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A very long chimney is constructed of two different materials (ignoring mortar joints):
the
inner layer is 1.0 inch thick concrete,
k = 0.07 BTU/hr-in-oF
the
outer layer is brick,
k = 0.04 BTU/hr-in-oF
The
chimney cross-section is shown with all dimensions in inches. All corners
are sharp.
The temperature of the hot gas inside the chimney is 140 oF.
Outside the
chimney, the surrounding air is 10 oF
To do:
- Determine 2D or 3D modeling ?
- Determine symmetry ?
- Linear or nonlinear ?
- Will the sharp corners be a problem for thermal FEA ? How about for the stress analysis ?
Determine the proper convective heat transfer film coefficients (h) for free convection of air along the vertical, flat walls, inside and outside. ASSUME (just for estimating film coefficients): the inside wall average temperature is 80 oF and the outside wall average temperature is 54 oF. The chimney height is 28 feet.
Using the FEA solution reactions, find the total heat flow through the ENTIRE wall of the chimney (per inch of chimney height)
Find the temperature distribution through the chimney wall.
Use the same model for calculation of the thermal stress in the chimney caused only by the temperature distribution through the wall.
For the inner layer of concrete,
E = 3,500,000 psi
Poisson's ratio = 0.1
Coefficient of Thermal Expansion = 5.5x10-6 in/in/oF
For the outer layer of brick,
E = 2,500,000 psi
Poisson's ratio = 0.2
Coefficient of Thermal Expansion = 3.2x10-6 in/in/oFSince the chimney is "very long" compared to the cross-section and we choose to ignore the "end effects", plane strain behavior is the best choice.
Assume the structure is stress-free at 70oF
Apply appropriate constraints. Apply the temperature distribution from the heat transfer solution as a (body force) load on the structural analysis model.
Evaluate deflections, tensile (S1) and compressive (S3) stress responses.
In DesignModeler:
In DesignSimulation:
/SHOW,PNG ! send plots to PNG file
/GFILE,350 ! plot file resolution
/RGB,INDEX,100,100,100,0 ! switch the
/RGB,INDEX,0,0,0,15 ! B/W colorsesel,s,mat,,1 ! select one body by material ID number
nsle,s ! select the nodes attached to those elements
prerr ! print error for that body of model
PLDISP,1 ! plot the temperature/deflection results of that bodyesel,s,mat,,2 ! select one body by material ID number
nsle,s ! select the nodes attached to those elements
prerr ! print error for that body of model
PLDISP,1 ! plot the temperature/deflection results of that bodyALLSEL ! select everything
/SHOW,TERM ! direct plots back to the screen