(*^

::[	frontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.1";
	macintoshStandardFontEncoding; 
	paletteColors = 128; automaticGrouping; currentKernel; 
	fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8,  24, "Times"; ;
	fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6,  18, "Times"; ;
	fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6,  14, "Times"; ;
	fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20,  18, "Times"; ;
	fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15,  14, "Times"; ;
	fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12,  12, "Times"; ;
	fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; ;
	fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5,  12, "Courier"; ;
	fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; ;
	fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5,  12, "Courier"; ;
	fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; ;
	fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5,  12, "Courier"; ;
	fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287,  12, "Courier"; ;
	fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic,  10, "Geneva"; ;
	fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = leftheader, inactive, L2,  12, "Times"; ;
	fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7,  12, "Times"; ;
	fontset = leftfooter, inactive, L2,  12, "Times"; ;
	fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; ;
	fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
]
:[font = special1; inactive; preserveAspect; ]
                                                   Heat Flow, II

The cell below investigates a three brick model.  Evaluate it now.
;[s]
4:0,1;64,0;116,2;131,0;133,-1;
3:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[Interior, 
      Brick1, Brick2, Brick3, 
      Exterior, k, c, hight]

Exterior[t_] := Sin[Pi * t / 12]

hight := 216
k := 0.25
c := 0.25

solution = NDSolve[
{Interior'[t] == c * (Brick3[t] - Interior[t]),
 Brick3'[t] == k * (Brick2[t] - Brick3[t]) +
               k * (Interior[t] - Brick3[t]),
 Brick2'[t] == k * (Brick1[t] - Brick2[t]) +
               k * (Brick3[t] - Brick2[t]),
 Brick1'[t] == k * (Brick2[t] - Brick1[t]) +
               k * (Exterior[t] - Brick1[t]),
 Interior[0] == 4,
 Brick3[0] == 3,
 Brick2[0] == 2,
 Brick1[0] == 1},
 {Interior, Brick1, Brick2, Brick3}, 
 {t, 0, hight}];
 
Plot[{Interior[t] /. solution,
      Brick1[t] /. solution,
      Brick2[t] /. solution,
      Brick3[t] /. solution,
      Exterior[t]},
     {t, 0, hight},
     PlotRange -> {-1, 4},
     PlotStyle -> {{RGBColor[0, 0, 0]},
                   {RGBColor[1, 0, 1]},
                   {RGBColor[0, 0, 1]},
                   {RGBColor[1, 0, 1]},
                   {RGBColor[1, 0, 0]}}]
                   
Plot[{Interior[t] /. solution,
      Brick2[t] /. solution,
      Exterior[t]},
     {t, 0, hight},
     PlotRange -> {-1, 4},
     PlotStyle -> {{RGBColor[0, 0, 0]},
                   {RGBColor[0, 0, 1]},
                   {RGBColor[1, 0, 0]}}]
                   
Plot[{Interior[t] /. solution,
      Brick2[t] /. solution,
      Exterior[t]},
     {t, 2*hight/3, hight},
     PlotRange -> {-1, 1},
     PlotStyle -> {{RGBColor[0, 0, 0]},
                   {RGBColor[0, 0, 1]},
                   {RGBColor[1, 0, 0]}}]
:[font = special1; inactive; preserveAspect; ]
Three graphs are produced by the cell above.  The first graph shows all five temperatures -- the interior temperature, the exterior temperature, and the temperatures of each of the three bricks.  The second graph shows the interior temperature, the exterior temperature, and the temperature of the middle brick.  This graph is less cluttered.  The third graph shows a portion of the second graph after the system has run long enough to be close to equilibrium.  The roughly 12 hour time lag is easily seen in this last graph.
^*)