# How to find the average temperature a surface? ABAQUS -Heat transfer -user subroutine

I want to model a concrete slab with a void inside the concrete. It is a thermal analyse where I apply a heat flux to the bottom surface. Within the void heat is transferred by radiation and convection. For simulating heat convection within the void, I use the surface film condition function in interaction module. I have to define the film coefficient and sink temperature. I decided to use the average temperature of the void surface for sink temperature. I don’t know how to define the average surface temperature. I think I have to use Abaqus Subroutine.

I used the FILM user subroutine interface to assign the average temperature of the void surface to the enclose air but I don’t know how to find average temperature of the void surface.

I would appreciate any ideas from anyone who has worked in a similar area in Abaqus.

SUBROUTINE FILM(H,SINK,TEMP,KSTEP,KINC,TIME,NOEL,NPT,
1 COORDS,JLTYP,FIELD,NFIELD,SNAME,NODE,AREA)
C
INCLUDE 'ABA_PARAM.INC'
C
DIMENSION H(2),TIME(2),COORDS(3), FIELD(NFIELD)
CHARACTER*80 SNAME
H(1)=1.5
SINK=TEMP
RETURN
END ### heat transfer

Radiation is significant at extreme temperatures only, and depends on the emissivity coefficient. Do you intend to melt the thing ?

I guess that heat conduction through the concrete is much more significant and faster than the heat convection through the air. You might even dispose of it.

But if you insist: the "average temperature of the void surface for sink temperature" evolves with time, as the concrete is heating. My understanding is that in this case you impose convection dictated by the temperature of other concrete elements, irrespective of the air temperature within the void. You'd push Watts across the void even if the air is hotter than the concrete.

My approach would be to model the void with elements that feature temperature as a degree of freedom. Then define two surfaces: one for the concrete around the circumference, another one for the circumference of these elements that represent the air. Set a constant film coefficient, and let the air have the same initial temperature (=sink temperature). Conduction should occur. The air should gain temperature. Within the air heat is conducted (not convected), so set the heat conductivity coefficient for air.

For heat transfer coefficients and heat conductivity you might want to consult the "VDI Heat Atlas" by VDI Gesellschaft (VDI = Union of German Engineers) or other reference books.

When you have assembled your model make a comparison: only heat conduction and heat conduction combined wíth convection. Is convection significant ?

Done (in my humble opinion, but I didn't deal much with heat transfer).

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Ruhr-University
Bochum
Germany 