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The purpose of this paper is to present an efficient method for dynamic analysis of structures utilizing a modal analysis with the main purpose of decreasing the computational complexity of the problem. In traditional methods, the solution of initial-value problems (IVPs) using numerical methods like finite difference method leads to step by step and time-consuming recursive solutions.

The present method is based on converting the IVP into boundary-value problems (BVPs) and utilizing the features of the latter problems in efficient solution of the former ones. Finite difference formulation of BVPs leads to matrices with repetitive tri-diagonal and block tri-diagonal patterns wherein the eigensolution and matrix inversion are obtained using graph products rules. To get advantage of these efficient solutions for IVPs like the dynamic analysis of single DOF systems, IVPs are converted to boundary-value ones using mathematical manipulations. The obtained formulation is then generalized to the multi DOF systems by utilizing modal analysis.

Applying the method to the modal analysis leads to a simple and efficient formulation. The laborious matrix inversion and eigensolution operations, of computational complexities of O(n2.373) and O(n3), respectively, are converted to a closed-form formulation with summation operations.

No limitation.

Swift analysis has become possible.

Suitability of solving IVPs and modal analysis using conversion and graph product rules is presented and applied to efficient seismic optimal analysis and preliminary design.

A parallel linelet preconditioner has been implemented to accelerate finite element (FE) solvers for incompressible flows when highly anisotropic meshes are used. The convergence of the standard preconditioned conjugate gradient (PCG) solver that is commonly used to solve the discrete pressure equations, greatly deteriorates due to the presence of highly distorted elements, which are of mandatory use for high Reynolds‐number flows. The linelet preconditioner notably accelerates the convergence rate of the PCG solver in such situations, saving an important amount of CPU time. Unlike other more sophisticated preconditioners, parallelization of the linelet preconditioner is almost straighforward. Numerical examples and some comparisons with other preconditioners are presented to demonstrate the performance of the proposed preconditioner.

Proposes a measure to stabilize the fourth(fifth)‐order high resolution schemes for the compressible Navier‐Stokes equations. Solves the N‐S equations of the volume fluxes and the low‐Reynolds number k‐ε turbulence model in general curvilinear co‐ordinates by the delta‐form implicit finite difference methods. Notes that, in order to simulate the flow containing weak discontinuities accurately, it is very effective to use some higher‐order TVD upstream‐difference schemes in the right‐hand side of the equations of these methods; however, the higher‐order correction terms of such schemes in general amplify the numerical disturbances. Therefore, restricts these terms here by operating the minmod functions to the curvatures so as to suppress the occurrence of new inflection points. Computes an unsteady transonic turbine cascade flow where vortex streets occur from the trailing edge of blades and interact with shock waves. Finds that the stabilization measure improves not only the computational results but also the convergency for such a complicated flow problem.

This study aims to investigate the unsteady magnetohydrodynamic mixed convective nanofluid flow by using Buongiorno two-phase model to achieve an appropriate mechanism to improve the efficiency of solar energy systems by mitigating the energy losses.

The transport phenomena occurring in this physical problem are modelled using nonlinear partial differential equations and are non-dimensionalised by using non-similar transformations. The quasilinearisation technique is used to solve the resulting system with the help of a finite difference scheme.

The study reveals that the effect of the applied transverse magnetic parameter is to increase the temperature profile and to reduce the wall heat transfer rate. The Brownian diffusion and thermophoresis parameters that characterise the nanofluids contribute to the reduction in wall heat transfer rate. The presence of nanoparticles in the fluid gives rise to critical values for the thermophoresis parameter describing the behaviour of the wall heat and mass transfer rates. Wall heating and cooling are analysed by considering the percentage increase or percentage decrease in the heat and mass transfer rates in the presence of nanoparticles in the fluid.

The investigation on wall cooling/heating leads to the analysis of control parameters applicable to the industrial design of thermal systems for energy storage, energy harvesting and cooling applications.

The analysis of the control parameters is of practical value to the solar industry.

In countries, such as South Africa, daily power cuts are a reality. Any research into improving the quality of energy obtained from alternate sources is a national necessity.

From the literature survey in the present study, it is found that no similar work has been reported in the open literature that analyses the time-dependent mixed convection flow along the exponentially stretching surface in the presence of the effects of a magnetic field, nanoparticles and non-similar solutions.

The purpose of this paper is to present a novel model on the unsteady MHD flow of heat transfer in carbon nanotubes with variable viscosity over a shrinking surface.

The temperature-dependent viscosity makes the proposed model non-linear and coupled. Consequently, the resulting non-linear partial differential equations are first reformed into set of ordinary differential equations through appropriate transformations and boundary layer approximation and are then solved numerically by the Keller box method.

Graphical and numerical results are executed keeping temperature-dependent viscosity of nanofluid. It is noted that, for diverse critical points, it is found that at one side of these critical values, multiple solutions exist; on the other side, no solution exists. A comparison is also computed for the special case of existing study. The temperature and pressure profiles are also plotted for various effective parameters.

The work is original.

This paper aims to present a novel numerical technique for solving the incompressible multiphase mixture model.

The multiphase mixture model contains a set of momentum and continuity equations for the mixture phase, a second phase continuity equation and the algebraic equation for the relative velocity. For solving continuity equation for the second phase and advection term of momentum, an improved approach fine grid advection-multiphase mixture flow (FGA-MMF) is developed. In the FGA-MMF method, the continuity equation for the second phase is solved with higher-order schemes in a two times finer grid. To solve the advection term of the momentum equation, the advection fluxes of the volume fraction in the continuity equation for the second phase are used.

This approach has been used in various tests to simulate unsteady flow problems. Comparison between numerical results and experimental data demonstrates a satisfactory performance. Numerical examples show that this approach increases the accuracy and stability of the solution and decreases non-monotonic results.

