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The numerical solution of problems involving two‐dimensional flow in an infinite or a semi‐infinite channel is considered. Beyond a certain finite region, where the flow and geometry may be general, a “tail” region is assumed where the flow is potential and the channel is uniform. This situation is typical in many cases of fluid‐structure interaction and flow around obstacles in a channel. The unbounded domain is truncated by means of an artificial boundary B, which separates between the finite computational domain and the “tail.” On B, special boundary conditions are devised. In the finite computational domain, the problem is solved using a finite element scheme. Both non‐local and local artificial boundary conditions are considered on B, and their performance is compared via numerical examples.

The current investigation is communicated to analyze the characteristics of squeezed second grade nanofluid flow enclosed by infinite channel in the existence of both heat generation and variable viscosity. The leading non-linear energy and momentum PDEs are converted into non-linear ODEs by using suitable analogous approach.

Then the acquired non-linear problem is numerically calculated by using Bvp4c (built in) technique in MATLAB.

The influence of certain appropriate physical parameters, namely, squeezed number, fluid parameter, Brownian motion, heat generation, thermophoresis parameter, Prandtl number, Schmidt number and variable viscosity parameter on temperature, velocity and concentration distributions are studied and deliberated in detail. Numerical calculations of Sherwood number, Nusselt number and skin friction for distinct estimations of appearing parameters are analyzed through graphs and tables. It is examined that for large values of squeezing parameter, the velocity profile increases, whereas opposite behavior is noticed for large values of variable viscosity and fluid parameter. Moreover, temperature profile increases for large values of Brownian motion, thermophoresis parameter and squeezed parameter and decreases by increases Prandtl number and heat generation. Moreover, concentration profile increases for large values of Brownian motion parameter and decreases by increases thermophoresis parameter, squeezed parameter and Schmidt number.

No one has ever taken infinite squeezed channel having second grade fluid model with variable viscosity and heat generation.

Numerical computations were performed for the heat transfer and fluid flow characteristics of natural convection with an internal vertical channel composed by a pair of parallel plates in a rectangular enclosure. The inner plates and the bounding wall of the enclosure were maintained at uniform but different temperatures. The plates were symmetrically arranged. Unsteady computation was performed to simulate the evolution process of the natural convection developing from the zero initial field. The cases of Ra = 2 × 10⁴, 2 × 10⁵ and 10⁶ were studied. A symmetrical steady solution was achieved for the case of Ra = 2 × 10⁴. For Ra = 2 × 10⁵ and 10⁶, time dependent asymmetrical processes were observed. The flow oscillating process seemed to be more complex at Ra = 2 × 10⁵ than that at Ra = 10⁶, which is quasi‐periodic with two frequencies.

The purpose of this paper is to investigate the approximate solution of the couple stress fluid equations in a semi‐infinite rectangular channel with porous and uniformly expanding or contracting walls.

Perturbation method is a traditional method depending on a small parameter which is difficult to be found for real‐life nonlinear problems. The governing partial differential equations are transformed using a transformation into an ordinary differential equation that is solved by homotopy analysis method (HAM) and shooting technique.

To assess the accuracy of the solutions, the comparison of the obtained results reveals that both methods are tremendously effective. Analytical and numerical solutions comparison indicates an excellent agreement and this comparison is also presented. Graphs are portrayed for the effects of some values of parameters.

Expansion or contraction problems occur naturally in the transport of biological fluids, the air circulation in the respiratory system, expanding or contracting jets and the synchronous pulsating of porous diaphragms. This work provides a very useful source of information for researchers on this subject.

In the present study, the flow of couple stress fluids in expanding and contracting scenarios is investigated.

As transferring biological fluid through an artery is nowadays a pivotal subject, the purpose of this paper is to study the mathematical model of hybrid nanofluid flow comprising pure blood as base fluid and TiO₂ and Ag as nanoparticles through the porous channel, which can be an applicable model for drug delivery.

Both walls of the channel have different permeability, which enables the fluid to enter and exit, and variable height, which dilates and squeezes at the uniform rate. By taking advantage of the similarity transformation technique, governing equations have been converted into a system of the non-linear ordinary differential equation. This problem is solved numerically by utilizing BVP4C built-in function in MATLAB software to explore the impacts of pertinent parameters.

The plots of velocity and temperature profile, normal pressure distribution and wall shear stress, as well as Nusselt number for involved parameters, are presented and the logic and physical reasons beyond them are highlighted. It has been observed that the asymmetry of the channel, caused by different permeability at walls, affects the nature of flow significantly.

To the best of the authors’ knowledge, no one has ever attempted to study the flow through a deformable porous channel with blood as a base fluid and as hybrid nanoparticles to describe medical phenomena and treatment applications. Indeed, the achievements of this paper are purely original and the numerical results were never published by any researcher.

The article focuses on the magnetohydrodynamic (MHD) convective flow of MoS₂-SiO₂ /ethylene glycol (EG) hybrid nanofluid. The effectiveness of Hall current, periodically heating wall and shape factor of nanoparticles on the magnetized flow of hybrid nanocomposite molybdenum disulfide- silicon dioxide (MoS₂-SiO₂) suspended in ethylene glycol (EG) in a vertical rotating channel under the influence of strong magnetic dipole (Hall effect) and thermal radiation is assessed. One of the channel walls has an oscillatory temperature gradient. Four different shapes (i.e. brick, cylinder, platelet and blade) of nanoparticles disseminated in base fluid (EG) are considered for simulation of the flow.

