A Differential Quadrature Element Method for Nonlinear Transient Heat Transfer Analysis of Extended Surfaces

ABSTRACT

A rapidly converging differential quadrature element method (DQEM) for nonlinear transient heat conduction analysis of extended surfaces is developed. In employing the method, the spatial domain is decomposed into subdomains or elements. At the boundary grid points of any two adjacent elements, boundary conditions and/or compatibility conditions are exactly enforced. A simultaneously incremental differential quadrature scheme in time domain is also used for time discretization. Convective-radiative heat transfer conditions are considered along all the surfaces of the domain. Temperature-dependent thermal conductivities are also considered for the domain materials. Convergence, accuracy, and numerical stability of the results are verified via a series of test cases with various levels of complexity in geometry and loading. Employing a few grid points, it is shown that DQEM solutions are accurate compared with those of analytical and finite-difference solutions.

Notes

^a L _i /L, i = 1, 2,…, 5 : 0.1, 0.15, 0.25, 0.5.

^b L _i /L, i = 1, 2,…, 10 : 0.05, 0.07, 0.03, 0.1, 0.25, 0.02, 0.17, 0.06, 0.05, 0.2.

^a Values in ( ) are the temperature at x = 0 and t = 2τ.