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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 13 "Heat Flow, II" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "The cell below \+
investigates a three brick model.  " }{TEXT 256 16 "Evaluate it now." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 1190 "with(plottools):\nwith(plots):\n\nAmbient := t -> sin(3.1416
 * t / 12):\n\nEndTime := 216:\nk := 0.25:\nc := 0.25:\n\nExterior := \+
t -> sin(3.1416 * t / 12):\n\nIVP := \{diff(Interior(t), t) = c * (Bri
ck3(t) - Interior(t)),\n        diff(Brick3(t), t) = k * (Interior(t) \+
- 2 * Brick3(t) +\n                                  Brick2(t)),\n    \+
    diff(Brick2(t), t) = k * (Brick3(t) - 2 * Brick2(t) + \n          \+
                        Brick1(t)),\n        diff(Brick1(t), t) = k * \+
(Exterior(t) - Brick1(t)),\n        Interior(0) = 4,\n        Brick3(0
) = 3,\n        Brick2(0) = 2,\n        Brick1(0) = 1\}:\n\nsolution :
= dsolve(IVP, \n              \{Interior(t), Brick1(t), Brick2(t), Bri
ck3(t)\}, numeric):\n\nplot1 := display(\{odeplot(solution, [t, Brick3
(t)], \n                  0..EndTime, color=red)\}):\n\nplot2 := displ
ay(\{odeplot(solution, [t, Interior(t)], \n                  0..EndTim
e, color=blue)\}):\n\nplot3 := display(\{odeplot(solution, [t, Brick2(
t)], \n                  0..EndTime, color=red)\}):\n\nplot4 := displa
y(\{odeplot(solution, [t, Brick1(t)], \n                  0..EndTime, \+
color=blue)\}):\n\n\n\ngraf := plot(Exterior(t), t = 0..EndTime, -1..3
, color=black):\n\ndisplay([plot1, plot2, plot3, plot4, graf]);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 180 "Y
ou may want to enlarge the graph above to see it more clearly.  Notice
 that the interior temperature is lagging roughly 12 hours (one-half p
eriod) behind the exterior temperature." }}}}{MARK "0 0 0" 13 }
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