untitled
Report date
May 5, 2025 2:50:15 PM
1
Contents
1.
Global Definitions ........................................................................................................................... 3
2.
Component 1 .................................................................................................................................. 4
2.1.
Definitions .................................................................................................................................................................... 4
2.2.
Geometry 1 .................................................................................................................................................................. 5
2.3.
Materials ....................................................................................................................................................................... 6
2.4.
Laminar Flow .............................................................................................................................................................11
2.5.
Heat Transfer in Fluids ..........................................................................................................................................27
2.6.
Mesh 1 .........................................................................................................................................................................50
3.
Study 1........................................................................................................................................... 55
3.1.
Time Dependent ......................................................................................................................................................55
3.2.
Solver Configurations ............................................................................................................................................55
4.
Results ........................................................................................................................................... 61
4.1.
Data Sets.....................................................................................................................................................................61
4.2.
Plot Groups ................................................................................................................................................................62
2
1 Global Definitions
Date
May 5, 2025 2:41:37 PM
GLOBAL SETTINGS
Name
untitled.mph
Version
COMSOL Multiphysics 5.4 (Build: 388)
Unit system
SI
USED PRODUCTS
COMSOL Multiphysics
3
2 Component 1
Date
May 5, 2025 2:41:39 PM
SETTINGS
Description
Value
Unit system
Same as global system
Geometry shape order
Automatic
SPATIAL FRAME COORDINATES
First
Second
Third
r
phi
z
MATERIAL FRAME COORDINATES
First
Second
Third
R
PHI
Z
GEOMETRY FRAME COORDINATES
First
Second
Third
Rg
PHIg
Zg
MESH FRAME COORDINATES
First
Second
Third
Rm
PHIm
Zm
2.1 DEFINITIONS
2.1.1 Coordinate Systems
Boundary System 1
Coordinate system type
Boundary system
Tag
sys1
COORDINATE NAMES
First
Second
Third
t1
to
n
SETTINGS
Description
Value
Axis
phi
4
2.2 GEOMETRY 1
Geometry 1
UNITS
Length unit
mm
Angular unit
deg
GEOMETRY STATISTICS
Description
Value
Space dimension
2
Number of domains
1
Number of boundaries
3
Number of vertices
3
2.2.1 Polygon 1 (pol1)
OBJECT TYPE
Description
Value
Type
Solid
COORDINATES
Description
Value
Data source
Table
COORDINATES
r (mm)
z (mm)
5
r (mm)
z (mm)
0
0
50
0
0
120
2.3 MATERIALS
2.3.1 Water, liquid
Water, liquid
SELECTION
Geometric entity level
Domain
Selection
Domain 1
MATERIAL PARAMETERS
Name
Value
Unit
Dynamic viscosity
eta(T)
Pa·s
Ratio of specific heats
gamma_w(T)
1
Heat capacity at constant pressure
Cp(T)
J/(kg·K)
Density
rho(T)
kg/m³
Thermal conductivity
k(T)
W/(m·K)
BASIC SETTINGS
Description
Value
Coefficient of thermal expansion
{{alpha_p(T), 0, 0}, {0, alpha_p(T), 0}, {0, 0, alpha_p(T)}}
Bulk viscosity
muB(T)
6
Description
Value
Dynamic viscosity
eta(T)
Ratio of specific heats
gamma_w(T)
Electrical conductivity
{{5.5e-6[S/m], 0, 0}, {0, 5.5e-6[S/m], 0}, {0, 0, 5.5e-6[S/m]}}
Heat capacity at constant pressure
Cp(T)
Density
rho(T)
Thermal conductivity
{{k(T), 0, 0}, {0, k(T), 0}, {0, 0, k(T)}}
Speed of sound
cs(T)
FUNCTIONS
Function name
Type
eta
Piecewise
Cp
Piecewise
rho
Piecewise
k
Piecewise
cs
Interpolation
alpha_p
Analytic
gamma_w
Analytic
muB
Analytic
eta
7
Cp
rho
8
k
cs
9
alpha_p
gamma_w
10
muB
2.4 LAMINAR FLOW
USED PRODUCTS
COMSOL Multiphysics
Laminar Flow
SELECTION
Geometric entity level
Domain
Selection
Domain 1
EQUATIONS
11
2.4.1 Interface settings
Discretization
SETTINGS
Description
Value
Discretization of fluids
P1 + P1
Physical model
SETTINGS
Description
Value
Compressibility
Incompressible flow
Reference temperature
User defined
Reference temperature
293.15[K]
Reference pressure level
1[atm]
Turbulence
SETTINGS
Description
Value
Turbulence model type
None
2.4.2 Variables
Name
Expression
Unit
Description
Selection
Details
spf.Tref
model.input.Tref
K
Reference
temperature
Global
Meta
spf.dz
1
m
Thickness
Domain 1
spf.pref
1[atm]
Pa
Reference
pressure level
Domain 1
spf.pA
p+spf.pref
Pa
Absolute
pressure
Domain 1
spf.hasWF
0
Help variable
Boundaries 1–
3
spf.usePseudoTime
Stepping
0
Help variable
Global
spf.localCFLvalue
1.3^min(niterCMP,9)
+if(niterCMP>=25,9*
Local CFL
Domain 1
1
12
+ operation
Name
Expression
Unit
1.3^min(25+niterCMP,9),0)+if
(niterCMP>=45,90*1.
3^min(45+niterCMP,9),0)
Description
Selection
number
spf.locCFL
CFLCMP
1
Local CFL
number
Domain 1
spf.geometryLength
Scale
0.0125
m
Geometry
length scale
Domain 1
spf.time_step_inv
max(sqrt(emetric_spa
tial(u,w)*2^gmg_leve
l^2),spf.nu/spf.geom
etryLengthScale^2)
Hz
Inverse time
step
Domain 1
spf.tsti
nojac(spf.time_step_i
nv/spf.locCFL)
1/s
Help variable
Domain 1
spf.nr
dnr
1
Normal vector,
r component
Boundaries 1–
3
spf.nphi
0
1
Normal vector,
phi component
Boundaries 1–
3
spf.nz
dnz
1
Normal vector,
z component
Boundaries 1–
3
spf.nrmesh
dnrmesh
1
Normal vector,
r component
Boundaries 1–
3
spf.nphimesh
0
1
Normal vector,
phi component
Boundaries 1–
3
spf.nzmesh
dnzmesh
1
Normal vector,
z component
Boundaries 1–
3
13
Details
2.4.3 Fluid Properties 1
Fluid Properties 1
SELECTION
Geometric entity level
Domain
Selection
Domain 1
EQUATIONS
Fluid properties
SETTINGS
Description
Value
Density
From material
Dynamic viscosity
From material
Model input
SETTINGS
Description
Value
Temperature
Common model input
PROPERTIES FROM MATERIAL
14
Property
Material
Property group
Density
Water, liquid
Basic
Dynamic viscosity
Water, liquid
Basic
Variables
Name
Expression
Unit
Description
Selection
Details
spf.Fr
0
N/m³
Volume force, r
component
Domain 1
+ operation
spf.Fphi
0
N/m³
Volume force,
phi component
Domain 1
+ operation
spf.Fz
0
N/m³
Volume force, z
component
Domain 1
+ operation
spf.rho
subst(material.rho
,spf.fp1.minput_te
mperature,spf.Trh
o,spf.fp1.minput_
pressure,spf.prho)
kg/m³
Density
Domain 1
Meta
spf.mu
material.mu
Pa·s
Dynamic
viscosity
Domain 1
Meta
spf.Trho
spf.Tref
K
Temperature for
density
evaluation
Domain 1
spf.prho
spf.pref
Pa
Pressure for the
evaluation of
density
Domain 1
spf.rhoref
subst(material.rho
,spf.fp1.minput_te
mperature,spf.Tref
,spf.fp1.minput_pr
essure,spf.pref)
kg/m³
Reference
density
Domain 1
Meta
spf.mumat
material.mu
Pa·s
Dynamic
viscosity
Domain 1
Meta
spf.srijrr
ur
1/s
