Variational Embedding Research Articles

Variational Embedding Technique to Inward Solidification Subject to Convection and Radiation

The variational embedding method is presented for solving the solidified lines in the inward solidification of Cartesian, cylindrical and spherical systems with convection-radiation boundary conditions. Typical results are represented in graphical form for comparison.

Application of variational embedding technique to nonlinear heat transfer problems

Application of variational embedding technique to nonlinear heat transfer problems

Transient Response of Fins by Optimal Linearization and Variational Embedding Methods

Transient Response of Fins by Optimal Linearization and Variational Embedding Methods

Optimal linearization and variational embedding solutions for convective fins with variable thermal conductivity

The optimal linearization method is used to obtain an approximate analytical solutions for steady state of convective fins with variable thermal conductivity. Furthermore, an approximate analytical solutions for transient state of convective fins with variable thermal conductivity is achieved by using the variational embedding method.

Variational embedding method and application to distributed systems control

The main aim of the present paper is to show the variational embedding method as a powerful tool for solving control problems associated with distributed systems. It is shown that, variational embedding subsumes many approximation methods that are available in the literature for solving constitutive equations of distributed systems. The well-known method of weighted residuals and its ramifications are shown to be the appropriate specializations of the embedding method. The method thus offers a vantage point from which it is conceptually easy to see both the plurality and unity of these methods. In the process of illustrating the hierarchy of the method, the attendant dilemma associated with the method of weighted residuals is successfully resolved. The variational embedding method yields a unified approach for obtaining lumped models for distributed parameter systems. The application is demonstrated by considering examples of engineering importance, and it is shown how lumped models of non-linear distribu...