Civil Engineering Reference
In-Depth Information
convenient for output identification and for specifying prescribed temper-
atures and fluxes with varying magnitudes. Any fluxes or boundary condi-
tion changes to be applied during a steady-state heat transfer step should be
given within the step, using appropriate amplitude references to specify their
“time” variations. If fluxes and boundary conditions are specified for the step
without amplitude references, they are assumed to change linearly with
“time” during the step, from their magnitudes at the end of the previous step
(or zero, if this is the beginning of the analysis) to their newly specified mag-
nitudes at the end of the heat transfer step.
Time integration in transient problems is done with the backward Euler
method (sometimes also referred to as the modified Crank-Nicolson oper-
ator) in the pure conduction elements. This method is unconditionally stable
for linear problems. The forced convection/diffusion elements use the trap-
ezoidal rule for time integration. They include numerical diffusion control
and, optionally, numerical dispersion control. The elements with dispersion
control offer improved solution accuracy in cases where the transient
response of the fluid is important. The velocity of a fluid moving through
the mesh can be prescribed if forced convection/diffusion heat transfer
elements are used. Conduction between the fluid and the adjacent forced
convection/diffusion heat transfer elements will be affected by the mass flow
rate of the fluid. Natural convection occurs when differences in fluid density
created by thermal gradients cause motion of the fluid. The forced convec-
tion/diffusion elements are not designed to handle this phenomenon;
the flow must be prescribed. Modelers can specify the mass flow rates
per unit area (or through the entire section for 1D elements) at the nodes.
ABAQUS (Standard) interpolates the mass flow rates to the material points.
The numerical solution of the transient heat transfer equation including
convection becomes increasingly difficult as convection dominates diffu-
sion. Cavity radiation can be activated in a heat transfer step. This feature
involves interacting heat transfer between all of the facets of the cavity
surface, dependent on the facet temperatures, facet emissivities, and the
geometric view factors between each facet pair. When the thermal emissiv-
ity is a function of temperature or field variables, modelers can specify the
maximum allowable emissivity change during an increment in addition to
the maximum temperature change to control the time incrementation.
It should be noted that, by default, the initial temperature of all nodes is zero.
Modelers can specify nonzero initial temperatures.
Boundary conditions can be used to prescribe temperatures (degree of
freedom 11) at nodes in a heat transfer analysis. Shell elements have
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