FlexPDE Descriptor File

TITLE 'Temperature vs. Time at 0.0040 m/sec' { intel.pde }

SELECTerrlim=1e-3 spectral_colors

VARIABLES

temp( range=400)

DEFINITIONS

Lx = .2286 { in meters }

Ly = .1294 { in meters }

RealHeight = .1524 { in meters }

d0 = .0275 { length of heat source in meters }

heat_flux = -33517 { W / m^2 }

time_interval = 120

vx = .0040 { Moving heat source velocity in m/sec }

period = (Lx - d0) / vx

oscillations = time_interval / period

length = Lx

heat = 0

tempi = 26.5 { degrees Celsius }

k = 386 {Thermal conductivity of copper }

rcp= 8954 * 383.1

{ Density of copper times specific heat }

{ Source: p. 657 of Heat Conduction Ed. 2 by Ozisik [7] }

fluxd_x = -k*dx(temp)

fluxd_y = -k*dy(temp)

fluxd = vector(fluxd_x, fluxd_y)

fluxdm = magnitude(fluxd)

step = abs(ustep( mod(t, period * 2) - period)

* period - mod(t, period) )

{ In FlexPDE, mod does accept floats. This means repeated subtraction rather than remainder. }

fluxd0 = heat_flux * [ustep(vx* step + d0 - x)

- ustep(vx * step - x)]

INITIAL VALUES

temp = tempi

EQUATIONS

div(fluxd) + rcp * dt(temp) = 0

BOUNDARIES

region 'domain'

start (0,0) natural(temp) = 0 line to (Lx,0)

natural(temp) = 0 line to (Lx,Ly)

natural(temp) = fluxd0 line to (0,Ly)

natural(temp)= 0 line to finish

TIME

from 0 to oscillations * period

PLOTS

for t=0 by period * .1 to

oscillations * period

contour( temp) painted

vector( fluxd) norm

elevation( fluxd0 ) from (0,0) to (Lx,0)

HISTORIES

HISTORY(temp) at

(Lx/5,2*RealHeight/3) (2*Lx/5, 2*RealHeight/3)

(3*Lx/5,2*RealHeight/3) (4*Lx/5, 2*RealHeight/3)

(Lx/5,RealHeight/3) (2*Lx/5, RealHeight/3)

(3*Lx/5,RealHeight/3) (4*Lx/5, RealHeight/3)

END