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' Temperature distribution in a thin, square plate.
' The plate is isolated on both sides, heat can only
' escape along the edges. A heat source warms up the plate
' in one point; this point may be repositioned by tapping
' somewhere on the plate. The strenght of the heat source
' can be regulated by the slider. The other slider sets the
' thermal conductivity, wich is a material property. The
' temperature distribution is shown in colors an in numbers.
' The "outside" temperature along the edges is fixed on 0 degrees.
'
graphics ! graphics clear .8,.8,.8
fill color .8,.8,.8 ! draw color 0,0,0
dim to(13,13), tn(13,13), q(12,12)
q_in=75 ! qx=4 ! qy=7 ! labda=0.1 ! cv=1 ! tmax=300
for i=1 to 11 ! for j=1 to 11
to(i,j)=20 ! q(i,j)=20*cv
next j ! next i
for i=0 to 12
to(0,i)=0 ! to(12,i)=0 ! to(i,0)=0 ! to(i,12)=0
next i
for i=0 to 10
t=i/10 ! t_color(t) ! fill circle 85+60*i,750 size 15
draw text n2a$(i*tmax/10,3,0) at 55+60*i,770
next i
draw font size 16
slider "heat" value .5 at 70,820 hsize 630
draw text "heat source" at 330,815
draw text "zero" at 70,815 ! draw text "max" at 670,815
slider "cond" value .5 at 70,880 hsize 630
draw text "thermal conductivity" at 285,875
draw text "zero" at 70,875 ! draw text "max" at 670,875
draw color .3,.3,.3
loop:
disp(to)
for i=1 to 11 ! for j=1 to 11
q(i,j) += labda*(to(i-1,j)+to(i+1,j)+to(i,j-1)+to(i,j+1)-4*to(i,j))
next j ! next i
q(qx,qy) += q_in
for i=1 to 11 ! for j=1 to 11 ! to(i,j)=q(i,j)/cv ! next j ! next i
if slider_changed("heat") then q_in=150*slider_value("heat")
if slider_changed("cond") then labda=0.25*slider_value("cond")
get touch 0 as xt,yt
if xt>0 and xt>50 and xt<720 and yt>50 and yt<720 then
qx=floor((xt+10)/60) ! qy=floor((yt+10)/60)
end if
goto loop
end
def t_color(t)
if t<0 then t=0 ! if t>1 then t=1
if t<0.2 then
r=0 ! g=0 ! b=5*t
else
if t<0.7 then
r=2*(t-0.2) ! g=0 ! b=2*(0.7-t)
else
if t<0.9 then
r=1 ! g=5*(t-0.7) ! b=0
else
r=1 ! g=1 ! b=10*(t-0.9)
end if
end if
end if
fill color r,g,b
end def
def disp (t(,))
graphics lock
for i=1 to 11 ! for j=1 to 11
x=50+60*(i-1) ! y=50+60*(j-1)
t_color(t(i,j)/.tmax)! fill rect x,y to x+60,y+60
draw text floor(t(i,j)) at x+10,y+20
next j ! next i
for s=50 to 710 step 60
draw line 50,s to 710,s ! draw line s,50 to s,710
next s
graphics unlock
end def
def n2a$(num,lang,dec)
b$=" "
fac=10^dec
num$=floor(fac*num+.5)/fac
tot=lang-len(num$)
if tot<1 then tot=1
a$=substr$(b$,1,tot) & num$
n2a$=a$
end def
