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Exact Finite Element Solutions for Linear Steadystate Thermal
A Predictive Simulation
Steep Gradient Modelling in Diffusion Problems
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analysis analytical solution approximation B. A. Schrefler behaviour boundary conditions boundary element method calculated cavity CFEM CFET coefficient computed constant cooling coordinates derived DFET model differential equations diffusion equation dT/dn duct effects energy equation system error evaluated finite difference finite element analysis finite element method flow network fluid temperature formulation given grid heat conduction heat exchanger heat flux heat transfer insulated integration isotherms iteration layer mass flow rate Mass Transfer matrix mesh natural convection Navier-Stokes equations nodal nodes nonlinear Numerical Methods numerical solution Nusselt number O. C. Zienkiewicz obtained one-dimensional parameter pellets perature Prandtl number predict pressure procedure R. W. Lewis radiation Rayleigh number region scheme shown in Figure simulation sinter solid solved steady-state step stress surface Swansea temperature temperature distribution temperature gradient thermal conductivity thermal diffusivity three-dimensional transient turbulent flow two-dimensional values vapour variable variation vector velocity vertical wall zero