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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



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