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This study examines Darcy-Forchheimer 3D nanoliquid flow caused by a rotating disk with heat generation/absorption. The impacts of Brownian motion and thermophoretic are considered. Velocity, concentration, and thermal slips at the surface of the rotating disk are considered. The change from the non-linear partial differential framework to the non-linear ordinary differential framework is accomplished by utilizing appropriate variables. A shooting technique is utilized to develop a numerical solution of the resulting framework. Graphs have been sketched to examine how the concentration and temperature fields are affected by several pertinent flow parameters. Skin friction and local Sherwood and Nusselt numbers are additionally plotted and analyzed. Furthermore, the concentration and temperature fields are enhanced for larger values of the thermophoresis parameter.

In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.

The paper investigates the squeeze film process for non-Newtonian fluids between two circular parallel profiled surfaces. The lower surface is characterized by the existence of a cylindrical or spherical dimple in the center, which is specific for profiled surfaces by texturing. In order to integrate the Reynolds equation, the slip boundary conditions on the upper surface have been assumed. Finally, the pressure distribution and the loading capacity of the non-Newtonian film are obtained. [ABSTRACT FROM AUTHOR]

The present study makes a numerical assessment of magnetohydrodynamics stream of Casson liquid over a deformable porous layer with slip conditions. The governing ordinary differential equations are settled Runge–Kutta fourth-order method along with the shooting technique. The impact of relevant parameters on the liquid velocity, the solid displacement, the temperature and the concentration are shown graphically, while the mass stream rate is contemplated numerically shown in tabular structure. The present outcomes have been great concurrence with existing assessments under some exceptional cases. We can see that the liquid velocity and solid displacements are rotted for higher estimations of magnetic parameter and the contrary nature found for the impact of Casson parameter. The effect of slip boundary conditions on the fluid velocity, the temperature and the concentration is additionally inspected. [ABSTRACT FROM AUTHOR]

This work models new formulation for peristaltic activity of Rabinowitsch material in a compliant walls channel. Energy equation is accounted in the presence of viscous dissipation and heat source/sink. Chemical reaction is included in concentration expression. Nanomaterial characteristics are due to Brownian motion and thermophoresis. Slip condition is utilized for velocity, temperature and concentration. Exact solution is obtained for velocity. Further NDSolve is utilized for the graphical analysis of temperature, concentration, entropy and heat transfer coefficient at the wall. Results are also analyzed for viscous, shear thickening and shear thinning fluids. This study reveals the results that the shear thinning fluids move with greater velocity than the viscous and shear thickening fluids. Similarly, temperature and entropy generation also has higher values for shear thinning case when compared with others. Further heat source parameter enhances the temperature, whereas sink parameter leads to decay. Slip parameter for velocity and temperature caused an increase in the respective velocity and temperature. Moreover, chemical reaction parameter leads to enhancement in temperature and entropy generation in case of viscous, shear thickening and shear thinning fluids. However, shear thinning fluids are found prominent. [ABSTRACT FROM AUTHOR]

An earlier asymptotic analysis identified the flow-induced power and log singularities present when two nonmiscible, incompressible, viscous fluids contact a wall with no slip permitted. Here a parallel asymptotic analysis identifies such singularities in pressures and stresses when slip is admitted. While the singularity exponents for the two types of contact conditions are similar, the angles of interface impingement that have either power or log singularities are usually quite distinct. [ABSTRACT FROM AUTHOR]

We have presented a comparison between steady and unsteady magnetohydrodynamic boundary layer flow, heat transfer features of Au–kerosene‐based nanoliquid over a stretching surface by taking variable viscosity, variable thermal conductivity, and slip boundary conditions in this study. Appropriate similarity translations are engaged to reduce nonlinear partial differential equations into a set of ordinary differential equations. These equations along with boundary conditions are elucidated numerically by finite‐element technique. Influence of several pertinent parameters on velocity, temperature, and concentration scatterings, in addition to that, the values of Nusselt number, skin‐friction coefficient, and Sherwood number are scrutinized in detail and the outcomes are exhibited through plots and tables. It is perceived that the values of Nusselt number, skin‐friction coefficient, and Sherwood number intensify in both steady–unsteady cases as the values of volume fraction parameter (ϕ) rise. [ABSTRACT FROM AUTHOR]

We derive a Nitsche-based formulation for fluid-structure interaction (FSI) problems with contact. The approach is based on the work of Chouly and Hild (SIAM J. Numer. Anal. 51 (2013) 1295–1307) for contact problems in solid mechanics. We present two numerical approaches, both of them formulating the FSI interface and the contact conditions simultaneously in equation form on a joint interface-contact surface Γ(t). The first approach uses a relaxation of the contact conditions to allow for a small mesh-dependent gap between solid and wall. The second alternative introduces an artificial fluid below the contact surface. The resulting systems of equations can be included in a consistent fashion within a monolithic variational formulation, which prevents the so-called "chattering" phenomenon. To deal with the topology changes in the fluid domain at the time of impact, we use a fully Eulerian approach for the FSI problem. We compare the effect of slip and no-slip interface conditions and study the performance of the method by means of numerical examples. [ABSTRACT FROM AUTHOR]

