The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title:	Analysis of unsteady-state heat conduction in a cylinder with the finite element method
Author:	Bernard, Richard F.
View Online:	njit-etd1980-008 (viii, 87 pages ~ 2.9 MB pdf)
Department:	Department of Chemical Engineering and Chemistry
Degree:	Master of Science
Program:	Chemical Engineering
Document Type:	Thesis
Advisory Committee:	McCormick, John E. (Committee chair) Roche, Edward Charles, Jr. (Committee member) Lewandowski, Gordon (Committee member)
Date:	1980-05
Keywords:	Heat -- Conduction Cylinders
Availability:	Unrestricted
Abstract:	Unsteady-state heat conduction in a cylinder of finite dimensions with constant physical and thermal properties was analyzed with the finite element method. Symmetry of the cylinder and application of Newman's method reduced the problem to two independent one-dimensional problems. Finite element equations for the axial and radial dimensions were developed utilizing Galerkin's method of weighted residuals. Crank-Nicholson approximations were used for time derivatives. A computer program was written for solution of the finite element equations. Solutions obtained were conditionally stable; dependent on the value of the ratio KΔt/ρCpl2. For values of the ratio less than 1/3, errors in solutions at small times result. For values of the ratio greater than 2.0, very large errors result. The magnitude of the errors increase with increasing values of the ratio. For proper values of the ratio KΔt/ρCpl2, finite element solutions converge to the analytical solutions by increasing the number of finite elements in the problem.