The Chebyshev orthogonal collocation is a powerful and accurate numerical technique, which is also relatively easy to implement using modern mathematical software (e.g., MATHEMATICA and MATLAB). This technique allows the elucidation of engineering problems involving partial differentials equations or boundary value problems. Six chemical engineering problems concerning the transfer of momentum,...

In this paper, the orthogonal collocation technique is utilized to solve the Poppe method equations for heat and mass transfer in counter flowing wet-cooling towers. The six differential equations for unsaturated and supersaturated air from the Poppe method are simplified, yielding three differential equations that use the Heaviside function. The humidity ratio is demonstrated to be a finite po...

The primal hybrid method for solving second-order elliptic equations is extended from finite element approximations to general bases. Variational techniques are used to show convergence of approximations to the solution of the homogeneous Dirichlet problem for selfadjoint equations. Error estimates are obtained and examples are given. Introduction Lagrange multipliers have been employed to defi...

It is known that the optimal control may introduce significant economical benefits into production processes, thus being an important and challenging research area with practical relevance. The modeling and optimization of biotechnological processes has been object of research and their related results have generated improvements in operating conditions and strategies, however, the inherent fea...

the built up layer thickness in secondary deformation zone is one of the important parameters in metal cutting process. the built up layer (bul) is formed in second deformation zone near the tool-chip interface in the back of the chip. this parameter influences the tool life and machined surface quality. this bul should not be confused with the built up edge (bue). the deformation of the bul in...