The solver for the multi-phase mixture model can only be adopted to solve the incompressible fluid flow.

The paper developed an innovative solution (FGA-MMF) to find multi-phase flow field value in the multi-phase mixture model. Advantages of the FGA-MMF technique are the ability to accurately determine the phases interpenetrating, decreasing the numerical diffusion of the interface and preventing instability and non-monotonicity in solution of large density variation problems.

The purpose of this paper is to consider steady two‐dimensional mixed convection flow along a vertical semi‐infinite power‐law stretching sheet. The velocity and temperature of the sheet are assumed to vary in a power‐law form.

The problem is formulated in terms of non‐similar equations. These equations are solved numerically by an efficient implicit, iterative, finite‐difference method in combination with a quasi‐linearization technique.

It was found that the skin‐friction coefficient increased with the ratio of free‐stream velocity to the composite reference velocity and the buoyancy parameter while it decreased with exponent parameter. The heat transfer rate increased with the Prandtl number, buoyancy parameter and the exponent parameter.

A very useful source of information for researchers on the subject of convective flow over stretching sheets.

This paper illustrates mixed convective flow over a power‐law stretched surface with variable wall temperature.

Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many applications, the variability of these properties plays a significant role in modifying transport characteristics while the temperature difference in the boundary layer is notable. These include drag reduction in heavy oil transport systems, petroleum purification and coating manufacturing. The purpose of this study is to develop, a comprehensive mathematical model, motivated by the last of these applications, to explore the impact of variable viscosity and variable thermal conductivity characteristics in magnetohydrodynamic non-Newtonian nanofluid enrobing boundary layer flow over a horizontal circular cylinder in the presence of cross-diffusion (Soret and Dufour effects) and appreciable thermal radiative heat transfer under a static radial magnetic field.

The Williamson pseudoplastic model is deployed for rheology of the nanofluid. Buongiorno’s two-component model is used for nanoscale effects. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. Extensive validation with earlier studies in the absence of nanoscale and variable property effects is included.

The influence of notable parameters such as Weissenberg number, variable viscosity, variable thermal conductivity, Soret and Dufour numbers on heat, mass and momentum characteristics are scrutinized and visualized via graphs and tables.

Buongiorno (two-phase) nanofluid model is used to express the momentum, energy and concentration equations with the following assumptions. The laminar, steady, incompressible, free convective flow of Williamson nanofluid is considered. The body force is implemented in the momentum equation. The induced magnetic field strength is smaller than the external magnetic field and hence it is neglected. The Soret and Dufour effects are taken into consideration.

The variable viscosity and thermal conductivity are considered to investigate the fluid characteristic of Williamson nanofluid because of viscosity and thermal conductivity have a prime role in many industries such as petroleum refinement, food and beverages, petrochemical, coating manufacturing, power and environment.

This fluid model displays exact rheological characteristics of bio-fluids and industrial fluids, for instance, blood, polymer melts/solutions, nail polish, paint, ketchup and whipped cream.

The outcomes disclose that the Williamson nanofluid velocity declines by enhancing the Lorentz hydromagnetic force in the radial direction. Thermal and nanoparticle concentration boundary layer thickness is enhanced with greater streamwise coordinate values. An increase in Dufour number or a decrease in Soret number slightly enhances the nanofluid temperature and thickens the thermal boundary layer. Flow deceleration is induced with greater viscosity parameter. Nanofluid temperature is elevated with greater Weissenberg number and thermophoresis nanoscale parameter.

The purpose of this paper is to study the effects of surface mass transfer on the steady mixed convection flow from a vertical stretching sheet in a parallel free stream with variable wall temperature and concentration.

An implicit finite difference scheme in combination with the quasilinearisation technique is employed to obtain non‐similar solutions of the governing boundary layer equations for momentum, temperature and concentration fields.

The numerical results are reported here to display the effects of mixed convection parameter, ratio of buoyancy forces, surface mass transfer (suction and injection), the ratio of free stream velocity to the composite reference velocity, Prandtl number and Schmidt number on velocity, temperature and concentration profiles as well as on skin friction, Nusselt number and Sherwood number.

Thermophysical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate density changes, and to couple in this way the temperature and concentration fields to the flow field. The concentration of diffusing species is assumed to be very small in comparison with other chemical species far away from the surface. Hence the Soret and Dufour effects are neglected. The stretching sheet is assumed to be subject to a power‐law wall temperature as well as to a power‐law wall concentration, in a parallel free stream.

Convective heat and mass transfer over a vertical stretching sheet in a parallel stream is very important for various design of technological process are hot rolling, wire drawing, glass‐fiber paper production, both metal and polymer sheets, for instance, in cooling of an infinite metallic plate in a cooling bath, the boundary layer along material handling conveyors, etc.

The paper studies the combined effects of thermal and mass diffusion over a vertical stretching sheet with surface mass transfer.

The purpose of this paper is to investigate the magnetohydrodynamics mixed convection flow over an exponentially stretching surface in the presence of non-uniform heat source/sink and cross-diffusion. Adequate non-similar transformations are used to transform governing mixed convection boundary layer equations to dimensionless form.

These dimensionless partial differential equations are solved by using implicit finite difference scheme in conjunction with Quasi-linearization technique.

The effects of admissible parameters such as Eckert number (Ec), the ratio of buoyancy forces parameter (N), non-uniform heat source/sink, Soret and Dufour numbers on flow, temperature and concentration distributions are discussed and analysed through graphs. In addition, the results for skin friction coefficient, Sherwood number and Nusselt number are presented and discussed graphically.

In literature, no research work has been found in similar to this research paper.