In this paper, recommended spiral passive micromixer was designed and simulated. spiral design has the potential to create and strengthen the centrifugal force and the secondary flow. A series of simulations were carried out to evaluate the effects of channel width, channel depth, the gap between loops, and flowrate on the micromixer performance. These features impact the contact area of the two fluids and ultimately lead to an increment in the quality of the mixture. In this study, for the flow rate of 25 μl/min and molecular diffusion coefficient of 1×10-10 m2/s, mixing efficiency of more than 90% is achieved after 30 (approximately one-third of the total channel length). Finally, the optimized design fabricated using proposed 3D printing method.

Strains are applied to the INTEGRATION procedure in nonlinear increments to decrease the errors arising from the linearization of plastic equations. Two deformation vectors are used to achieve this. The first vector is based on the deformations obtained by the first iteration of the equilibrium step, and the second is acquired from the sum of the succeeding iterations. By applying these vectors and using sub-increments, the total strain increment can vary nonlinearly during the INTEGRATION of the flow rule. Four individual variation schemes are presented for this purpose. In this paper, the strain space formulation is investigated. NUMERICAL examples are analyzed using the traditional linear method and the suggested schemes. The examples are solved using the von Mises yield criterion and Prager's linear hardening rule. Results indicate that all nonlinear techniques increase the convergence rate of plastic analysis. In addition, such INTEGRATION methods are shown to increase the stability of incremental-iterative analyses.

In this paper, a new method is given to evaluate a definite integral. This method is obtained from a generalized Taylor series and using the derivatives of a integrand function at a certain point.

Investigation of the step variable NUMERICAL INTEGRATION methods is the main purpose of this paper. Also it is shown how the one-dimensional NUMERICAL INTEGRATION method of solving an ordinary differential equation can be employed to solve a three-dimensional differential equation NUMERICALly. In order to integrate the orbit, the step variable methods of Runge-Kutta-Fehlberg and Adams are employed and their accuracies are investigated.

In this paper, based on CAS wavelets we present quadrature rules for NUMERICAL solution of double and triple integrals with variable limits of INTEGRATION. To construct new method, first, we approximate the unknown function by CAS wavelets. Then by using suitable collocation points, we obtain the CAS wavelet coefficients that these coefficients are applied in approximating the unknown function. The major advantage of new approach is that this method can approximate the value of some improper integrals. To illustrate the efficiency and the accuracy of the method, some NUMERICAL examples are given.

In this article, an attempt has been made to model the process of double INTEGRATION for different data spacing. The trapezoidal rule has been used to perform INTEGRATION, whereas Newton's divided difference handles the inconsistent data points. The whole process of NUMERICAL INTEGRATION has been automated in Python programming language. The developed code is tested against two example problems, and the results obtained agree with the one shown in the literature.