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category: thermal

intro: |

# Transient heat conduction from steady-state by "turning off" BCs

This problem solves the transient over a slender cylider arising from "turning off" a heat source that provided a fixed heat flux at both ends, while the cylindrical surface is subject to convection conditions.

The transient goes from $t=0~\text{s}$ up to end time $t=1000~\text{s}$.

We force the time stepper to pass exactly through the following times $t$

* 1

* 10

* 100

* `end_time`/2

At these times, the special variable `in_time_path` is true.

We use an `IF` condition to write the profile along the $x$ axis on

1. a single file named `profiles.dat` with an extra column for the time $t$

2. one file for each time step `profile-t.dat`

for the selected times (or during the static step at $t=0$ and the final step at $t=1000$).

terminal: |

$ gmsh -3 barra3d.geo

$ feenox barra3d.fee

...

# "barra" means "rod" in Spanish

PROBLEM thermal 3d MESH barra3d.msh

# times

end_time = 1000

TIME_PATH 1 10 100 end_time/2

# problem constants [SI]

# D = 0.02

# A = pi*(0.5*D)^2

# instead of computing the area from the geometry we can ask

# feenox to do it for us by explicitly defining a physical

# group with the right dimension, we'll have the variable

# hot_area available with, well you guessed, the group's area

PHYSICAL_GROUP hot DIMENSION 2

L = 1 # length

k = 50 # conductivity

rho = 8000 # density

cp = 400 # heat capaccity

# boundary conditions

# 30 watts, turned off starting at t=eps and ending at t=2*eps

eps = 1e-2

BC hot q=30/hot_area*(1-heaviside(t-eps,eps)) # "hot" has two areas

BC cool h=10 Tref=300

# advance one step

SOLVE_PROBLEM

# sample the 1d profile along the x axis at the time paths

profile(x) = T(x,0,0)

IF in_static|in_time_path|done

# one single file with all the profiles

PRINT_FUNCTION profile t MIN 0 MAX L NSTEPS 100 FILE profiles.dat

# one file fore ach profile

FILE profilet PATH profile-%g.dat t

PRINT_FUNCTION profile MIN 0 MAX L NSTEPS 100 FILE profilet

CLOSE profilet

ENDIF

# print the progress so we know how much is left when we run it

PRINT t T(0.1,0,0)

# write the full transient in a .msh and vtu (+pvd)

WRITE_RESULTS FILE barra3d-transient.msh

WRITE_RESULTS FILE barra3d.vtu

# TODO

# WRITE_RESULTS FILE barra3d-transient.vtk

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figures: |

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