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The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform technique by using it to study magnetohydrodynamic flow of electrically conductive Newtonian fluids inside flat parallel-plate channels subjected to a uniform and constant external magnetic field.

The mathematical formulation of the analyzed problem is given in terms of a streamfunction, obtained from the Navier–Stokes and energy equations, by considering steady state laminar and incompressible flow and constant physical properties.

Convergence analyses are performed and presented to illustrate the consistency of the integral transformation technique. The results for the velocity and temperature fields are generated and compared with those in the literature as a function of the main governing parameters.

A detailed analysis of the parametric sensibility of the main dimensionless parameters, such as the Reynolds number, Hartmann number, Eckert number, Prandtl number and electrical parameter, for some typical situations is performed.

Our recent results on stability and multiplicity of flow states for confined flows of an incompressible Newtonian fluid are surveyed. The considered laminar flows are caused by either thermal, mechanical, or electromagnetic effects and beyond the stability limit exhibit multiplicity of stable, steady or oscillatory, asymptotic states. Stability diagrams as well as examples of multiple flow states are given. It is concluded that beyond the critical value of the characteristic non‐dimensional parameter, and below the threshold to stochastic or turbulent state, multiple stable asymptotic flow states can be expected. This means that at such flow regimes, any computational (experimental) result may be strongly dependent on its initial condition and/or computational (experimental) path. Uncertainties of experimental and numerical modeling, which follow from this conclusion, are discussed. The global spectral Galerkin method using divergence free basis functions has been employed for the spatial approximation of the velocity and temperature fields. Several numerical experiments were performed comparing the present and other formulations, each of which confirmed the computational efficiency of the present approach over other classical numerical methods.

A detailed analysis on the characteristics of laminar flow over a bell‐shaped stenosis for a physiological pulsatile flow is presented in this study. In order to have a good understanding of the physiological pulsatile flow, a comparison of the numerical solutions to three types of pulsatile flows, including a physiological flow, an equivalent pulsatile flow and a pure sinusoidal flow, are made in this work. The comparison shows that the flow behavior cannot be properly estimated if the equivalent or simple pulsatile inlet flow is used in the study of flow fields through stenosed arteries instead of actual physiological one. Then the physiological pulsatile flow is further studied by considering the effect of constriction ratio of stenosis, Womersley number and Reynolds number on the flow behavior through stenosed arteries. The analysis shows that the variation of these flow parameters puts significant impacts on the pulsatile flow field for the physiological flow.

The purpose of this paper is to numerically investigate the flow characteristics and extend the data of friction factor and Reynolds number product of hydrodynamically developing laminar flow in three-dimensional rectangular microchannels with different aspect ratios.

Using a finite-volume approach, the friction factor characteristics of Newtonian fluid in three-dimensional rectangular ducts with aspect ratios from 0.1 to 1 are conducted numerically under no-slip boundary conditions. A simple model that approximately predicts the apparent friction factor and Reynolds number product f_appRe is referenced as a semi-theoretical fundamental analysis for numerical simulations.

The accurate and reliable results of f_appRe are obtained, which are compared with classic numerical data and experimental data, and the simple semi-theoretical model used and all comparisons show good agreement. Among them, the maximum relative error with the classic numerical data is less than 3.9 per cent. The data of f_appRe are significantly extended to other different aspect ratios and the novel values of f_appRe are presented in the tables. The characteristics of f_appRe are analyzed as a function of a non-dimensional axial distance and the aspect ratios. A more effective and accurate fourth-order fitting equation for the Hagenbach's factor of rectangular channels is proposed.

From the reliable data, it is shown that the values of f_appRe and the model can be references of pressure drop and friction factor for developing laminar flow in rectangular channels for researchers and engineering applications.

The purpose of this paper is to study the laminar boundary layer flow between a stationary nonporous disk and a porous rotating disk, both being immersed in large amount of fluid.

The governing nonlinear momentum equations in cylindrical polar coordinates together with relevant boundary conditions are reduced to a system of coupled nonlinear ordinary differential equations (NODEs) using similarity transformations. The resulting coupled NODEs are solved using computer-extended series solution and homotopy analysis method.

The analytical solutions are explicitly expressed in terms of recurrence relation for determining the universal coefficients. The nature and location of singularity which restricts the convergence of series is analyzed by using Domb–Sykes plot. Reversion of series is used for the improvement of series. The region of validity of series is extended for much larger values of Reynolds number (R), i.e. R = 6 to 15.

The resulting solutions are compared with earlier works in the literature and are found to be in good agreement.

The purpose of this paper is to present numerical study on the behaviour of 2D unsteady incompressible laminar wakes behind square cylinders.

The numerical method that has been developed is based on a finite point formulation characterised by its weak connectivity requirements. This formulation allows for a patched unstructured approach to computational domain modelling that is of interest for industrial applications. Time evolution of pressure is computed by using a pseudo‐compressibility relaxation model that is based on physical considerations.

This model is characterised by the fact that no sub‐iterations on a numerical pseudo‐time are required so that computational efficiency is increased. Algorithm stability requires the use of second and fourth order artificial viscosity operators that effectively change the order of the equations. A discussion is included regarding the boundary conditions for these operators that do not influence vortex shedding behaviour.