Strain rate
tensor, rr
component
Domain 1
spf.srijphir
0
1/s
Strain rate
tensor, phir
component
Domain 1
spf.srijzr
0.5*(wr+uz)
1/s
Strain rate
tensor, zr
component
Domain 1
spf.srijrphi
0
1/s
Strain rate
tensor, rphi
Domain 1
15
Name
Expression
Unit
Description
Selection
component
spf.srijphiphi
spf.srijzphi
if(abs(r)<0.001*h_
spatial,ur,u/r)
0
1/s
Strain rate
tensor, phiphi
component
Domain 1
1/s
Strain rate
tensor, zphi
component
Domain 1
Domain 1
spf.srijrz
0.5*(uz+wr)
1/s
Strain rate
tensor, rz
component
spf.srijphiz
0
1/s
Strain rate
tensor, phiz
component
Domain 1
spf.srijzz
wz
1/s
Strain rate
tensor, zz
component
Domain 1
spf.srijmeanrr
0.5*root.comp1.sp
f.elemint(2*ur)/ro
ot.comp1.spf.ele
mint(1)
1/s
Strain rate
tensor, rr
component
Domain 1
spf.srijmeanphir
0.5*root.comp1.sp
f.elemint(0)/root.c
omp1.spf.elemint(
1)
1/s
Strain rate
tensor, phir
component
Domain 1
spf.srijmeanzr
0.5*root.comp1.sp
f.elemint(wr+uz)/r
oot.comp1.spf.ele
mint(1)
1/s
Strain rate
tensor, zr
component
Domain 1
spf.srijmeanrphi
0.5*root.comp1.sp
f.elemint(0)/root.c
omp1.spf.elemint(
1)
1/s
Strain rate
tensor, rphi
component
Domain 1
spf.srijmeanphip
hi
0.5*root.comp1.sp
f.elemint(2*if(abs(
r)<0.001*h_spatial
,ur,u/r))/root.com
p1.spf.elemint(1)
1/s
Strain rate
tensor, phiphi
component
Domain 1
spf.srijmeanzphi
0.5*root.comp1.sp
f.elemint(0)/root.c
omp1.spf.elemint(
1)
1/s
Strain rate
tensor, zphi
component
Domain 1
spf.srijmeanrz
0.5*root.comp1.sp
f.elemint(uz+wr)/r
1/s
Strain rate
tensor, rz
Domain 1
16
Details
Name
Expression
Unit
Description
oot.comp1.spf.ele
mint(1)
spf.srijmeanphiz
0.5*root.comp1.sp
f.elemint(0)/root.c
omp1.spf.elemint(
1)
spf.srijmeanzz
0.5*root.comp1.sp
f.elemint(2*wz)/ro
ot.comp1.spf.ele
mint(1)
Selection
component
1/s
Strain rate
tensor, phiz
component
Domain 1
1/s
Strain rate
tensor, zz
component
Domain 1
Domain 1
spf.rrijrr
0
1/s
Rotation rate
tensor, rr
component
spf.rrijphir
0
1/s
Rotation rate
tensor, phir
component
Domain 1
spf.rrijzr
0.5*(wr-uz)
1/s
Rotation rate
tensor, zr
component
Domain 1
spf.rrijrphi
0
1/s
Rotation rate
tensor, rphi
component
Domain 1
spf.rrijphiphi
0
1/s
Rotation rate
tensor, phiphi
component
Domain 1
spf.rrijzphi
0
1/s
Rotation rate
tensor, zphi
component
Domain 1
spf.rrijrz
0.5*(uz-wr)
1/s
Rotation rate
tensor, rz
component
Domain 1
spf.rrijphiz
0
1/s
Rotation rate
tensor, phiz
component
Domain 1
Domain 1
Domain 1
spf.rrijzz
0
1/s
Rotation rate
tensor, zz
component
spf.sr
sqrt(2*spf.srijrr^2
+2*spf.srijrphi^2
+2*spf.srijrz^2+2
*spf.srijphir^2+2*
spf.srijphiphi^2+2
*spf.srijphiz^2+2*
1/s
Shear rate
17
Details
Name
Expression
Unit
Description
Selection
Details
spf.srijzr^2+2*spf.
srijzphi^2+2*spf.s
rijzz^2+eps)
spf.divu
ur+if(abs(r)<0.001
*h_spatial,ur,u/r)+
wz
1/s
Divergence of
velocity field
Domain 1
spf.U
sqrt(u^2+w^2)
m/s
Velocity
magnitude
Domain 1
spf.vorticityr
0
1/s
Vorticity field, r
component
Domain 1
spf.vorticityphi
-wr+uz
1/s
Vorticity field,
phi component
Domain 1
spf.vorticityz
0
1/s
Vorticity field, z
component
Domain 1
spf.vort_magn
sqrt(spf.vorticityr
^2+spf.vorticityp
hi^2+spf.vorticity
z^2)
1/s
Vorticity
magnitude
Domain 1
spf.cellRe
0.25*spf.rho*sqrt(
emetric_spatial(ud(r,TIME),wd(z,TIME))/emetric
2_spatial)/spf.mu
1
Cell Reynolds
number
Domain 1
spf.nu
spf.mu/spf.rho
m²/s
Kinematic
viscosity
Domain 1
spf.betaT
0
1/Pa
Isothermal
compressibility
coefficient
Domain 1
spf.Qm
0
kg/(m³·s)
Source term
Domain 1
+ operation
spf.Fgtotr
0
N/m³
Gravity force, r
component
Domain 1
+ operation
spf.Fgtotphi
0
N/m³
Gravity force,
phi component
Domain 1
+ operation
spf.Fgtotz
0
N/m³
Gravity force, z
component
Domain 1
+ operation
spf.mu_eff
spf.mu+spf.muT
Pa·s
Dynamic
viscosity
Domain 1
spf.muT
0
Pa·s
Turbulent
dynamic
viscosity
Domain 1
spf.T_stressr
spf.K_stressrp*spf.nrmesh
N/m²
Total stress, r
component
Boundaries 1–
3
18
+ operation
Name
Expression
Unit
Description
Selection
Details
spf.T_stressphi
spf.K_stressphip*spf.nphimesh
N/m²
Total stress, phi
component
Boundaries 1–
3
+ operation
spf.T_stressz
spf.K_stresszp*spf.nzmesh
N/m²
Total stress, z
component
Boundaries 1–
3
+ operation
spf.K_stressr
spf.mu_eff*(2*ur*s
pf.nrmesh+(uz+w
r)*spf.nzmesh)
N/m²
Viscous stress, r
component
Boundaries 1–
3
+ operation
spf.K_stressphi
2*spf.mu_eff*if(ab
s(r)<0.001*h_spati
al,ur,u/r)*spf.nphi
mesh
N/m²
Viscous stress,
phi component
Boundaries 1–
3
+ operation
spf.K_stressz
spf.mu_eff*((wr+u
z)*spf.nrmesh+2*
wz*spf.nzmesh)
N/m²
Viscous stress, z
component
Boundaries 1–
3
+ operation
Domain 1
+ operation
spf.K_stress_tens
orrr
2*spf.mu_eff*ur
N/m²
Viscous stress
tensor, rr
component
spf.K_stress_tens
orphir
0
N/m²
Viscous stress
tensor, phir
component
Domain 1
+ operation
spf.K_stress_tens
orzr
spf.mu_eff*(wr+uz
)
N/m²
Viscous stress
tensor, zr
component
Domain 1
+ operation
spf.K_stress_tens
orrphi
0
N/m²
Viscous stress
tensor, rphi
component
Domain 1
+ operation
spf.K_stress_tens
orphiphi
2*spf.mu_eff*if(ab
s(r)<0.001*h_spati
al,ur,u/r)
N/m²
Viscous stress
tensor, phiphi
component
Domain 1
+ operation
spf.K_stress_tens
orzphi
0
N/m²
Viscous stress
tensor, zphi
component
Domain 1
+ operation
spf.K_stress_tens
orrz
spf.mu_eff*(uz+wr
)
N/m²
Viscous stress
tensor, rz
component
Domain 1
+ operation
N/m²
Viscous stress
tensor, phiz
component
Domain 1
+ operation
Domain 1
+ operation
Domain 1
+ operation
spf.K_stress_tens
orphiz
0
spf.K_stress_tens
orzz
2*spf.mu_eff*wz
N/m²
Viscous stress
tensor, zz
component
spf.K_stress_tens
2*spf.mu_eff*test(
N/m²
Viscous stress
tensor test, rr
19
Name
Expression
Unit
Description
Selection
Details
or_testrr
ur)
component
spf.K_stress_tens
or_testphir
N/m²
Viscous stress
tensor test, phir
component
0
Domain 1
+ operation
spf.K_stress_tens
or_testzr
spf.mu_eff*(test(w
r)+test(uz))
N/m²
Viscous stress
tensor test, zr
component
Domain 1
+ operation
N/m²
Viscous stress
tensor test, rphi
component
Domain 1
+ operation
Domain 1
+ operation
spf.K_stress_tens
or_testrphi
0
spf.K_stress_tens
or_testphiphi
2*spf.mu_eff*if(ab
s(r)<0.001*h_spati
al,test(ur),test(u)/r
)
N/m²
Viscous stress
tensor test,
phiphi
component
spf.K_stress_tens
or_testzphi
0
N/m²
Viscous stress
tensor test, zphi
component
Domain 1
+ operation
spf.K_stress_tens
or_testrz
spf.mu_eff*(test(u
z)+test(wr))
N/m²
Viscous stress
tensor test, rz
component
Domain 1
+ operation
N/m²
Viscous stress
tensor test, phiz
component
Domain 1
+ operation
Domain 1
+ operation
spf.K_stress_tens
or_testphiz
0
spf.K_stress_tens
or_testzz
2*spf.mu_eff*test(
wz)
N/m²
Viscous stress
tensor test, zz
component
spf.upwind_help
r
u-d(r,TIME)
m/s
Upwind term, r
component
Domain 1
+ operation
spf.upwind_help
phi
0
m/s
Upwind term,
phi component
Domain 1
+ operation
spf.upwind_help
z
w-d(z,TIME)
m/s
Upwind term, z
component
Domain 1
+ operation
spf.tau_vdrr
2*spf.mu*spf.srijrr
Pa
Viscous stress
tensor, rr
component
Domain 1
+ operation
spf.tau_vdphir
2*spf.mu*spf.srijp
hir
Pa
Viscous stress
tensor, phir
component
Domain 1
+ operation
spf.tau_vdzr
2*spf.mu*spf.srijzr
Pa
Viscous stress
tensor, zr
component
Domain 1
+ operation
spf.tau_vdrphi
2*spf.mu*spf.srijr
Pa
Viscous stress
Domain 1
+ operation
20
Name
Expression
Unit
Description
Selection
Details
tensor, rphi
component
phi
spf.tau_vdphiphi
2*spf.mu*spf.srijp
hiphi
Pa
Viscous stress
tensor, phiphi
component
Domain 1
+ operation
spf.tau_vdzphi
2*spf.mu*spf.srijz
phi
Pa
Viscous stress
tensor, zphi
component
Domain 1
+ operation
