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