Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model

Ferrohydrodynamic and magnetohydrodynamic effects on ferrofluid flow and convective heat transfer

Economic reasons (material and energy saving) leads to make efforts for making more efficient heat exchange. The heat transfer enhancement techniques are widely used in many applications in the heating process to make possible reduction in weight and size or enhance the performance of heat exchangers. These techniques are classified as active and passive techniques. The active technique required external power while the passive technique does not need any external power. The passive techniques are valuable compared with the active techniques because the swirl inserts manufacturing process is simple and can be easily employed in an existing heat exchanger. Insertion of swirl flow devices enhance the convective heat transfer by making swirl into the bulk flow and disrupting the boundary layer at the tube surface due to repeated changes in the surface geometry. An effort has been made in this paper to carry out an extensive literature review of various turbulators (coiled tubes, extended surfaces (fin, louvered strip, winglet), rough surfaces (Corrugated tube, Rib) and swirl flow devices such as twisted tape, conical ring, snail entry turbulator, vortex rings, coiled wire) for enhancing heat transfer in heat exchangers. It can be concluded that wire coil gives better overall performance if the pressure drop penalty is considered. The use of coiled square wire turbulators leads to a considerable increase in heat transfer and friction loss over those of a smooth wall tube.

Review of heat transfer enhancement methods: Focus on passive methods using swirl flow devices

KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel

T HE two-point boundary-value problem (TPBVP) plays a fundamental role in optimal control problems of aerospace engineering, including the problem of spacecraft orbit transfer [1], the optimal reconfiguration of spacecraft formations [2], and continuous thrust rendezvous problems [3]. Therefore, many techniques and methods for solving TPBVP have been proposed and developed [4–7]. The optimal control problem is as follows. The dynamic system is

Symplectic Approaches for Solving Two-Point Boundary-Value Problems

An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method (PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples show that the IPIM is stable and gives the machine accuracy solutions.

Qiang Gao

Papers

Symplectic Approaches for Solving Two-Point Boundary-Value Problems

Improved precise integration method for differential Riccati equation

A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel–rail contact

Non-stationary random ground vibration due to loads moving along a railway track

A precise integration boundary element method for solving transient heat conduction problems