spf.tau_vdrz
2*spf.mu*spf.srijrz
Pa
Viscous stress
tensor, rz
component
Domain 1
+ operation
spf.tau_vdphiz
2*spf.mu*spf.srijp
hiz
Pa
Viscous stress
tensor, phiz
component
Domain 1
+ operation
spf.tau_vdzz
2*spf.mu*spf.srijzz
Pa
Viscous stress
tensor, zz
component
Domain 1
+ operation
spf.Qvd
spf.tau_vdrr*ur+s
pf.tau_vdrz*uz+sp
f.tau_vdphiphi*if(a
bs(r)<0.001*h_spa
tial,ur,u/r)+spf.tau
_vdzr*wr+spf.tau_
vdzz*wz
W/m³
Viscous
dissipation
Domain 1
+ operation
spf.epsilon_p
1
1
Porosity
Domain 1
spf.Fst_tensorrr
0
N/m²
Surface tension
force, rr
component
Domain 1
+ operation
spf.Fst_tensorph
ir
0
N/m²
Surface tension
force, phir
component
Domain 1
+ operation
spf.Fst_tensorzr
0
N/m²
Surface tension
force, zr
component
Domain 1
+ operation
N/m²
Surface tension
force, rphi
component
Domain 1
+ operation
N/m²
Surface tension
force, phiphi
component
Domain 1
+ operation
N/m²
Surface tension
force, zphi
component
Domain 1
+ operation
spf.Fst_tensorrp
hi
spf.Fst_tensorph
iphi
spf.Fst_tensorzp
hi
0
0
0
21
Name
Expression
spf.Fst_tensorrz
spf.Fst_tensorph
iz
0
0
Unit
Description
Selection
Details
N/m²
Surface tension
force, rz
component
Domain 1
+ operation
N/m²
Surface tension
force, phiz
component
Domain 1
+ operation
Domain 1
+ operation
spf.Fst_tensorzz
0
N/m²
Surface tension
force, zz
component
spf.continuityEq
uation
spf.rho*spf.divu
kg/(m³·s)
Continuity
equation
Domain 1
spf.contCoeff
spf.rho
kg/m³
Help variable
Domain 1
spf.res_u
spf.rho*ut+pr+spf
.rho*u*ur+spf.rho
*w*uz(d(2*ur,r)+if(abs(r)
<0.001*h_spatial,
d(2*ur,r),2*ur/r)+d
(uz+wr,z)2*if(abs(r)<0.001*
h_spatial,ur,u/r)/r)
*spf.mu-spf.Fr
N/m³
Equation
residual
Domain 1
spf.res_v
-spf.Fphi
N/m³
Equation
residual
Domain 1
spf.res_w
spf.rho*wt+spf.rh
o*u*wr+pz+spf.rh
o*w*wz(d(wr+uz,r)+if(abs
(r)<0.001*h_spatia
l,d(wr+uz,r),(wr+u
z)/r)+d(2*wz,z))*s
pf.mu-spf.Fz
N/m³
Equation
residual
Domain 1
spf.res_p
spf.rho*spf.divu
kg/(m³·s)
Pressure
equation
residual
Domain 1
Shape functions
Name
Shape function
Unit
Description
Shape frame
Selection
u
Lagrange (Linear)
m/s
Velocity field, r
component
Spatial
Domain 1
w
Lagrange (Linear)
m/s
Velocity field, z
component
Spatial
Domain 1
p
Lagrange (Linear)
Pa
Pressure
Spatial
Domain 1
22
Weak expressions
Weak expression
Integration order
Integration frame
Selection
2*spf.rho*(-ut*test(u)-wt*test(w))*pi*r
2
Spatial
Domain 1
2*((p-spf.K_stress_tensorrr)*test(ur)spf.K_stress_tensorrz*test(uz)+(pspf.K_stress_tensorphiphi)*if(abs(r)<0.0
01*h_spatial,test(ur),test(u)/r)spf.K_stress_tensorzr*test(wr)+(pspf.K_stress_tensorzz)*test(wz))*pi*r
2
Spatial
Domain 1
2*(spf.Fr*test(u)+spf.Fz*test(w))*pi*r
2
Spatial
Domain 1
2*spf.rho*(-(d(u,r)*u+d(u,z)*w)*test(u)(d(w,r)*u+d(w,z)*w)*test(w))*pi*r
2
Spatial
Domain 1
-2*spf.continuityEquation*test(p)*pi*r
2
Spatial
Domain 1
2*spf.streamlinens*pi*r
2
Spatial
Domain 1
2*spf.crosswindns*pi*r
2
Spatial
Domain 1
2.4.4 Initial Values 1
Initial Values 1
SELECTION
Geometric entity level
Domain
Selection
Domain 1
Initial values
SETTINGS
Description
Value
23
Description
Value
Velocity field, r component
0
Velocity field, phi component
0
Velocity field, z component
0
Pressure
0
Coordinate system selection
SETTINGS
Description
Value
Coordinate system
Global coordinate system
Variables
Name
Expression
Unit
Description
Selection
spf.u_initr
0
m/s
Velocity field, r component
Domain 1
spf.u_initphi
0
m/s
Velocity field, phi component
Domain 1
spf.u_initz
0
m/s
Velocity field, z component
Domain 1
spf.p_init
0
Pa
Pressure
Domain 1
2.4.5 Axial Symmetry 1
Axial Symmetry 1
SELECTION
Geometric entity level
Boundary
Selection
Boundary 1
24
Constraints
Constraint
Constraint force
Shape function
Selection
Details
-u
test(-u)
Lagrange (Linear)
Boundary 1
Elemental
2.4.6 Wall 1
Wall 1
SELECTION
Geometric entity level
Boundary
Selection
Boundaries 2–3
EQUATIONS
Boundary condition
SETTINGS
Description
Value
Wall condition
No slip
Wall movement
SETTINGS
Description
Value
Translational velocity
Automatic from frame
Sliding wall
Off
25
Variables
Name
Expression
Unit
Description
Selection
Details
spf.ubndr
0
m/s
Velocity at
boundary, r
component
Boundaries 2–
3
+ operation
spf.ubndphi
0
m/s
Velocity at
boundary, phi
component
Boundaries 2–
3
+ operation
spf.ubndz
0
m/s
Velocity at
boundary, z
component
Boundaries 2–
3
+ operation
m/s
Leakage
velocity, r
component
Boundaries 2–
3
+ operation
m/s
Leakage
velocity, phi
component
Boundaries 2–
3
+ operation
Boundaries 2–
3
+ operation
Boundaries 2–
3
spf.uLeakager
spf.uLeakagephi
0
0
spf.uLeakagez
0
m/s
Leakage
velocity, z
component
spf.noSlipWall
1
1
Help variable
Constraints
Constraint
Constraint
force
Shape
function
Selection
Details
-u+spf.ubndr+spf.uLeakager
test(-u)
Lagrange
(Linear)
Boundaries 2–
3
Elemental
spf.ubndphi+spf.uLeakagephi
0
Boundaries 2–
3
Elemental
-w+spf.ubndz+spf.uLeakagez
test(-w)
Boundaries 2–
3
Elemental
26
Lagrange
(Linear)
2.4.7 Volume Force 1
Volume Force 1
SELECTION
Geometric entity level
Domain
Selection
Domain 1
EQUATIONS
Variables
Name
Expression
Unit
Description
Selection
Details
spf.Fr
0
N/m³
Volume force, r
component
Domain 1
+ operation
spf.Fphi
0
N/m³
Volume force, phi
component
Domain 1
+ operation
spf.Fz
-9816
N/m³
Volume force, z
component
Domain 1
+ operation
2.5 HEAT TRANSFER IN FLUIDS
USED PRODUCTS
COMSOL Multiphysics
27
Heat Transfer in Fluids
SELECTION
Geometric entity level
Domain
Selection
Domain 1
EQUATIONS
2.5.1 Interface settings
Discretization
SETTINGS
Description
Value
Temperature
Linear
Physical model
SETTINGS
Description
Value
Reference temperature
User defined
Reference temperature
293.15[K]
2.5.2 Variables
Name
Expression
Unit
Description
28
Selection
Details
Name
Expression
Unit
Description
Selection
Details
ht.q0
0
W/m²
Inward heat flux
Boundaries 2–
3
+ operation
ht.Tu
T
K
Temperature
Boundaries 2–
3
ht.Td
T
K
Temperature
Boundaries 2–
3
ht.Tref
model.input.Tref
K
Reference
temperature
Global
ht.d
1
1
Thickness
Domain 1
ht.HRef
0
J/kg
Reference
enthalpy
Domain 1
ht.DeltaH
0
J/kg
Sensible
enthalpy
Domain 1
+ operation
ht.H
0
J/kg
Enthalpy
Domain 1
+ operation
ht.H0
ht.H+ht.Ek
J/kg
Total enthalpy
Domain 1
ht.Ei
0
J/kg
Internal energy
Domain 1
ht.Ei0
ht.Ei+ht.Ek
J/kg
Total internal
energy
Domain 1
ht.Ek
0
J/kg
Kinetic energy
Domain 1
+ operation
ht.dfluxr
0
W/m²
Conductive heat
flux, r
component
Domain 1
+ operation
ht.dfluxphi
0
W/m²
Conductive heat
flux, phi
component
Domain 1
+ operation
ht.dfluxz
0
W/m²
Conductive heat
flux, z
component
Domain 1
+ operation
W/m²
Conductive heat
flux, r
component
Boundaries 1–
3
+ operation
W/m²
Conductive heat
flux, phi
component
Boundaries 1–
3
+ operation
Boundaries 1–
3
+ operation
ht.dfluxr
ht.dfluxphi
mean(ht.dfluxr)
mean(ht.dfluxphi)
Meta
+ operation
ht.dfluxz
mean(ht.dfluxz)
W/m²
Conductive heat
flux, z
component
ht.dfluxtestr
0
W/m²
Conductive heat
flux, r
component
Domain 1
+ operation
ht.dfluxtestphi
0
W/m²
Conductive heat
Domain 1
+ operation
29
Name
Expression
Unit
Description
Selection
Details
flux, phi
component
ht.dfluxtestz
0
W/m²
Conductive heat
flux, z
component
Domain 1
+ operation
ht.dfluxtestr
mean(ht.dfluxtest
r)
W/m²
Conductive heat
flux, r
component
Boundaries 1–
3
+ operation
ht.dfluxtestphi
mean(ht.dfluxtest
phi)
W/m²
Conductive heat
flux, phi
component
Boundaries 1–
3
+ operation
ht.dfluxtestz
mean(ht.dfluxtest
z)
W/m²
Conductive heat
flux, z
component
Boundaries 1–
3
+ operation
ht.dfluxMag
sqrt(ht.dfluxr^2+
ht.dfluxphi^2+ht.