The analytical solution of governing equations has been presented. Influences of emerging physical parameters on the velocity and temperature profiles, the shear stresses and the rate of heat transfer are pointed out and discussed via graphs and tables.

The analysis revealed that Hall parameter has suppressing behavior on the velocity profiles within the rotating channel. The impact of nanoparticle shape factor advances the temperature characteristics significantly in the rotating channel. Brick-shape nanoparticles put up relatively low-temperature distribution in the rotating channel. The Hall parameter reduces the amplitudes of the shear stresses at the channel wall. However, the radiation parameter enhances the amplitude of the rate of heat transfer at the channel wall.

The important technical advantage of hybrid composition of nanoparticles as a drug carrier is its stability, high thermal conductivity, high load carrying capacity, etc. The proposed model may be beneficial in biomedical engineering, automobile parts, mineral and cleaning oils manufacturing, rubber and plastic industries.

To the best of our knowledge, there is little or no report on the aspects of assessment of the effectiveness of Hall current and nanoparticle shape factor on an MHD flow and heat transfer of an electrically conducting MoS₂-SiO₂/EG ethylene glycol-based hybrid nanofluid confined in a vertical channel with periodically varying wall temperature subject to a rotating frame. The present work furnishes a robust benchmark for the dynamics of nanofluids.

The purpose of this paper is to provide a quantitative assessment on the effect of wall roughness on the pressure drop of fluid flow in microchannels.

The wall roughness is generated by the method of random midpoint displacement (RMD) and the lattice Boltzmann BGK model is applied. The influences of Reynolds number, relative roughness and the Hurst exponent of roughness profile on the Poiseuille number are investigated.

Unlike the smooth channel flow, Reynolds number, relative roughness and the Hurst exponent of roughness profiles play critical roles on the Poiseuille number Po in rough microchannels. Modeling results indicate that, in rough microchannels, the rough surface configuration intensifies the flow-surface interactions and the wall conditions turn to dominate the flow characteristics. The perturbance of the local flows near the channel wall and the formation of recirculation regions are two main features of the flow-surface interactions.

The fluid flow in parallel planes with surface roughness is considered in the current study. In other words, only two-dimensional fluid flow is investigated.

The LBM is a very useful tool to investigate the microscale flows.

A new method (RMD) is applied to generate the wall roughness in parallel plane and LBM is conducted to investigate the pressure drop characteristics in rough microchannels.

Free convection heat transfer due to the simultaneous action of buoyancy, radiation and transverse magnetic field is investigated for a semi‐infinite vertical plate. Solutions are derived by expanding the stream function and the temperature into a series in terms of the parameter ζ = x^1/2 L^–1/2, where L is the length of the plate. Velocity and temperature functions are shown on graphs and the numerical values of functions affecting the shear stress and the rate of heat transfer are entered in a table. The effects of the magnetic field parameter λ and the radiation parameter F on these functions are discussed.

The purpose of this paper is to conduct a detailed investigation of the two-dimensional natural convection flow of a dusty fluid. Therefore, the incompressible boundary layer flow of a two-phase particulate suspension is investigated numerically over a semi-infinite vertical flat plate. Comprehensive flow formations of the gas and particle phases are given in the boundary layer region. Primitive variable formulation is employed to convert the nondimensional governing equations into the non-conserved form. Three important two-phase mechanisms are discussed, namely, water-metal mixture, oil-metal mixture and air-metal mixture.

The full coupled nonlinear system of equations is solved using implicit two point finite difference method along the whole length of the plate.

The authors have presented numerical solution of the dusty boundary layer problem. Solutions obtained are depicted through the characteristic quantities, such as, wall shear stress coefficient, wall heat transfer coefficient, velocity distribution and temperature distribution for both phases. Results are interpreted for wide range of Prandtl number Pr (0.005-1,000.0). It is observed that thin boundary layer structures can be formed when mass concentration parameter or Prandtl number (e.g. oil-metal particle mixture) are high.

The results of the study may be of some interest to the researchers of the field of chemical engineers.

The purpose of this paper is to examine the combined effects of thermal radiation and magnetic field of molybdenum disulfide nanofluid in a channel with changing walls. Water is considered as a Newtonian fluid and treated as a base fluid and MoS₂ as nanoparticles with different shapes (spherical, cylindrical and laminar). The main structures of partial differential equations are taken in the form of continuity, momentum and energy equations.

The governing partial differential equations are converted into a set of nonlinear ordinary differential equations by applying a suitable similarity transformation and then solved numerically via a three-stage Lobatto III-A formula.

All obtained unknown functions are discussed in detail after plotting the numerical results against different arising physical parameters. The validations of numerical results have been taken into account with other works reported in literature and are found to be in an excellent agreement. The study reveals that the Nusselt number increases by increasing the solid volume fraction for different shapes of nanoparticles, and an increase in the values of wall expansion ratio α increases the velocity profile f′(η) from lower wall to the center of the channel and decreases afterwards.

In this paper, a numerical method was utilized to investigate the influence of molybdenum disulfide (MoS₂) nanoparticles shapes on MHD flow of nanofluid in a channel. The validity of the literature review cited above ensures that the current study has never been reported before and it is quite new; therefore, in case of validity of the results, a three-stage Lobattoo III-A formula is implemented in Matlab 15 by built in routine “bvp4c,” and it is found to be in an excellent agreement with the literature published before.