TITLE 'heat transfer through composite' COORDINATES cartesian2 select ngrid = 5 VARIABLES u (threshold=0.01) DEFINITIONS {SI-units} k=85 {conductivity} pulse=10*upulse(t-0.5,t+1) {periodically heat supply along this edge} cp {heat capacity} rho {density} ra=6.25e-3 {sample radius} d1=2e-3 {thickness of material 1} d2=4e-3 {thickness of material 2} EQUATIONS u: dx(k*dx(u))+dy(k*dy(u))=cp*rho*dt(u) BOUNDARIES REGION 1 "sample chamber" {filled with inert gas} cp=5193 k=0.1513 rho=0.1785 START (-3.25e-3,0.01) natural(u)=0 line to (0.01,0.01) natural(u)=0 line to (0.01,-3.25e-3) natural(u)=0 line to (-3.25e-3,-3.25e-3) natural(u)=0 line to close REGION 2 "material 1" {with low conductivity} {initial temperature = 300 K} k=3 rho=6e-9 cp=418 START(0,0) value(u) = 300 natural(u)=pulse LINE TO (0,ra) value(u)=300 LINE TO (d1,ra) LINE TO (d1,0) value(u)=300 LINE TO CLOSE REGION 3 "material 2" {with high conductivity} k=85 rho=8.9e-9 cp=230 START(d1,0) LINE TO(d1,ra) value(u)=300 LINE TO(d1+d2,ra) value(u)=300 LINE TO(d1+d2,0) value(u)=300 LINE TO CLOSE TIME 0 TO 4 by 0.01 MONITORS for t=0 by 0.01to 4 elevation(u) from (0,0) to (d1+d2,0) elevation(u) from (0,ra) to (d1+d2,0) history(u) at (0,0) (d1+d2,0) history(u) at (0,ra) (d1+d2,0) elevation(u) from (0,ra) to (d1+d2,ra) elevation(u) from (0,0) to (d1+d2,0) elevation(u) from (0,ra) to (d1+d2,0) history(u) at (0,ra) (d1,ra) (d1+d2,ra) history(u) at (0,0) (d1,0) (d1+d2,0) PLOTS for t=0 by 0.01 to 4 CONTOUR(u) SURFACE(u) elevation(u) from (0,ra) to (d1+d2,ra) elevation(u) from (0,0) to (d1+d2,0) elevation(u) from (0,ra) to (d1+d2,0) history(u) at (0,ra) (d1,ra) (d1+d2,ra) history(u) at (0,0) (d1,0) (d1+d2,0) END