dfluxz^2)
W/m²
Conductive heat
flux magnitude
Domain 1
ht.cfluxr
0
W/m²
Convective heat
flux, r
component
Domain 1
+ operation
W/m²
Convective heat
flux, phi
component
Domain 1
+ operation
Domain 1
+ operation
ht.cfluxphi
0
ht.cfluxz
0
W/m²
Convective heat
flux, z
component
ht.cfluxMag
sqrt(ht.cfluxr^2+
ht.cfluxphi^2+ht.
cfluxz^2)
W/m²
Convective heat
flux magnitude
Domain 1
ht.tfluxr
ht.dfluxr+ht.cfluxr
W/m²
Total heat flux, r
component
Domain 1
ht.tfluxphi
ht.dfluxphi+ht.cfl
uxphi
W/m²
Total heat flux,
phi component
Domain 1
ht.tfluxz
ht.dfluxz+ht.cflux
z
W/m²
Total heat flux, z
component
Domain 1
ht.tfluxMag
sqrt(ht.tfluxr^2+h
t.tfluxphi^2+ht.tfl
uxz^2)
W/m²
Total heat flux
magnitude
Domain 1
ht.tefluxr
0
W/m²
Total energy
flux, r
component
Domain 1
+ operation
ht.tefluxphi
0
W/m²
Total energy
Domain 1
+ operation
30
Name
Expression
Unit
Description
Selection
Details
+ operation
flux, phi
component
ht.tefluxz
0
W/m²
Total energy
flux, z
component
Domain 1
ht.tefluxMag
sqrt(ht.tefluxr^2+
ht.tefluxphi^2+ht
.tefluxz^2)
W/m²
Total energy flux
magnitude
Domain 1
ht.dflux_ur
up(ht.dfluxr)
W/m²
Conductive heat
flux, r
component
Boundaries 1–
3
ht.dflux_uphi
up(ht.dfluxphi)
W/m²
Conductive heat
flux, phi
component
Boundaries 1–
3
ht.dflux_uz
up(ht.dfluxz)
W/m²
Conductive heat
flux, z
component
Boundaries 1–
3
ht.dflux_dr
down(ht.dfluxr)
W/m²
Conductive heat
flux, r
component
Boundaries 1–
3
W/m²
Conductive heat
flux, phi
component
Boundaries 1–
3
W/m²
Conductive heat
flux, z
component
Boundaries 1–
3
W/m²
Conductive heat
flux, r
component
Boundaries 1–
3
Boundaries 1–
3
ht.dflux_dphi
ht.dflux_dz
down(ht.dfluxphi)
down(ht.dfluxz)
ht.dfluxtest_ur
up(ht.dfluxtestr)
ht.dfluxtest_uphi
up(ht.dfluxtestphi
)
W/m²
Conductive heat
flux, phi
component
ht.dfluxtest_uz
up(ht.dfluxtestz)
W/m²
Conductive heat
flux, z
component
Boundaries 1–
3
ht.dfluxtest_dr
down(ht.dfluxtest
r)
W/m²
Conductive heat
flux, r
component
Boundaries 1–
3
ht.dfluxtest_dph
i
down(ht.dfluxtest
phi)
W/m²
Conductive heat
flux, phi
component
Boundaries 1–
3
ht.dfluxtest_dz
down(ht.dfluxtest
z)
W/m²
Conductive heat
flux, z
Boundaries 1–
3
31
Name
Expression
Unit
Description
Selection
Details
+ operation
component
ht.rflux
0
W/m²
Radiative heat
flux
Boundaries 1–
3
ht.ncflux
mean(ht.cfluxr)*h
t.nr+mean(ht.cflu
xphi)*ht.nphi+me
an(ht.cfluxz)*ht.nz
W/m²
Normal
convective heat
flux
Boundaries 1–
3
ht.ncflux_u
up(ht.cfluxr)*ht.u
nr+up(ht.cfluxphi
)*ht.unphi+up(ht.
cfluxz)*ht.unz
W/m²
Internal normal
convective heat
flux, upside
Boundaries 1–
3
ht.ncflux_d
down(ht.cfluxr)*h
t.dnr+down(ht.cfl
uxphi)*ht.dnphi+
down(ht.cfluxz)*h
t.dnz
W/m²
Internal normal
convective heat
flux, downside
Boundaries 1–
3
ht.ndflux
0.5*(ht.ndflux_dht.ndflux_u)
W/m²
Normal
conductive heat
flux
Boundaries 1–
3
+ operation
ht.ndflux_u
-ht.ndflux_d
W/m²
Internal normal
conductive heat
flux, upside
Boundaries 1–
3
+ operation
ht.ndflux_d
0
W/m²
Internal normal
conductive heat
flux, downside
Boundaries 1–
3
+ operation
ht.ntflux
ht.ndflux+ht.ncflu
x
W/m²
Normal total
heat flux
Boundaries 1–
3
ht.ntflux_u
ht.ndflux_u+ht.nc
flux_u
W/m²
Internal normal
total flux, upside
Boundaries 1–
3
ht.ntflux_d
ht.ndflux_d+ht.nc
flux_d
W/m²
Internal normal
total flux,
downside
Boundaries 1–
3
ht.nteflux
mean(ht.tefluxr)*
ht.nr+mean(ht.tef
luxphi)*ht.nphi+
mean(ht.tefluxz)*
ht.nzmean(ht.dfluxr)*h
t.nrmean(ht.dfluxphi)
*ht.nphimean(ht.dfluxz)*h
t.nz+ht.ndflux
W/m²
Normal total
energy flux
Boundaries 1–
3
32
Name
Expression
Unit
Description
Selection
ht.nteflux_u
up(ht.tefluxr)*ht.u
nr+up(ht.tefluxph
i)*ht.unphi+up(ht.
