{"1.506","1.795","3","3"}
5
off
off
step
none
{"T"}
off
K
off
{"T"}
m^2*K
solid
cyclecolor
none
off
off
255,0,0
{"0 0 0 ","4 5 5 "}
step
none
step
none
255,0,0
0
0
stored
step
none
on
on
on
{"lin","lin"}
on
0
{"T"}
off
K
element
2
{"T"}
off
off
K
element
2
{"T"}
off
off
K
10
off
10
off
step
none
step
none
element
2
0
0
stored
step
none
on
ptd
off
2
coorddata
off
off
on
0
0
stored
step
none
step
none
{"T"}
off
K
{"0","0"}
{"ntflux_htgh"}
{"ntflux_htgh"}
off
solid
cyclecolor
none
off
off
255,0,0
on
on
on
{"lin","lin"}
0
0
stored
step
none
{}
{}
{}
0
0,1,0,0,0,1,0,0,0
0,1,0,0,0,0,1,0,0,0,0,1
Geom1
10
0
up
on
off
128,128,128
off
on
192,192,192
on
0,0,0
off
all
1
random
Rainbow
off
on
sr com.femlab.geom.Rectȉ,E6 D lxD lyL lxExprt !Lcom/femlab/geom/Geom$Expression;L lyExprq ~ )xr com.femlab.geom.Prim2Z~ D rotL baseq ~ L constrq ~ [ post [D[ posExprt "[Lcom/femlab/geom/Geom$Expression;L rotExprq ~ )xr com.femlab.geom.Geom2Vc/O xr com.femlab.geom.Geom6{ L geomAssoct Lcom/femlab/geom/GeomAssoc;L versionq ~ xpw q ~ w ur [BT xp G e o m 2 |=-C 6? "~? jt?"~? jt?\(\@ \(\@ ? ? ? ? B e z i e r C u r v e "~? ?jt?"~? ? B e z i e r C u r v e jt?"~? ?jt?\(\@ ? B e z i e r C u r v e jt?\(\@ ? \(\@ ? B e z i e r C u r v e \(\@ ? "~? ? A s s o c A t t r i b V e c t o r I n t B xw xw t cornerur [D>cZ xp ?~"ur "[Lcom.femlab.geom.Geom$Expression;\2YU xp sr com.femlab.geom.Geom$Expression
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