(*^

::[	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 and Diffusion, I

The work in the cell below is similar to work we did in the previous module.  We repeat it here to make it easier to compare our work in this module with our work in the previous module.  Evaluate it now.
;[s]
4:0,1;65,0;255,2;270,0;272,-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[solution, Ambient, k, hight]

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

hight := 72
k := 0.50

solution = NDSolve[
   {T'[t] == k * (Ambient[t] - T[t]),
    T[0] == 3}, 
    T, {t, 0, hight}];
         
Plot[{T[t] /. solution, Ambient[t]},
     {t, 0, hight},
     PlotRange -> {-3, 3},
     PlotStyle -> {{RGBColor[0, 0, 1]},
                   {RGBColor[1, 0, 0]}}]
:[font = special1; inactive; preserveAspect; ]
The next cell works with a model like the one discussed in this module.  Evaluate it now and then compare it to the model above.  Then use this cell as a basis for further experimentation.
;[s]
3:0,0;73,1;187,0;189,-1;
2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[Interior, Brick, Exterior, k, c, hight]

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

hight := 72
k := 0.50
c := 0.50

solution = NDSolve[
{Interior'[t] == c * (Brick[t] - Interior[t]),
 Brick'[t] == k * (Exterior[t] - Brick[t]) +
              k * (Interior[t] - Brick[t]),
 Interior[0] == 3,
 Brick[0] == 2},
 {Interior, Brick}, {t, 0, hight}];
 
Plot[{Interior[t] /. solution,
      Brick[t] /. solution,
      Exterior[t]},
     {t, 0, hight},
     PlotRange -> {-3, 3},
     PlotStyle -> {{RGBColor[1, 0, 0]},
                   {RGBColor[0, 0, 1]},
                   {RGBColor[0, 0, 0]}}]
^*)