tefluxz)*ht.unzup(ht.dfluxr)*ht.u
nrup(ht.dfluxphi)*ht
.unphiup(ht.dfluxz)*ht.u
nz+ht.ndflux_u
W/m²
Internal normal
total energy flux,
upside
Boundaries 1–
3
ht.nteflux_d
down(ht.tefluxr)*
ht.dnr+down(ht.t
efluxphi)*ht.dnph
i+down(ht.tefluxz
)*ht.dnzdown(ht.dfluxr)*h
t.dnrdown(ht.dfluxphi)
*ht.dnphidown(ht.dfluxz)*h
t.dnz+ht.ndflux_d
W/m²
Internal normal
total energy flux,
downside
Boundaries 1–
3
ht.Qm
0
kg/(m³·s)
Mass source
Domain 1
ht.Q
0
W/m³
Heat source
Domain 1
+ operation
ht.Qoop
0
W/m³
Out-of-plane
heat source
Domain 1
+ operation
ht.Qtot
0
W/m³
Total heat
source
Domain 1
+ operation
ht.Qbtot
0
W/m²
Total boundary
heat source
Boundaries 2–
3
+ operation
ht.qs
0
W/(m³·K)
Production/abso
rption
coefficient
Domain 1
+ operation
Domain 1
+ operation
ht.qs_oop
0
W/(m³·K)
Out-of-plane
production/abso
rption
coefficient
ht.Tvar
T
K
Temperature
Domain 1
ht.Tvar
T
K
Temperature
Boundaries 1–
3
ht.Tvar
T
K
Temperature
Points 1–3
ht.nr
dnr
1
Normal vector, r
component
Boundaries 1–
3
ht.nphi
0
1
Normal vector,
Boundaries 1–
33
Details
Name
Expression
Unit
Description
Selection
phi component
3
ht.nz
dnz
1
Normal vector, z
component
Boundaries 1–
3
ht.nrmesh
dnrmesh
1
Normal vector
(mesh), r
component
Boundaries 1–
3
ht.nphimesh
0
1
Normal vector
(mesh), phi
component
Boundaries 1–
3
1
Normal vector
(mesh), z
component
Boundaries 1–
3
1
Normal vector
down direction,
r component
Boundaries 1–
3
Boundaries 1–
3
ht.nzmesh
ht.dnr
dnzmesh
dnr
Details
ht.dnphi
0
1
Normal vector
down direction,
phi component
ht.dnz
dnz
1
Normal vector
down direction,
z component
Boundaries 1–
3
ht.unr
unr
1
Normal vector
up direction, r
component
Boundaries 1–
3
ht.unphi
0
1
Normal vector
up direction, phi
component
Boundaries 1–
3
ht.unz
unz
1
Normal vector
up direction, z
component
Boundaries 1–
3
ht.dEiInt
0
W
Total
accumulated
heat rate
Global
+ operation
ht.dEi0Int
0
W
Total
accumulated
energy rate
Global
+ operation
ht.ntfluxInt
ht.intExtBnd(ht.nt
flux*ht.varIntSpa)
W
Total net heat
rate
Global
ht.ntefluxInt
ht.intExtBnd(ht.nt
eflux*ht.varIntSpa
)
W
Total net energy
rate
Global
ht.QInt
ht.intDom(ht.Qtot
W
Total heat
Global
34
Name
Expression
Unit
Description
*ht.varIntSpa)ht.intIntBnd((ht.n
dflux_u+ht.ndflux
_d)*ht.varIntSpa)
Selection
Details
source
ht.WnsInt
0
W
Total work
source
Global
+ operation
ht.WInt
0
W
Total work
source
Global
+ operation
ht.varIntSpa
2*ht.d*pi*r
m
Intermediate
variable
Domain 1
2.5.3 Fluid 1
Fluid 1
SELECTION
Geometric entity level
Domain
Selection
Domain 1
EQUATIONS
Heat conduction, fluid
SETTINGS
Description
Value
35
Description
Value
Thermal conductivity
From material
Thermodynamics, fluid
SETTINGS
Description
Value
Fluid type
Gas/Liquid
Density
From material
Heat capacity at constant pressure
From material
Ratio of specific heats
From material
Coordinate system selection
SETTINGS
Description
Value
Coordinate system
Global coordinate system
Model input
SETTINGS
Description
Value
Velocity
User defined
Velocity
{0, 0, 0}
Absolute pressure
User defined
Absolute pressure
1[atm]
PROPERTIES FROM MATERIAL
Property
Material
Property group
Thermal conductivity
Water, liquid
Basic
Density
Water, liquid
Basic
Heat capacity at constant pressure
Water, liquid
Basic
Ratio of specific heats
Water, liquid
Basic
Variables
Name
Expression
Unit
Description
Selection
domflux.Tr
2*ht.dfluxr*ht.d*pi*
r
W/m
Domain flux, r
component
Domain 1
domflux.Tz
2*ht.dfluxz*ht.d*pi
*r
W/m
Domain flux, z
component
Domain 1
ht.DeltaH
integrate(subst(ht.
Cp,ht.fluid1.minpu
J/kg
Sensible
enthalpy
Domain 1
36
Details
+ operation
Name
Expression
Unit
Description
Selection
Details
t_pressure,ht.pref),
T,ht.Tref,T)+integr
ate(ht.mujtT,ht.flui
d1.minput_pressur
e,ht.pref,ht.pA)
ht.H
ht.HRef+ht.DeltaH
J/kg
Enthalpy
Domain 1
+ operation
ht.Ei
ht.H-ht.pA/ht.rho
J/kg
Internal energy
Domain 1
+ operation
ht.Ek
0.5*(ht.ur^2+ht.up
hi^2+ht.uz^2)
J/kg
Kinetic energy
Domain 1
+ operation
ht.dfluxr
-ht.k_effrr*Trht.k_effrz*Tz
W/m²
Conductive heat
flux, r
component
Domain 1
+ operation
ht.dfluxphi
-ht.k_effphir*Trht.k_effphiz*Tz
W/m²
Conductive heat
flux, phi
component
Domain 1
+ operation
ht.dfluxz
-ht.k_effzr*Trht.k_effzz*Tz
W/m²
Conductive heat
flux, z
component
Domain 1
+ operation
ht.dfluxtestr
-ht.k_effrr*test(Tr)ht.k_effrz*test(Tz)
W/m²
Conductive heat
flux, r
component
Domain 1
+ operation
ht.dfluxtestphi
ht.k_effphir*test(Tr
)ht.k_effphiz*test(Tz
)
W/m²
Conductive heat
flux, phi
component
Domain 1
+ operation
ht.dfluxtestz
-ht.k_effzr*test(Tr)ht.k_effzz*test(Tz)
W/m²
Conductive heat
flux, z
component
Domain 1
+ operation
Domain 1
+ operation
ht.cfluxr
ht.rho*ht.ur*ht.Ei
W/m²
Convective heat
flux, r
component
ht.cfluxphi
ht.rho*ht.uphi*ht.E
i
W/m²
Convective heat
flux, phi
component
Domain 1
+ operation
ht.cfluxz
ht.rho*ht.uz*ht.Ei
W/m²
Convective heat
flux, z
component
Domain 1
+ operation
ht.tefluxr
ht.dfluxr+ht.rho*ht
.ur*ht.H0
W/m²
Total energy
flux, r
component
Domain 1
+ operation
ht.tefluxphi
ht.dfluxphi+ht.rho
*ht.uphi*ht.H0
W/m²
Total energy
flux, phi
Domain 1
+ operation
37
Name
Expression
Unit
Description
Selection
Details
Domain 1
+ operation
component
ht.tefluxz
ht.dfluxz+ht.rho*ht
.uz*ht.H0
W/m²
Total energy
flux, z
component
ht.ndflux_d
if(r>0.001/sqrt(sqrt
(mean(emetric2))),
0.5*dflux_spatial(T)
/(pi*r),NaN)/ht.d
W/m²
Internal normal
conductive heat
flux, downside
Boundaries 1–
3
+ operation
ht.dEiInt
ht.fluid1.dEiInt
W
Total
accumulated
heat rate
Global
+ operation
Global
+ operation
ht.dEi0Int
ht.fluid1.dEi0Int
W
Total
accumulated
energy rate
ht.WnsInt
ht.fluid1.WnsInt
W
Total work
source
Global
+ operation
ht.krr
material.k11
W/(m·K)
Thermal
conductivity, rr
component
Domain 1
Meta
W/(m·K)
Thermal
conductivity,
phir component
Domain 1
Meta
W/(m·K)
Thermal
conductivity, zr
component
Domain 1
Meta
W/(m·K)
Thermal
conductivity,
rphi component
Domain 1
Meta
Domain 1
Meta
ht.kphir
ht.kzr
ht.krphi
material.k21
material.k31
material.k12
ht.kphiphi
material.k22
W/(m·K)
Thermal
conductivity,
phiphi
component
ht.kzphi
material.k32
W/(m·K)
Thermal
conductivity,
zphi component
Domain 1
Meta
ht.krz
material.k13
W/(m·K)
Thermal
conductivity, rz
component
Domain 1
Meta
ht.kphiz
material.k23
W/(m·K)
Thermal
conductivity,
phiz component
Domain 1
Meta
ht.kzz
material.k33
W/(m·K)
Thermal
Domain 1
Meta
38
Name
Expression
Unit
Description
Selection
Details
conductivity, zz
component
ht.k_iso
material.k_iso
W/(m·K)
Thermal
conductivity,
isotropic value
Domain 1
Meta
ht.rho
subst(material.rho,
ht.fluid1.minput_pr
essure,ht.prho,ht.fl
uid1.minput_temp
erature,ht.Trho)
kg/m³
Density
Domain 1
Meta
Domain 1
Meta
ht.Cp
material.Cp
J/(kg·K)
Heat capacity at
constant
pressure
ht.gamma
material.gamma
1
Ratio of specific
heats
Domain 1
Meta
ht.fluid1.pref
model.input.pref
Pa
Reference
pressure level
Domain 1
Meta
ht.res_T
Tt*ht.C_effht.k_effrr*Trrht.k_effrz*Trzht.k_effzr*Tzrht.k_effzz*Tzz(ht.qs+ht.qs_oop)*
T+ht.rho*ht.Cp*(ht
.ur*Tr+ht.uz*Tz)ht.Q-ht.Qoop
W/m³
Equation
residual
Domain 1
+ operation
ht.alphap
d(ht.rho,T)/max(ht.
