﻿ Sample Problems > Usage > Sequenced_Equations > initialeq

# initialeq

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# initialeq

{  INITIALEQ.PDE

This example illustrates use of the INITIAL EQUATIONS section.

It is s modification of the FLOAT_ZONE.PDE example that first

solves for a gaussian initial temperature distribution.

}

title "Float Zone"

coordinates xcylinder('Z','R')

variables

temp (threshold=100)

temp2(threshold=100)

definitions

k = 0.85     {thermal conductivity}

cp = 1       { heat capacity }

long = 18

H = 0.4       {free convection boundary coupling}

Ta = 25       {ambient temperature}

A = 4500     {amplitude}

source = A*exp(-((z-1*t)/.5)^2)*(200/(t+199))

tsource = time_integral(vol_integral(source))

t1 = time_integral(1.0)

initial value

temp = Ta

temp2 = Ta

initial equations

equations

Temp:  div(k*grad(temp)) + source = cp*dt(temp)

Temp2:  div(k*grad(temp2)) + source = cp*dt(temp2)

boundaries

region 1

start(0,0)

natural(temp) = 0

natural(temp2) = 0

line to (long,0)

value(temp) = Ta

value(temp2) = Ta

line to (long,1)

natural(temp) = -H*(temp - Ta)

natural(temp2) = -H*(temp2 - Ta)

line to (0,1)

value(temp) = Ta

value(temp2) = Ta

line to close

feature

start(0.01*long,0) line to (0.01*long,1)

time -0.5 to 19

monitors

for t = -0.5 by 0.5 to (long + 1)

elevation(temp, temp2) from (0,1) to (long,1) range=(0,1800) as "Surface Temp"

contour(temp)

contour(dt(temp))

contour(temp2)

plots

for t = -0.5 by 0.5 to (long + 1)

elevation(temp, temp2) from (0,0) to (long,0) range=(0,1800) as "Axis Temp"

histories

history(temp,dt(temp)) at (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0) (7,0) (8,0)

(9,0) (10,0) (11,0) (12,0) (13,0) (14,0) (15,0) (16,0)

(17,0) (18,0)

history(temp2,dt(temp2)) at (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0) (7,0) (8,0)

(9,0) (10,0) (11,0) (12,0) (13,0) (14,0) (15,0) (16,0)

(17,0) (18,0)

history(t1) as "Tintegral(1)"

history(tsource) as "Tintegral(Source)"

end