{ Th2LS_1.PDE - program for FlexPDE }
title "Heat flow in 2D region"
select
errlim = 1e-3 {error tolerance}
Variables
Temp {variable for temperature}
definitions
hl=1.4 {height}
wl=0.8 {width}
wwl=0.2 {wall width}
hal=0.7 {additional dimensions}
K = 46.7 {thermal conductivity}
Source = 0 {heat generation rate per unit volum (can be omitted)}
hf=60 {film coefficient}
Text = 0 {bulk temperature of the adjacent medium}
Tinp1 = 90 {temperature on left bottom boundary}
Tinp2 = 180 {temperature on right bottom boundary}
flux = -K*grad(Temp) {thermal flux vector}
pel=(hal/2)/(wl-wwl) {elliptic factor}
equations
div(flux) = Source {thermal conductivity equation}
{ (or in the form div(flux) = 0 with Source = 0) }
boundaries {problem domain and boundary conditions}
Region 1 {domain 1}
start (0,0)
value(Temp)=Tinp1 {boundary with specified temperature}
line to (wwl,0)
natural(Temp)=0 {heat flux is equal to zero}
line to (wwl,hl-hal-wwl)
line to (wl-wwl,0)
value(Temp)=Tinp2 {boundary with specified temperature}
line to (wl,0)
natural(Temp)=0 {thermally insulated boundary}
line to (wwl,hl-hal)
arc (center=wwl,hl-hal/2) to (wl,hl-hal/2) {arc in the form of ellipse part}
arc (center=wwl,hl-hal/2) to (wwl,hl)
natural(Temp)=-hf*(Text-Temp) {convective heat transfer}
line to (0,hl)
natural(Temp)=0
line to close
natural(Temp)=0
start (wwl,hl-hal/2-(wl-2*wwl)*pel) {hole in the domain}
arc (center=wwl,hl-hal/2) to (wl-wwl,hl-hal/2)
arc (center=wwl,hl-hal/2) to (wwl,hl-hal/2+(wl-2*wwl)*pel)
line to close
monitors
contour(Temp) {show contour plots of solution in progress}
plots {resulting plots}
grid(x,y) as "Finite element mesh"
contour(Temp) painted as "Temperature"
contour(magnitude(flux)) painted as "Heat flow vector magnitude"
vector(flux) as "Heat Flow vector"
end