rho,eps)
1/K
Isobaric
compressibility
coefficient
Domain 1
ht.pA
ht.fluid1.minput_pr
essure
Pa
Absolute
pressure
Domain 1
ht.gradTmag
sqrt(ht.gradTr^2+
ht.gradTphi^2+ht.
gradTz^2)
K/m
Temperature
gradient
magnitude
Domain 1
ht.Qmet
0
W/m³
Metabolic heat
source
Domain 1
ht.pref
ht.fluid1.pref
Pa
Reference
pressure level
Domain 1
ht.rhoInit
subst(ht.rho,ht.flui
d1.minput_pressur
e,1[atm],T,ht.Tinit)
kg/m³
Initial density
Domain 1
ht.rho_eff
ht.rho
kg/m³
Effective density
Domain 1
ht.C_eff
ht.rho*ht.Cp
J/(m³·K)
Effective
Domain 1
39
+ operation
Name
Expression
Unit
Description
Selection
volumetric heat
capacity
ht.mujtT
ht.k_effrr
ht.k_effphir
ht.k_effzr
ht.k_effrphi
ht.k_effphiphi
ht.k_effzphi
ht.k_effrz
ht.k_effphiz
0
ht.krr
ht.kphir
ht.kzr
ht.krphi
ht.kphiphi
ht.kzphi
ht.krz
ht.kphiz
m³/kg
Isothermal
Joule-Thomson
coefficient
Domain 1
W/(m·K)
Effective
thermal
conductivity, rr
component
Domain 1
W/(m·K)
Effective
thermal
conductivity,
phir component
Domain 1
W/(m·K)
Effective
thermal
conductivity, zr
component
Domain 1
W/(m·K)
Effective
thermal
conductivity,
rphi component
Domain 1
W/(m·K)
Effective
thermal
conductivity,
phiphi
component
Domain 1
W/(m·K)
Effective
thermal
conductivity,
zphi component
Domain 1
W/(m·K)
Effective
thermal
conductivity, rz
component
Domain 1
W/(m·K)
Effective
thermal
conductivity,
phiz component
Domain 1
Domain 1
Domain 1
ht.k_effzz
ht.kzz
W/(m·K)
Effective
thermal
conductivity, zz
component
ht.kappaTrr
0
W/(m·K)
Turbulent
thermal
40
Details
Name
Expression
Unit
Description
Selection
Details
conductivity, rr
component
ht.kappaTphir
ht.kappaTzr
ht.kappaTrphi
ht.kappaTphiphi
ht.kappaTzphi
ht.kappaTrz
ht.kappaTphiz
0
0
0
0
0
0
0
W/(m·K)
Turbulent
thermal
conductivity,
phir component
Domain 1
W/(m·K)
Turbulent
thermal
conductivity, zr
component
Domain 1
W/(m·K)
Turbulent
thermal
conductivity,
rphi component
Domain 1
W/(m·K)
Turbulent
thermal
conductivity,
phiphi
component
Domain 1
W/(m·K)
Turbulent
thermal
conductivity,
zphi component
Domain 1
W/(m·K)
Turbulent
thermal
conductivity, rz
component
Domain 1
W/(m·K)
Turbulent
thermal
conductivity,
phiz component
Domain 1
W/(m·K)
Turbulent
thermal
conductivity, zz
component
Domain 1
Domain 1
ht.kappaTzz
0
ht.kmean
0.5*(ht.k_effrr+ht.k
_effzz)
W/(m·K)
Mean effective
thermal
conductivity
ht.ur
ht.u_inputr
m/s
Velocity field, r
component
Domain 1
+ operation
ht.uphi
ht.u_inputphi
m/s
Velocity field,
phi component
Domain 1
+ operation
ht.uz
ht.u_inputz
m/s
Velocity field, z
Domain 1
+ operation
41
Name
Expression
Unit
Description
Selection
Details
component
ht.gradTr
ht.gradTphi
Tr
0
K/m
Temperature
gradient, r
component
Domain 1
K/m
Temperature
gradient, phi
component
Domain 1
Domain 1
ht.gradTz
Tz
K/m
Temperature
gradient, z
component
ht.cellPe
0.5*ht.rho*ht.Cp*h
*sqrt(ht.ur^2+ht.u
phi^2+ht.uz^2)/ht
.kmean
1
Cell Péclet
number
Domain 1
ht.Qltot
0
W/m
Total line heat
source
Point 3
ht.alphaTdrr
ht.k_effrr/ht.C_eff
m²/s
Thermal
diffusivity, rr
component
Domain 1
ht.alphaTdphir
ht.k_effphir/ht.C_ef
f
m²/s
Thermal
diffusivity, phir
component
Domain 1
ht.alphaTdzr
ht.k_effzr/ht.C_eff
m²/s
Thermal
diffusivity, zr
component
Domain 1
ht.alphaTdrphi
ht.k_effrphi/ht.C_ef
f
m²/s
Thermal
diffusivity, rphi
component
Domain 1
ht.alphaTdphiphi
ht.k_effphiphi/ht.C
_eff
m²/s
Thermal
diffusivity,
phiphi
component
Domain 1
ht.alphaTdzphi
ht.k_effzphi/ht.C_e
ff
m²/s
Thermal
diffusivity, zphi
component
Domain 1
ht.alphaTdrz
ht.k_effrz/ht.C_eff
m²/s
Thermal
diffusivity, rz
component
Domain 1
ht.alphaTdphiz
ht.k_effphiz/ht.C_e
ff
m²/s
Thermal
diffusivity, phiz
component
Domain 1
ht.alphaTdzz
ht.k_effzz/ht.C_eff
m²/s
Thermal
diffusivity, zz
Domain 1
42
+ operation
Name
Expression
Unit
Description
Selection
component
ht.alphaTdMean
ht.kmean/ht.C_eff
m²/s
Mean thermal
diffusivity
Domain 1
ht.Tradu
ht.Tu
K
Upside
temperature
Domain 1
ht.Tradu
ht.Tu
K
Upside
temperature
Boundaries 1–
3
ht.Tradd
ht.Td
K
Downside
temperature
Domain 1
ht.Tradd
ht.Td
K
Downside
temperature
Boundaries 1–
3
ht.fluid1.dEiInt
ht.fluid1.intDom((h
t.dEiht.Qm*ht.Ei)*ht.flui
d1.varIntSpa)
W
Total
accumulated
heat rate
Global
Domain 1
ht.dEi
d(ht.rho*ht.Ei,t)
W/m³
Total
accumulated
heat rate
density
ht.fluid1.dEi0Int
ht.fluid1.intDom((h
t.dEi0ht.Qm*ht.H)*ht.flui
d1.varIntSpa)
W
Total
accumulated
energy rate
Global
Domain 1
ht.dEi0
d(ht.rho*ht.Ei0,t)
W/m³
Total
accumulated
energy rate
density
ht.fluid1.ntfluxIn
t
ht.fluid1.intExtBnd(
ht.ntflux*ht.fluid1.v
arIntSpa)+ht.fluid1
.intExtBndUp(ht.ntf
lux_u*ht.fluid1.varI
ntSpa)+ht.fluid1.in
tExtBndDown(ht.nt
flux_d*ht.fluid1.var
IntSpa)
W
Total net heat
rate
Global
ht.fluid1.ntefluxI
nt
ht.fluid1.intExtBnd(
ht.nteflux*ht.fluid1.
