➤DIAGRAM :
➤BOUNDARY CONDITIONS :
Left wall :
Any temperature (℃)
Bottom wall : Any temperature (℃)
Right wall : Any temperature (℃)
Top wall : Any temperature (℃)
➤SCILAB CODE :
clc
disp("********2D CONSTANT WALL TEMPERATURE PROBLEM********")
disp("GEOMETRIC DETAILS")
L=input("Domain Length (in m):")
H=input("Domain Height (in m):")
disp("GRID DETAILS")
Nx=input("No. of divisions in X direction :")
Ny=input("No. of divisions in Y direction :")
dx=L/Nx
dy=H/Ny
m=(dx/dy)
disp("DOMAIN PROPERTIES")
K=input("Enter the thermal conductivity of plate material (in W/mK) :")
disp("BOUNDARY CONDITIONS")
Tl=input("Enter the left wall temperature (in Degree C) :")
Tb=input("Enter the bottom wall temperature (in Degree C) :")
Tr=input("Enter the right wall temperature (in Degree C) :")
Tt=input("Enter the top wall temperature (in Degree C) :")
Ta=input("Enter the ambient temperature (in Degree C) :")
n=input("Enter the number of iterations :")
//***INITIAL TEMPERATURE OF DOMAIN***//
T=Ta*ones(Nx+1,Ny+1)
//***LEFT WALL TEMPERATURE***//
for j=2:1:Ny
T(1,j)=Tl
end
//***LEFT BOTTOM TEMPERATURE***//
for i=2:1:Nx
T(i,1)=Tb
end
//***LEFT RIGHT TEMPERATURE***//
for j=2:1:Ny
T(Nx+1,j)=Tr
end
//***LEFT TOP TEMPERATURE***//
for i=2:1:Nx
T(i,Ny+1)=Tt
end
//***CORNER POINT TEMPERATURES***//
T(1,1)=(Tl+Tb)/2
T(Nx+1,1)=(Tr+Tb)/2
T(Nx+1,Ny+1)=(Tr+Tt)/2
T(1,Ny+1)=(Tl+Tt)/2
//***TEMPERATURE DISTRIBUTION IN INTERIOR POINTS***//
for k=1:1:n
for j=2:1:Ny
for i=2:1:Nx
T(i,j)=(T(i+1,j)+T(i-1,j)+(m^2)*(T(i,j+1)+T(i,j-1)))/(2*(1+m^2))
end
end
end
//***PLOTTING CONTOUR FOR TEMPERATURE DISTRIBUTION***//
Tmax=0
Tmin=0
xp=0:dx:L
yp=0:dy:H
for j=1:1:Ny+1
for i=1:1:Nx+1
if T(i,j)<Tmin then
Tmin=T(i,j)
end
if T(i,j)>Tmax then
Tmax=T(i,j)
end
end
end
clf()
f=gcf();
f.color_map=jetcolormap(64);
colorbar(Tmin,Tmax)
Sgrayplot(xp,yp,T,strf="041")
//***TEMPERATURE DISTRIBUTION AT HORIZONTAL MID LINE***//
xset('window',1)
plot2d(xp,T(:,(Ny/2)+1))
//***TEMPERATURE DISTRIBUTION AT VERTICAL MID LINE***//
xset('window',2)
plot2d(yp,T((Nx/2)+1,:))
disp(T)
//***END***//
➤CONSIDER :
No. of divisions in x
& y directions : 100
Thermal conductivity of
plate material : 237 W/mK
No. of iterations : 1000
➤RESULT :
For Tl=100
Tb=Tr=Tt=25
