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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.

The current study is mainly motivated by the need to the development of the transient MHD mixed convection stagnation-point flow and heat transfer of an electrically conducting nanofluid over a vertical permeable stretching/shrinking sheet by means of Tiwari-Das nanofluid model. The purpose of this paper is to investigate the effects of the parameters governing the flow i.e. the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter on dimensionless velocity and temperature distributions, skin friction coefficient and local Nusselt number.

The mathematical model has been formulated based on Tiwari-Das nanofluid model. Three different types of water-based nanofluid with copper, aluminum oxide (alumina) and titanium dioxide (titania) as nanoparticles are considered in this investigation. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved analytically by the well-know homotopy analysis method. The present simulations agree closely with the previous studies in the especial cases.

The results show that by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter or reducing the velocity ratio parameter, the skin friction coefficient enhances. Furthermore, the local Nusselt number enhances with different rates by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter. Besides, the skin friction coefficient and the local Nusselt number are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids.

Tiwari-Das nanofluid model has not been applied for the flow with these characteristics as mentioned in the paper. A comprehensive survey on boundary layer behavior has been presented. There are few studies regarding as analysis on thermal and hydrodynamics boundary layer. All plots presented in the paper are new and did not report in any other study. The effects of the parameters governing the flow on skin friction coefficient and local Nusselt number have been illustrated in the paper while there are some conflicts with previous published article that have been interpreted in details in the paper.

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 purpose of this paper is to investigate the nanofluid flow and heat transfer induced by two co- axially rotating disks using Buongiorno’s model. This model took into account the Brownian diffusion and thermophoresis effects due to the presence of nanoparticles.

The governing partial differential equation was transformed into a set of nonlinear ordinary differential equations by using similarity transformation and solved numerically using shooting techniques.

The present work is a comparison study of Maxwell-Garnett model and modified Maxwell model for the effective thermal conductivity of nanofluids. The effects of different involved parameters on velocity and temperature profile are examined graphically. Numerical values of skin friction coefficient and Nusselt number are computed and studied.

It is found that the results of azimuthal velocity profile are an increasing function of upper disk stretching parameter. The radial and axial velocity profile is enlarged for a large value of lower stretching parameter. Fluid temperature decays for large values Reynolds number and lower disk stretching parameter.

This paper aims to investigate a linear and temporal stability analysis of hybrid nanofluid flow between two parallel plates filled with a porous medium and whose lower plate is fixed and the upper plate animated by a uniform rectilinear motion.

The nanofluid is composed of water as a regular fluid, silver (Ag) and alumina (Al₂O₃) as nanoparticles. The mathematical model takes into account other effects such as the magnetic field and the aspiration (injection/suction). Under the assumption of a low magnetic Reynolds number, a modified Orr–Sommerfeld-type eigenvalue differential equation governing flow stability was derived and solved numerically by Chebyshev’s spectral collocation method. The effects of parameters such as volume fraction, Darcy number, injection/suction Reynolds number, Hartmann number were analyzed.

It was found the following: the Darcy number affects the stability of the flow, the injection/suction Reynolds number has a negligible effect, the volume fraction damped disturbances and the magnetic field plays a very important role in enlarging the area of flow stability.

The originality of this work resides in the linear and temporal stability analysis of hydromagnetic Couette flow for hybrid nanofluid through porous media with small suction and injection effects.

An increment in energy efficiency by employing nanoparticles is a hot topic of research in present era due to its abundant implications in modern engineering and technological processes. Therefore, the current research analysis reported the viscoelastic nanofluid flow over porous oscillatory moving sheet in the presence of microorganisms. A rate-type fluid namely Maxwell fluid is employed with the addition of nanoparticles. The paper aims to discuss this issue.

First, acceptable dimensionless variables are defined to convert the system of dimensional form into the system of dimensionless forms. Later on, the self-similar solution of the boundary value problem is computed by using the homotopy analysis method. The obtained results of velocity, temperature, mass concentration and motile microorganism density profiles are interpreted through physical background.

The presence of both thermophoresis and Brownian motion parameters also improve the thermophysical features of non-Newtonian nanoparticles. It is also pointed out that the presence of porous medium and magnetic force enhances the nanoparticles concentration. Moreover, a weaker distribution of gyrotactic microorganism has been depicted with Peclet number and bioconvection Lewis parameter.

No such article exists in the literature yet.