varIntSpa)+ht.fluid
1.intExtBndUp(ht.n
teflux_u*ht.fluid1.v
arIntSpa)+ht.fluid1
.intExtBndDown(ht
.nteflux_d*ht.fluid1
W
Total net energy
rate
Global
43
Details
Name
Expression
Unit
Description
Selection
Details
ht.fluid1.QInt
ht.fluid1.intDom(ht
.Qtot*ht.fluid1.varI
ntSpa)ht.fluid1.intIntBnd(
(ht.ndflux_u+ht.nd
flux_d)*ht.fluid1.va
rIntSpa)
W
Total heat
source
Global
ht.fluid1.WnsInt
ht.fluid1.intDom(ht
.pA*(d(ht.ur,r)+if(a
bs(r)<0.001*h_spat
ial,d(ht.ur,r),ht.ur/r)
+d(ht.uz,z))*ht.flui
d1.varIntSpa)
W
Total work
source
Global
ht.fluid1.WInt
0
W
Total work
source
Global
ht.fluid1.varIntSp
a
2*ht.d*pi*r
m
Intermediate
variable
Domain 1
ht.T
ht.fluid1.minput_te
mperature
K
Temperature
Domain 1
ht.prho
ht.fluid1.minput_pr
essure
Pa
Pressure for the
evaluation of
density
Domain 1
ht.rhoref
subst(material.rho,
ht.fluid1.minput_pr
essure,ht.pref,ht.flu
id1.minput_temper
ature,ht.Tref)
kg/m³
Reference
density
Domain 1
Meta
ht.Cpmat
material.Cp
J/(kg·K)
Heat capacity at
constant
pressure
Domain 1
Meta
ht.kmatrr
material.k11
W/(m·K)
Thermal
conductivity, rr
component
Domain 1
Meta
ht.kmatphir
material.k21
W/(m·K)
Thermal
conductivity,
phir component
Domain 1
Meta
W/(m·K)
Thermal
conductivity, zr
component
Domain 1
Meta
W/(m·K)
Thermal
conductivity,
rphi component
Domain 1
Meta
.varIntSpa)
ht.kmatzr
ht.kmatrphi
material.k31
material.k12
44
Name
Expression
Unit
Description
Selection
Details
Domain 1
Meta
ht.kmatphiphi
material.k22
W/(m·K)
Thermal
conductivity,
phiphi
component
ht.kmatzphi
material.k32
W/(m·K)
Thermal
conductivity,
zphi component
Domain 1
Meta
ht.kmatrz
material.k13
W/(m·K)
Thermal
conductivity, rz
component
Domain 1
Meta
ht.kmatphiz
material.k23
W/(m·K)
Thermal
conductivity,
phiz component
Domain 1
Meta
ht.kmatzz
material.k33
W/(m·K)
Thermal
conductivity, zz
component
Domain 1
Meta
ht.c_s
sqrt(ht.gamma/ma
x(d(ht.rho,ht.fluid1.
minput_pressure),e
ps))
m/s
Speed of sound
Domain 1
ht.Ma
sqrt(ht.fluid1.minp
ut_velocityr^2+ht.f
luid1.minput_veloc
ityphi^2+ht.fluid1.
minput_velocityz^
2)/ht.c_s
1
Mach number
Domain 1
ht.Trho
ht.fluid1.minput_te
mperature
K
Temperature for
density
evaluation
Domain 1
ht.dfltopaque
-1
1
Default opacity
Domain 1
Domain 1
Domain 1
ht.timeDerivative
Tt
K/s
Temperature,
first time
derivative
ht.helem
h_spatial
m
Element size
Shape functions
Name
Shape function
Unit
Description
Shape frame
Selection
T
Lagrange (Linear)
K
Temperature
Spatial
Domain 1
Weak expressions
Weak expression
Integration order
Integration frame
Selection
2*ht.crosswind*pi*r
2
Spatial
Domain 1
45
Weak expression
Integration order
Integration frame
Selection
2*ht.streamline*pi*r
2
Spatial
Domain 1
2*(ht.dfluxr*test(Tr)+ht.dfluxz*test(Tz))*
ht.d*pi*r
2
Spatial
Domain 1
2*ht.C_eff*ht.timeDerivative*test(T)*ht.
d*pi*r
2
Spatial
Domain 1
2*ht.rho*ht.Cp*(ht.ur*Tr+ht.uz*Tz)*test
(T)*ht.d*pi*r
2
Spatial
Domain 1
2.5.4 Initial Values 1
Initial Values 1
SELECTION
Geometric entity level
Domain
Selection
Domain 1
Initial values
SETTINGS
Description
Value
Temperature
User defined
Temperature
310.15[K]
Variables
Name
Expression
Unit
Description
Selection
46
Name
Expression
Unit
Description
Selection
ht.Tinit
310.15[K]
K
Temperature
Domain 1
2.5.5 Axial Symmetry 1
Axial Symmetry 1
SELECTION
Geometric entity level
Boundary
Selection
Boundary 1
2.5.6 Thermal Insulation 1
Thermal Insulation 1
47
SELECTION
Geometric entity level
Boundary
Selection
No boundaries
EQUATIONS
Shape functions
Name
Shape
function
Unit
Description
Shape
frame
Selection
Details
T
Lagrange
(Linear)
K
Temperature
Spatial
No boundaries
Slit
T
Lagrange
(Linear)
K
Temperature
Material
No boundaries
Slit
T
Lagrange
(Linear)
K
Temperature
Geometry
No boundaries
Slit
T
Lagrange
(Linear)
K
Temperature
Mesh
No boundaries
Slit
2.5.7 Temperature 1
Temperature 1
SELECTION
Geometric entity level
Boundary
Selection
Boundaries 2–3
EQUATIONS
48
Temperature
SETTINGS
Description
Value
Temperature
User defined
Temperature
393.15[K]
Variables
Name
Expression
Unit
Description
Selection
Details
ht.T0
393.15[K]
K
Temperature
Boundaries 2–
3
+ operation
ht.temp1.Tave
nojac(ht.temp1.intBnd(
ht.temp1.varIntSpa*ht.
rho*ht.Cp*T*max(abs(
ht.ur*ht.nr+ht.uphi*ht.
nphi+ht.uz*ht.nz),eps))
)/nojac(ht.temp1.intBn
d(ht.temp1.varIntSpa*
ht.rho*ht.Cp*max(abs(
ht.ur*ht.nr+ht.uphi*ht.
nphi+ht.uz*ht.nz),eps))
)
K
Weighted
average
temperature
Global
ht.temp1.ntfluxIn
t
ht.temp1.intExtBnd(ht.
ntflux*ht.temp1.varInt
Spa)
W
Total net heat
rate
Global
ht.temp1.ntefluxI
nt
ht.temp1.intExtBnd(ht.
nteflux*ht.temp1.varIn
tSpa)
W
Total net energy
rate
Global
ht.temp1.ntfluxIn
t_u
ht.temp1.intIntBnd(ht.
ntflux_u*ht.temp1.varI
ntSpa)
W
Total net heat
rate, upside
Global
ht.temp1.ntefluxI
nt_u
ht.temp1.intIntBnd(ht.
nteflux_u*ht.temp1.var
IntSpa)
W
Total net energy
rate, upside
Global
ht.temp1.ntfluxIn
t_d
ht.temp1.intIntBnd(ht.
ntflux_d*ht.temp1.varI
ntSpa)
W
Total net heat
rate, downside
Global
ht.temp1.ntefluxI
nt_d
ht.temp1.intIntBnd(ht.
nteflux_d*ht.temp1.var
IntSpa)
W
Total net energy
rate, downside
Global
ht.temp1.varIntS
pa
2*ht.d*pi*r
m
Intermediate
variable
Boundaries 2–
3
49
Constraints
Constraint
Constraint force
Shape function
Selection
Details
ht.T0-ht.Tvar
test(ht.T0-ht.Tvar)
Lagrange (Linear)
Boundaries 2–3
Elemental
2.6 MESH 1
MESH STATISTICS
Description
Value
Minimum element quality
0.01606
Average element quality
0.8897
Triangle
5889
Quad
560
Edge element
371
Vertex element
3
Mesh 1
2.6.1 Size (size)
SETTINGS
Description
Value
Calibrate for
Fluid dynamics
Maximum element size
1.75
Minimum element size
0.05
Curvature factor
0.3
Maximum element growth rate
1.13
50
Description
Value
Predefined size
Fine
2.6.2 Size 1 (size1)
SELECTION
Geometric entity level
Boundary
Selection
Boundaries 2–3
Size 1
SETTINGS
Description
Value
Calibrate for
Fluid dynamics
Maximum element size
0.65
Minimum element size
0.0075
Curvature factor
0.25
Maximum element growth rate
1.08
Predefined size
Extra fine
2.6.3 Corner Refinement 1 (cr1)
SELECTION
Geometric entity level
Domain
Selection
Domain 1
51
Corner Refinement 1
2.6.4 Free Triangular 1 (ftri1)
SELECTION
Geometric entity level
Remaining
Free Triangular 1
2.6.5 Boundary Layers 1 (bl1)
SELECTION
Geometric entity level
Domain
Selection
Domain 1
52
Boundary Layers 1
SETTINGS
Description
Value
Handling of sharp corners
Trimming
Boundary Layer Properties 1 (blp1)
SELECTION
Geometric entity level
Boundary
Selection
Boundaries 2–3
Boundary Layer Properties 1
53
SETTINGS
Description
Value
Number of boundary layers
2
Thickness adjustment factor
5
54
3 Study 1
COMPUTATION INFORMATION
Computation time
15 s
CPU
Apple M1, 8 cores
Operating system
Mac OS X
3.1 TIME DEPENDENT
Times
Unit
range(0,10,600)
s
STUDY SETTINGS
Description
Value
Include geometric nonlinearity
Off
MESH SELECTION
Geometry
Mesh
mesh1
mesh1
PHYSICS AND VARIABLES SELECTION
Physics interface
Discretization
Laminar Flow (spf)
physics
Heat Transfer in Fluids (ht)
physics
MESH SELECTION
Geometry
Mesh
Geometry 1 (geom1)
mesh1
3.2 SOLVER CONFIGURATIONS
3.2.1 Solution 1
Compile Equations: Time Dependent (st1)
STUDY AND STEP
Description
Value
Use study
Study 1
Use study step
Time Dependent
LOG
55
<---- Compile Equations: Time Dependent in Study 1/Solution 1 (sol1) ----------Started at May 5, 2025 2:46:43 PM.
