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The purpose of this paper is to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. The principal question the authors address in this paper is in regard to the applicability of the no‐slip condition at a solid‐liquid boundary. The authors present the effects of slip, magnetohydrodynamics (MHD) and heat transfer for the plane Couette, plane Poiseuille and plane Couette‐Poiseuille flows in a homogeneous and thermodynamically compatible third grade fluid. The problem of a non‐Newtonian plane Couette flow, fully developed plane Poiseuille flow and Couette‐Poiseuille flow are investigated.

The present investigation is an attempt to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. A very effective and higher order numerical scheme is used to solve the resulting system of nonlinear differential equations with nonlinear boundary conditions. Numerical solutions are obtained by solving nonlinear ordinary differential equations using Chebyshev spectral method.

Due to the nonlinear and highly complicated nature of the governing equations and boundary conditions, finding an analytical or numerical solution is not easy. The authors obtained numerical solutions of the coupled nonlinear ordinary differential equations with nonlinear boundary conditions using higher order Chebyshev spectral collocation method. Spectral methods are proven to offer a superior intrinsic accuracy for derivative calculations.

To the best of the authors' knowledge, no such analysis is available in the literature which can describe the heat transfer, MHD and slip effects simultaneously on the flows of the non‐Newtonian fluids.

The purpose of this study is to examine theoretically the axisymmetric flow of a steady free-surface jet emerging from a tube for high inertia flow and moderate surface tension effect.

The method of matched asymptotic expansion is used to explore the rich dynamics near the exit where a stress singularity occurs. A boundary layer approach is also proposed to capture the flow further downstream where the free surface layer has grown significantly.

The jet is found to always contract near the tube exit. In contrast to existing numerical studies, the author explores the strength of upstream influence and the flow in the wall layer, resulting from jet contraction. This influence becomes particularly evident from the nonlinear pressure dependence on the upstream distance, as well as the pressure undershoot and overshoot at the exit for weak and strong gravity levels, respectively. The approach is validated against existing experimental and numerical data for the jet profile and centerline velocity where good agreement is obtained. Far from the exit, the author shows how the solution in the diffusive region can be matched to the inviscid far solution, providing the desired appropriate initial condition for the inviscid far flow solution. The location, at which the velocity becomes uniform across the jet, depends strongly on the gravity level and exhibits a non-monotonic behavior with respect to gravity and applied pressure gradient. The author finds that under weak gravity, surface tension has little influence on the final jet radius. The work is a crucial supplement to the existing numerical literature.

Given the presence of the stress singularity at the exit, the work constitutes a superior alternative to a computational approach where the singularity is typically and inaccurately smoothed over. In contrast, in the present study, the singularity is entirely circumvented. Moreover, the flow details are better elucidated, and the various scales involved in different regions are better identified.

In this article we report on progress in the development of software tools for fluid flow prediction in the polymer processing industry. This involves state‐of‐the‐art numerical techniques and the study of a number of non‐trivial model flow problems, in an effort to investigate realistic transient problems relevant to industrial processes. Here we study particularly the effects of variations in non‐Newtonian and heat transfer properties of the flowing materials in the flows, both throughout the transient development period and at steady‐state.

The purpose of this paper is to study the influence of different flow regimes on the dynamic characteristics of four-pad hydrostatic squeeze film dampers (SFDs) loaded between pads.

A numerical model based on Constantinescu’s turbulent lubrication theory using the finite difference method has been developed and presented to study the effect of eccentricity ratio on the performance characteristics of four-pad hydrostatic SFDs under different flow regimes.

It was found that the influence of turbulent flow on the dimensionless damping of four-pad hydrostatic SFDs appears to be essentially controlled by the eccentricity ratio. It was also found that the laminar flow presents higher values of load capacity compared to bearings operating under turbulent flow conditions.

In fact, the results obtained show that the journal bearing performances are significantly influenced by the turbulent flow regime. The study is expected to be useful to bearing designers.

This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The objectives are to handle internal and external flows in fairly complex geometries including shock waves, compressible turbulence and heat transfer.

The code is equipped with high-order discretization schemes to improve the computational accuracy of the solution algorithm. Besides, a new method to deal with the geometrical singularities, so-called domain decomposition method (DDM), is implemented. The DDM consists of using two different meshes communicating with each other, where the base mesh is Cartesian and the overlapped one a hollow cylinder.

The robustness of the present implemented code is appraised through several numerical test cases including a vortex advection, supersonic compressible flow over a cylinder, Poiseuille flow, turbulent channel and pipe flows. The results obtained here are in an excellent agreement when compared to the experimental data and the previous direct numerical simulation (DNS). As for the DDM strategy, it was successful as simulation time is clearly decreased and the connection between the two subdomains does not create spurious oscillations.

In sum, the developed solver was capable of solving, accurately and with high-precision, two- and three-dimensional compressible flows including fairly complex geometries. It is noted that the data provided by the DNS of supersonic pipe flows are not abundant in the literature and therefore will be available online for the community.

The purpose of the current research is to study the turbulent flow through microchannels having a micropost in aligned and staggered arrangements.

