Clean up code to run faster

*To*: mathgroup at smc.vnet.net*Subject*: [mg122246] Clean up code to run faster*From*: Michelle Maul <michellemaul312 at gmail.com>*Date*: Sat, 22 Oct 2011 06:07:04 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hello Mathematica friends, I am new to Mathematica and I have learned that it is a steep learning curve, I've spent a week trying to program an example problem from a heat transfer book. I need it to solve for several hundred time steps and my computer is only allowing me to do about 15 in an hour of solving. How can I clean up my code and what are some general tips that you can give me for the future when I need to do more hard core iteration problems and stuff? PS, I'm a mechanical engineer so I'm not very good at understanding how Mathematica thinks in computer language (anything is helpful). I am solving for the temperatures on the inside and outside of the wall while the sun is heating the outside at certain times of the day. << AutomaticUnits`; masonry = {WallThickness -> 1. Foot, \[Alpha] -> 4.78*10^-6 Foot^2/ Second, k -> 0.4 BTU/(Hour*Foot*Fahrenheit), \[Kappa] -> 0.77, Subscript[h, out] -> .7 BTU/(Hour*Foot^2*Fahrenheit), Subscript[T, in] -> 70 Fahrenheit, Subscript[h, in] -> 1.8 BTU/(Hour*Foot^2*Fahrenheit), \[CapitalDelta]x -> .2 Foot, Subscript[T, out, initial] -> 30 Fahrenheit}; Subscript[q, solar] = Piecewise[{{114 BTU/(Hour*Foot^2), 0 <= x <= 12}, {242 BTU/ (Hour*Foot^2), 12 < x <= 24}, {178 BTU/(Hour*Foot^2), 24 < x <= 36}}]; Subscript[T, out] = Piecewise[{{33 Fahrenheit, 0 <= x <= 12}, {43 Fahrenheit, 12 < x <= 24}, {45 Fahrenheit, 24 < x <= 36}, {37 Fahrenheit, 36 < x <= 48}, {32 Fahrenheit, 48 < x <= 60}, {27 Fahrenheit, 60 < x <= 72}, {26 Fahrenheit, 72 < x <= 84}, {25 Fahrenheit, 84 < x <= 96}}]; Plot[{Subscript[q, solar], Subscript[T, out]}, {x, 0, 96}] Nodes = (WallThickness/\[CapitalDelta]x + 1) /. masonry; (*Number of Nodes for analysis*) *Nodes will be numbered from 0 to 5 with Node 0 on the inside surface of the wall and Node 5 on the exterior surface of the wall* Initial Conditions are found by the assumption that the temperature varies linearly inside the wall. Temperatures are given in the format: T[node# , time step] (ex T[0,1] is the interior node at time i=1) tempstep = (Subscript[T, in] - Subscript[T, out, initial])/(Nodes - 1) /. masonry; (* Temperature change between each node *) T[0, 0] = Subscript[T, in] /. masonry; T[1, 0] = T[0, 0] - tempstep; T[2, 0] = T[1, 0] - tempstep; T[3, 0] = T[2, 0] - tempstep; T[4, 0] = T[3, 0] - tempstep; T[5, 0] = T[4, 0] - tempstep; EQUATIONS (* Node 0 has convection, can use Eqn 5-51 from book *) T[0, t_] := (1 - 2 \[Tau] - (2 \[Tau] Subscript[h, in] \ [CapitalDelta]x)/k) T[ 0, t - 1] + 2 \[Tau] T[1, t - 1] + (2 \[Tau] Subscript[h, in] \ [CapitalDelta]x)/k* Subscript[T, in] /. masonry; (* Nodes 1-4 take the more general form, use Eqn 5-47 *) T[m_, t_] := \[Tau] (T[m - 1, t - 1] + T[m + 1, t - 1]) + (1 - 2 \ [Tau]) T[m, t - 1] /. masonry; (* Node 5 is exposed to convection and heat flux outside *) T[5, t_] := (1 - 2 \[Tau] - 2 \[Tau] (Subscript[h, out] \[CapitalDelta]x)/k) T[5, t - 1] + 2 \[Tau] T[4, t - 1] + 2 \[Tau] (Subscript[h, out] \[CapitalDelta]x)/ k*(Subscript[T, out] /. {x -> t}) + 2 \[Tau] (\[Kappa] *(Subscript[q, solar] /. {x -> t}) \ [CapitalDelta]x)/ k /. masonry; \[CapitalDelta]t = .25 Hour; \[Tau] = 0.10755 T[0, t_] := (1 - 2 \[Tau] - (2 \[Tau] Subscript[h, in] \ [CapitalDelta]x)/k) T[ 0, t - 1] + 2 \[Tau] T[1, t - 1] + (2 \[Tau] Subscript[h, in] \ [CapitalDelta]x)/k* Subscript[T, in] /. masonry; T[m_, t_] := \[Tau] (T[m - 1, t - 1] + T[m + 1, t - 1]) + (1 - 2 \ [Tau]) T[m, t - 1] /. masonry; T[5, t_] := (1 - 2 \[Tau] - 2 \[Tau] (Subscript[h, out] \[CapitalDelta]x)/k) T[5, t - 1] + 2 \[Tau] T[4, t - 1] + 2 \[Tau] (Subscript[h, out] \[CapitalDelta]x)/ k*(Subscript[T, out] /. {x -> t}) + 2 \[Tau] (\[Kappa] *(Subscript[q, solar] /. {x -> t}) \ [CapitalDelta]x)/ k /. masonry; Transpose[Table[T[n, x], {n, 0, 5}, {x, 0, 100}]] // MatrixForm Thank you for taking the time to look at this