Geometry shape order: Linear
Running on Apple M1.
Using 1 socket with 8 cores in total on Ayushs-MacBook-Air.local.
Available memory: 8.19 GB.
Time: 2 s.
Physical memory: 1.4 GB
Virtual memory: 49.32 GB
Ended at May 5, 2025 2:46:45 PM.
----- Compile Equations: Time Dependent in Study 1/Solution 1 (sol1) ---------->
Dependent Variables 1 (v1)
GENERAL
Description
Value
Defined by study step
Time Dependent
RESIDUAL SCALING
Description
Value
Method
Manual
INITIAL VALUE CALCULATION CONSTANTS
Constant name
Initial value source
t
range(0,10,600)
timestep
0.6[s]
LOG
<---- Dependent Variables 1 in Study 1/Solution 1 (sol1) ----------------------Started at May 5, 2025 2:46:45 PM.
Solution time: 0 s.
Physical memory: 1.4 GB
Virtual memory: 49.32 GB
Ended at May 5, 2025 2:46:45 PM.
----- Dependent Variables 1 in Study 1/Solution 1 (sol1) ---------------------->
Pressure (comp1.p) (comp1_p)
GENERAL
Description
Value
Field components
comp1.p
Temperature (comp1.T) (comp1_T)
GENERAL
Description
Value
Field components
comp1.T
56
Velocity field (comp1.u) (comp1_u)
GENERAL
Description
Value
Field components
{comp1.u, comp1.w}
Time-Dependent Solver 1 (t1)
GENERAL
Description
Value
Defined by study step
Time Dependent
Times
{0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170,
180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320,
330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470,
480, 490, 500, 510, 520, 530, 540, 550, 560, 570, 580, 590, 600}
Relative tolerance
0.005
ABSOLUTE TOLERANCE
Description
Value
Tolerance factor
0.05
SETTINGS: PRESSURE (COMP1.P)
Description
Value
Method
Scaled
Tolerance factor
1
TIME STEPPING
Description
Value
Maximum BDF order
2
Nonlinear controller
On
Fraction of initial step for Backward Euler
0.01
Error estimation
Exclude algebraic
LOG
57
<---- Time-Dependent Solver 1 in Study 1/Solution 1 (sol1) --------------------Started at May 5, 2025 2:46:45 PM.
Time-dependent solver (BDF)
Number of degrees of freedom solved for: 14764 (plus 13273 internal DOFs).
Nonsymmetric matrix found.
Scales for dependent variables:
Pressure (comp1.p): 2e+03
Temperature (comp1.T): 3.1e+02
Velocity field (comp1.u): 4.6e+03
Step
Time
Stepsize
Res Jac Sol Order Tfail NLfail
LinErr
LinRes
0
0
- out
24
5
24
0
0.0016 4.1e-16
1
0.0065667
0.0065667
26
6
26
1
0
0 1.7e-06 1.2e-16
2
0.013133
0.0065667
28
7
28
1
0
0 5.3e-06 1.2e-16
3
0.026267
0.013133
30
8
30
2
0
0 1.8e-07 8.4e-17
4
0.0394
0.013133
32
9
32
2
0
0 3.4e-06
1e-16
5
0.065667
0.026267
34
10
34
2
0
0 3.3e-06 1.3e-16
6
0.091933
0.026267
36
11
36
2
0
0 2.8e-06 1.2e-16
7
0.14447
0.052533
38
12
38
2
0
0 1.3e-07 1.3e-16
8
0.197
0.052533
40
13
40
1
0
0
9e-10 1.2e-16
9
0.24953
0.052533
42
14
42
1
0
0 3.4e-09 1.3e-16
10
0.3546
0.10507
44
15
44
1
0
0 1.5e-09 1.7e-16
11
0.45967
0.10507
46
16
46
1
0
0 4.8e-09 1.5e-16
12
0.6698
0.21013
48
17
48
1
0
0 2.8e-09 1.6e-16
13
0.87993
0.21013
50
18
50
1
0
0 5.6e-09 1.5e-16
14
1.3002
0.42027
52
19
52
1
0
0 4.4e-09 1.8e-16
15
1.7205
0.42027
54
20
54
1
0
0
1e-08 1.8e-16
16
2.1407
0.42027
56
21
56
1
0
0 1.5e-08 1.8e-16
17
2.9813
0.84053
58
22
58
1
0
0 1.6e-08 2.3e-16
18
3.8218
0.84053
60
23
60
1
0
0
2e-08 2.3e-16
19
5.5029
1.6811
62
24
62
1
0
0 2.2e-08
3e-16
20
7.1839
1.6811
64
25
64
1
0
0 4.1e-08 2.9e-16
21
8.865
1.6811
66
26
66
1
0
0 7.7e-08 2.8e-16
10
- out
22
12.227
3.3621
68
27
68
1
0
0 5.9e-08 3.6e-16
23
15.589
3.3621
70
28
70
1
0
0 1.9e-07
4e-16
20
- out
24
22.313
6.7243
72
29
72
1
0
0 6.4e-08 5.5e-16
25
29.038
6.7243
74
30
74
1
0
0 9.9e-08 5.8e-16
30
- out
26
35.762
6.7243
76
31
76
1
0
0 2.7e-07 5.2e-16
40
- out
27
49.21
13.449
78
32
78
1
0
0 2.5e-07 7.9e-16
50
- out
60
- out
28
62.659
13.449
80
33
80
1
0
0 2.4e-07 8.3e-16
70
- out
29
76.108
13.449
82
34
82
1
0
0 1.9e-06 7.8e-16
80
- out
90
- out
100
- out
30
103
26.897
84
35
84
1
0
0 1.1e-07 1.2e-15
110
- out
120
- out
31
129.9
26.897
86
36
86
1
0
0 4.3e-07 1.1e-15
130
- out
140
- out
58
150
- out
32
156.8
26.897
160
- out
170
- out
180
- out
190
- out
200
- out
210
- out
33
210.59
53.794
220
- out
230
- out
240
- out
250
- out
260
- out
34
264.39
53.794
270
- out
280
- out
290
- out
300
- out
310
- out
35
318.18
53.794
320
- out
330
- out
340
- out
350
- out
360
- out
370
- out
36
378.18
60
380
- out
390
- out
400
- out
410
- out
420
- out
430
- out
37
438.18
60
440
- out
450
- out
460
- out
470
- out
480
- out
490
- out
38
498.18
60
500
- out
510
- out
520
- out
530
- out
540
- out
550
- out
39
558.18
60
560
- out
570
- out
580
- out
590
- out
600
- out
40
618.18
60
Time-stepping completed.
88
37
88
1
0
0
1e-06
1.1e-15
90
38
90
1
0
0
1.6e-06
1.6e-15
92
39
92
1
0
0
8.7e-06
1.6e-15
94
40
94
1
0
0
4.8e-06
1.6e-15
96
41
96
1
0
0
8.3e-06
1.6e-15
98
42
98
1
0
0
1.1e-05
1.6e-15
100
43
100
1
0
0
1.5e-05
1.5e-15
102
44
102
2
0
0
1.4e-05
1.1e-15
104
45
104
2
0
0
0.00014
9.2e-16
59
Solution time: 13 s.
Physical memory: 1.78 GB
Virtual memory: 49.34 GB
Ended at May 5, 2025 2:46:58 PM.
----- Time-Dependent Solver 1 in Study 1/Solution 1 (sol1) -------------------->
Advanced (aDef)
ASSEMBLY SETTINGS
Description
Value
Reuse sparsity pattern
On
Fully Coupled 1 (fc1)
GENERAL
Description
Value
Linear solver
Direct 1
METHOD AND TERMINATION
Description
Value
Damping factor
0.9
Jacobian update
Once per time step
Maximum number of iterations
8
Tolerance factor
0.5
Stabilization and acceleration
Anderson acceleration
Dimension of iteration space
5
Mixing parameter
0.9
Iteration delay
1
Direct 1 (d1)
GENERAL
Description
Value
Solver
PARDISO
Pivoting perturbation
1.0E-13
60
4 Results
4.1 DATA SETS
4.1.1 Study 1/Solution 1
SOLUTION
Description
Value
Solution
Solution 1
Component
Save Point Geometry 1
Data set: Study 1/Solution 1
4.1.2 Revolution 2D
DATA
Description
Value
Data set
Study 1/Solution 1
AXIS DATA
Description
Value
Axis entry method
Two points
Points
{{0, 0}, {0, 1}}
REVOLUTION LAYERS
Description
Value
Start angle
-90
61
Description
Value
Revolution angle
225
Data set: Revolution 2D
4.2 PLOT GROUPS
4.2.1 Velocity (spf)
Surface: Velocity magnitude (m/s)
62
4.2.2 Pressure (spf)
Contour: Pressure (Pa)
4.2.3 Velocity (spf) 1
Surface: Velocity magnitude (m/s)
63
4.2.4 Temperature, 3D (ht)
Surface: Temperature (K)
4.2.5 Isothermal Contours (ht)
Contour: Temperature (K)
64