Numerical calculations are performed on the basis of the finite volume approach, which is based on the SIMPLEC algorithm. In this work, the slip velocity, flow velocity distribution and friction factor for the two micropost patterns are examined at friction Reynolds numbers of R_eτ = 395 and 590, relative module widths of W_m = 0.1 and 1 and cavity fraction range of F_c = 0.1 to 0.9.

Results reveal that for the two micropost patterns, as the friction Reynolds number, relative module width or cavity fraction increases, the slip velocity increases and friction factor decreases. It is found that the aligned micropost configuration leads to higher slip velocity and lower friction factor. Numerical findings indicate that the existence of the continuous cavity surface along the flow direction could be a significant criterion to realize if the velocity distribution deviates from that of the smooth channel. It is also shown that the turbulent flows are capable of producing more drag reduction than the laminar ones.

Previous studies have shown that microchannels consisting of a micropost pattern in aligned and staggered arrangements could be viewed as a promising alternative in the microscale flows for the heat removal purposes. Therefore, understanding the fluid flow through microchannels consisting of these configurations (which is a prerequisite to better understand thermal performance of such microchannels) is a significant issue, which is the subject of the present work.

The purpose of this paper is the theoretical presentation of tensorial formulation with surface mobility forces and numerical verification of Reynolds thermal transpiration law in a contemporary experiment with nanoflow.

The velocity profiles in a single microchannel are calculated by solving the momentum equations and using thermal transpiration force as the boundary conditions. The mass flow rate and pressure of unstationary thermal transpiration modeling of the benchmark experiment has been achieved by the implementation of the thermal transpiration mobility force closure for the thermal momentum accommodation coefficient.

An original and easy-to-implement method has been developed to numerically prove that at the final equilibrium, i.e. zero-flow state, there is a connection between the Poiseuille flow in the center of channel and counter thermal transpiration flow on the surface. The numerical implementation of the Reynolds model of thermal transpiration has been performed, and its usefulness for the description of the benchmark experiment has been verified.

The simplified procedure requires the measurement or assumption of the helium-glass slip length.

The procedure can be very useful in the design of micro-electro-mechanical systems and nano-electro-mechanical systems, especially for accommodation pumping.

The paper discussed possible constitutive equations in the transpiration shell-like layer. The new approach can be helpful for modeling phenomena occurring at a fluid–solid phase interface at the micro- and nanoscales.

Fluid flows in pipes whose cross-sectional area are increasing in the stream-wise direction are prone to separation of the recirculation region. This paper aims to investigate such fluid flow in expansion pipe systems using direct numerical simulations. The flow in circular diverging pipes with different diverging half angles, namely, 45, 26, 14, 7.2 and 4.7 degrees, are considered. The flow is fed by a fully developed laminar parabolic velocity profile at its inlet and is connected to a long straight circular pipe at its downstream to characterise recirculation zone and skin friction coefficient in the laminar regime. The flow is considered linearly stable for Reynolds numbers sufficiently below natural transition. A perturbation is added to the inlet fully developed laminar velocity profile to test the flow response to finite amplitude disturbances and to characterise sub-critical transition.

Direct numerical simulations of the Navier–Stokes equations have been solved using a spectral element method.

It is found that the onset of disordered motion and the dynamics of the localised turbulence patch are controlled by the Reynolds number, the perturbation amplitude and the half angle of the pipe.

The authors clarify different stages of flow behaviour under the finite amplitude perturbations and shed more light to flow physics such as existence of Kelvin–Helmholtz instabilities as well as mechanism of turbulent puff shedding in diverging pipe flows.

The paper targets on providing new experimental data for validation of the well-established mathematical models within the framework of the lattice Boltzmann method (LBM), which are applied to problems of casting processes in complex mould cavities.

An experimental campaign aiming at the free-surface flow within a system of narrow channels is designed and executed under well-controlled laboratory conditions. An in-house lattice Boltzmann solver is implemented. Its algorithm is described in detail and its performance is tested thoroughly using both the newly recorded experimental data and well-known analytical benchmark tests.

The benchmark tests prove the ability of the implemented algorithm to provide a reliable solution when the surface tension effects become dominant. The convergence of the implemented method is assessed. The two new experimentally studied problems are resolved well by simulations using a coarse computational grid.

A detailed set of original experimental data for validation of computational schemes for simulations of free-surface gravity-driven flow within a system of narrow channels is presented.

Displacements of a miscible magnetic layer in a capillary tube under a moving ring‐shaped magnet are studied numerically. The magnet is adjusted dynamically to maintain a constant distance from the front mixing interface on the centerline. Control parameters, such as magnetic strength, effective viscosity variation due to magnetization, diffusion and the position of the magnet, are analyzed systematically. Motion of the magnetic layer is evaluated by two quantitative measurements, i.e. movement of center of gravity and spread of layer width. In general, the moving speed of the center of gravity depends only slightly on the magnetic strength, and is found slower at a higher viscosity ratio and a closer placement to the front interface as well if the magnet is placed amid the layer. A weaker spread occurs in situations of stronger magnetic strength, lower viscosity parameters and also placements near the rear interface. A multi‐front finger results if the magnet is positioned ahead of the front interface.