Bearing in mind the industrial drive (MEMS design) that the authors have in mind, solver validation has been addressed at two levels: global coefficients (lift, drag and Strouhal number) were compared with those published in the specialised literature, while local velocity and rms profiles were compared with those obtained after performing a specific low velocity wind tunnel testing campaign (Reynolds numbers in the range from 110 to 268).

A sensitivity analysis of the results obtained is presented and it shows that the solver numerical robustness makes it amenable for project oriented applications.

The formulation being presented is competitive and could be considered as a potential alternative to other approaches.

Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes are proposed to get efficient solutions. However, the number of inner iterations is set empirically and kept fixed during the whole computation for different problems, which is overestimated in some computations but underestimated in other computations. This paper aims to develop an algorithm with adaptive inner iteration processes for steady and unsteady incompressible flows.

In this work, with the use of two different criteria in two inner iterative processes, a mechanism is proposed to control inner iteration processes to make the number of inner iterations vary during computing according to different problems. By doing so, adaptive inner iteration processes can be achieved.

The adaptive inner iterative algorithm is verified to be valid by solving classic steady and unsteady incompressible problems. Results show that the adaptive inner iteration algorithm works more efficient than the fixed inner iteration one.

The algorithm with adaptive inner iteration processes is first proposed in this paper. As the mechanism for controlling inner iteration processes is based on physical meaning and the feature of iterative calculations, it can be used in any methods where there exist inner iteration processes. It is not limited for incompressible flows. The performance of the adaptive inner iteration processes in compressible flows is conducted in a further study.

The purpose of this study is to present the magnetohydrodynamic (MHD) flow and heat transfer in an accelerating film of a non-Newtonian pseudo-plastic nanofluid along an inclined surface with viscous dissipation and Joule heating.

An incompressible and inelastic fluid is assumed to obey the Ostwald-de-Waele power law model and the action of viscous stresses is confined to the developing momentum boundary layer adjacent to the solid surface. Viscous dissipation and Joule heating on the flow of electrically conducting film in the presence of uniform transverse magnetic field is considered for the Carboxyl Methyl Cellulose (CMC) water-based nanofluid. The fluid is the CMC-water-based with concentration (0.1-0.4 per cent) containing three types of nano-solid particles Cu, Al₂O₃ and TiO₂. The modeled boundary layer conservation equations are transformed to dimensionless, coupled and highly non-linear system of differential equations, and then solved numerically by means of a local non-similarity approach with shooting technique. To validate the numerical results, a comparison of the present results is made with the earlier published results and is found to be in good agreement.

The effects of magnetic parameter, Prandtl number, Eckert number and Biot numbers on the velocity and temperature fields are presented graphically and discussed for various values of thermo-physical parameters. It has been found that magnetic field decelerates the fluid velocity for both cases of Newtonian nanofluid and pseudo-plastic nanofluid because of the generated drag-like Lorentz force. This is of great benefit in magnetic materials processing operations, utilizing static transverse uniform magnetic field, as it allows a strong regulation of the flow field.

The numerical study is valid for two-dimensional, steady, laminar film flow of Ostwald-de-Waele power law non-Newtonian nanofluid along an inclined plate. A uniform transverse magnetic field of strength B₀ is applied perpendicular to the wall. Assume that the base fluid and the nano-solid particles are in thermal equilibrium with no slip effects. The interaction of magnetic field with nanofluid has several potential implications and may be used to deal with the problems such as cooling nuclear reactors by liquid sodium and inducting the flow meter which depends on the potential difference in the fluid along the direction perpendicular to the motion and to the magnetic field.

The study has significant applications in magnetic field control of materials processing systems.

The results of the present study may be attentiveness to the engineers and applied mathematicians who are interested in hydrodynamics and heat transfer enhancement associated with film flows.

Three‐dimensional flows over backward facing s.tif are analysed by means of a finite element procedure, which shares many features with the SIMPLER method. In fact, given an initial or guessed velocity field, the pseudovelocities, i.e. the velocities that would prevail in the absence of the pressure field, are found first. Then, by enforcing continuity on the pseudovelocity field, the tentative pressure is estimated, and the momentum equations are solved in sequence for velocity components. Afterwards, continuity is enforced again to find corrections that are used to modify the velocity field and the estimated pressure field. Finally, whenever necessary, the energy equation is solved before moving to the next step.

This study aims to investigate the effect of the simultaneous usage of active and passive methods (which in this case are rotational oscillation and attached splitter plate, respectively) on the flow and temperature fields to find an optimum situation which this combination results in heat transfer increment and drag reduction.

The method of the solution was based on finite volume discretization of Navier–Stokes equations. A dynamic grid is coupled with the solver by the arbitrary Lagrangian–Eulerian (ALE) formulation for modeling cylinder oscillation. Parametric studies were performed by altering oscillation frequency, splitter plate length and Reynolds number.

Oscillation in different frequencies was found to be complicated. Higher frequencies provide more heat transfer, but in the lock-on region, they bring remarkable increment to the drag coefficient. It was observed that simultaneous usage of oscillation and splitter plate may have both positive and negative effects on drag reduction and heat transfer increment. Finally F = 2 and L = 0.5 were chosen as an optimum combination.

In this study, the laminar incompressible flow and heat transfer from a confined rotationally oscillating circular cylinder with an attached splitter plate are investigated. Parametric studies are performed by changing oscillation frequency, splitter plate length and Reynolds number.