The purpose of this study is to investigate the impact of varying baffle height and spacing distance on heat transfer and cooling performance of electronic components in a baffled horizontal channel, using a Cu-H₂O nanofluid under mixed convection and laminar flow.

The mathematical model is two-dimensional and comprises a system of four governing equations, such as the conservation of continuity, momentum and energy. To obtain numerical solutions for these equations, the finite volume method was used for discretization. A validation process was performed by comparing this study’s results with those of previously published studies. The comparison revealed a close agreement. The numerical study was performed for a wide range of key parameters: The baffle height (0 ≤ h ≤ 0.7), the spacing distance between baffle and blocks (0.25 ≤ w ≤ 3), the Grashof and Reynolds numbers are kept equal to 10⁴ and 75, respectively, the channel aspect ratio is L/H = 10, and the volume fraction of Cu nanoparticles is fixed at φ = 5%.

The results of the study reveal a significant improvement in heat transfer in terms of total Nusselt number of the top and bottom hot components, which exhibited an improvement of 16.89% and 17.23% when the baffle height increases from h = 0 to h = 0.7. Additionally, the study found that reducing the distance between the baffle and the electronic components up to a certain limit can improve the heat transfer rate. Therefore, the optimal height of the baffle was found to be no lower than 0.6, and the recommended distance between the heaters and the baffle was 0.5.

This study provides valuable insights into the optimization of the design of baffled channels for improved heat transfer performance. The findings of study can be used to improve heat exchangers and cooling systems in various applications. The use of Cu-H₂O nanofluid under mixed convection and laminar flow conditions in channel with baffle and electronic components is also unique, making this study an original contribution to the field.

This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet. Heat transfer occurring during the melting process due to a stretching sheet is considered. The paper aims to discuss these issues.

The authors convert governing partial differential equations into ordinary differential equations by using suitable transformations. Analytic solutions of velocity and temperature are found by using homotopy analysis method (HAM). Further graphs are displayed to study the salient features of embedding parameters. Expressions of skin friction coefficient, local Nusselt number and local Sherwood number have also been derived and examined.

It is found that velocity and the boundary layer thickness are increasing functions of viscoelastic parameter (Deborah number). An increase in the melting process enhances the fluid velocity. An opposite effect of melting heat process is noticed on velocity and skin friction.

The boundary layer flow in non-Newtonian fluids is very important in many applications including polymer and food processing, transpiration cooling, drag reduction, thermal oil recovery and ice and magma flows. Further, the thermal diffusion effect is employed for isotope separation and in mixtures between gases with very light and medium molecular weight.

Very scarce literature is available on thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet with melting heat transfer. Series solution is developed using HAM. Further, the authors compare the present results with the existing in literature and found excellent agreement.

The purpose of this paper is to scrutinize the heat and mass transfer attributes of three-dimensional bio convective flow of nanofluid across a slendering surface with slip effects. The analysis is carried out subject to irregular heat sink/source, thermophoresis and Brownian motion of nanoparticles.

At first, proper transmutations are pondered to metamorphose the basic flow equations as ODEs. The solution of these ODEs is procured by the consecutive application of Shooting and Runge-Kutta fourth order numerical procedures.

The usual flow fields along with density of motile microorganisms for sundry physical parameters are divulged via plots and scrutinized. Further, the authors analyzed the impact of same parameters on skin friction, heat and mass transfer coefficients and presented in tables. It is discovered that the variable heat sink/source parameters play a decisive role in nature of the heat and mass transfer rates. The density of motile microorganisms will improve if we add Al-Cu alloy particles in regular fluids instead of Al particles solely. A change in thermophoresis and Brownian motion parameters dominates heat and mass transfer performance.

To the best of the knowledge, no author made an attempt to investigate the flow of nanofluids over a variable thickness surface with bio-convection, Brownian motion and slip effects.

The aim of this work is to analyze the combined effects of melting, thermal-diffusion and diffusion-thermo on the flow of non-Newtonian fluid.

An efficient approach namely homotopy analysis method is applied to compute the solution of the non-linear problem. Moreover, numerical results using MATLAB function bvp4c are also computed.

Main findings are an increase in the melting process corresponding to increase in the velocity and the boundary layer thickness. However, surface heat and mass transfer decrease by increasing the values of melting parameter M.

Combined effects of thermal-diffusion and diffusion-thermo are analyzed and the solutions are computed both numerically and analytically. Some deduced results can be obtained in a limiting sense.