Abstract
A finite element method is developed for the analysis of two dimensional, transient laminar convective heat transfer. The method is applied to three classes of problems over a range of flow and thermal conditions. The results of eight (8) example problems are compared with other numerical solutions, existing experimental data, and experimental data collected by the author. The method developed is particularly suitable for the study of transient natural convection from long horizontal bars of arbitrary cross section and inside enclosed spaces. The effects of combined forced and free convection are also considered. The governing equations of continuity, momentum, and energy are developed in dimensionless form after employing the Boussinesq approximation to the fluid medium. Pressure is eliminated as a variable by casting the dimensionless equations into a vorticity-stream function-temperature formulation. The finite element method chosen for the solution of this set of equations involves their re-formulation in variational form as functionals to be minimized. The time derivatives and convective terms in the vorticity and energy equation are treated as invariants over a small time interval. An implicit time stepping scheme is used to integrate forward with time from the initial conditions. The finite element method is shown to be a viable tool with which to numerically approximate the transient solution for free convection in two dimensional cavities. The results of the numerical experiments for the square cavity show that the time step limitations and nodal density requirements for accurate solutions are approximately equal to those required by previously developed finite difference methods. For Prandtl-number fluids near that of air, stable solutions are limited to Gr < 2 x 10^5. The results obtained from experimental measurements and numerical solutions for natural convection from a horizontal, isothermal cylinder in air demonstrate the validity of the finite element method for external free convection...
Holster, Jesse Louis (1979). Finite element analysis of laminar convective heat transfer. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -718858.