The present investigation aims to examine peristalsis in a symmetric channel having flexible walls. Sisko nanofluid is considered for the investigation. Joule heating and nonlinear thermal radiation are taken. Boundary conditions are subject to the slip conditions for velocity, temperature and concentration. Entropy generation analysis for viscous dissipation, Joule heating and nonlinear thermal radiation is carried out. System is numerically computed through NDSolve of Mathematica. Graphical analysis is made for velocity, temperature, concentration, heat transfer coefficient and entropy generation. Conclusions are drawn through discussion. This study discloses that magnetic field leads to slow down the fluid velocity and causes decay in heat transfer coefficient. Further, Brownian motion and thermophoresis parameter caused enhancement in temperature and entropy generation rate. Slip parameters for velocity and temperature lead to enhancement in the velocity and temperature, whereas opposite impact is observed for concentration via corresponding slip parameter. [ABSTRACT FROM AUTHOR]

The flow of hybrid nanoparticles with significant physical parameters with different base fluids in the presence of Biot number, velocity slip, and MHD effects has not been explored so far, particularly for a circular cylinder. Therefore, the current report is presented to offer a numerical solution for hybrid nanoparticles with base fluids (water and ethylene glycerol) via a circular cylinder. The physical situation is interpreted in terms of partial differential equations and is converted into ordinary differential equations after applying the similarity transformation. The results are presented in both tabular and graphical forms. The impact of physical parameters on velocity distribution is examined through graphs. The comparative results of hybrid nanoparticles for distinct base fluids as ethylene glycol and water are proposed and the hybrid nanoparticles with base fluid water seems to be greater than that of the hybrid nanoparticles with base fluid EG. The temperature profile of hybrid nanoparticles is found to be a decreasing function with growth in velocity slip parameter γ but an opposite trend is noted in case of nanoparticles Φ2. The skin friction and Nusselt number augmented for the increase in magnetic field, velocity slip, and nanoparticle while it shows a decreasing trend toward thermal slip parameter. For the both cases, improvement in Biot number helps enhance the heat transfer constantly. [ABSTRACT FROM AUTHOR]

This study examines the transport phenomenon in which host fluid completely mixed with three different nanoparticles types (ternary hybrid nanofluid) has attract scientist's attention for considering of its significance. The primary reason for the rising interest in tri-hybrid nanofluid is its unique ability to improve thermal performance, which is really useful in various heat exchangers. In the present analysis, the main objective of this article is to examining the laminar, time-dependent, incompressible and two dimensional (2D) trihybrid magnetized squeezing flow of a Boger-micropolar nanofluid between non-porous and porous disk to observe the thermal performance of fluid. This model describes the way to attain a more appropriate heat conductor as compared to bi-hybrid, mono nanofluid. The ternary nanofluid is formulated by adding three types of nano size particles with distinct chemical and physical bonds into water as a base liquid. This mixture helps in purification of environment, decomposing destructive substance and other devices that required cooling. At z = − H (1 − a t) 1 / 2 the lower disk is fixed and the liquid is squeezing due to movement of top disk with axial direction. At the lower surface a homogeneous suction/injection is imposed. Energy and velocity slip impacts are also considered at the fixed bottom disk. Appropriate similarity functions are imposed to transform the governs equations into non-linear ordinary differential equations (ODE's) and then numerically solved by bvp4c technique in MATLAB environment. The outcomes are then displayed in graphically to investigate the microrotation, velocity and temperature profiles. The temperature profile decreased against tri-hybrid case in the lower disk case and then are enhanced near to the top disk in tri-hybrid case, so finally, we conclude that ternary nano size particles have an excellent thermal conductivity as compared to single and hybrid nanoparticles. The present results are found to be good agreement with existence literature for limited cases. • Significance of tri-hybrid nanoparticles in thermal management is modeled. • Tiwari and Das model for nanoparticles is taken into account for modeling. • Ternary hybrid nanofluid have an excellent thermal conductivity. • Higher inputs of magnetic field cause to twisting behavior between disk. [ABSTRACT FROM AUTHOR]

This study presents the magnetized hybrid nanofluid flow with heat source/sink over an exponentially stretching/shrinking sheet. Slip conditions are implemented to analyze the hybrid nanofluid flow for both slip and no-slip conditions. Additionally, the hybrid nanofluid of alumina and copper (hybrid nanoparticles) with blood (base fluid) has been considered and discussed with both suction and injection parameters. The appropriate similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and solved analytically with the help of the homotopy analysis method (HAM). The impact of different embedded parameters has been shown in the form of graphs and tables. The numerical values of skin friction and Nusselt number are presented in the form of Tables for both slip and no-slip cases. It is summarized that the upsurge of the velocity slip parameter and magnetic parameter increases the skin friction, while the rising of the thermal slip parameter and heat generation parameter decreases the Nusselt number.

In this paper, we examine the combined effects of magnetic field, thermal radiation, heat source, velocity slip and thermal jump on peristaltic transport of an electrically conducting Walters-B fluid through a compliant walled channel. Using small wave number approach, the nonlinear model differential equations are obtained and tackled analytically by regular perturbation method. Expressions for the stream function, velocity, temperature, skin-friction coefficient and heat transfer coefficient are constructed. Pertinent results are presented graphically and discussed quantitatively. It is found that the velocity distribution depresses while the fluid temperature rises with an increase in Hartmann number. The trapping phenomenon is observed and the size of trapped bolus increases with an increase in Hartmann number.

The current research explores entropy generation and effect of magnetic field on peristaltic flow of copper‐water nanofluid in an asymmetric configuration saturated with porous medium. Slip conditions are invoked for velocity and temperature. Governing flow problem is constructed under the long wave length assumption. Analytical result for the problem is computed by exploiting homotopy analysis methodology. The influences of involved physical parameters are investigated through plots. [ABSTRACT FROM AUTHOR]

This study addresses the peristalsis of tangent hyperbolic liquid in a curved channel. Analysis has been prepared for chemical reaction, magnetohydrodynamics and thermophoretic deposition. The slip conditions for velocity, temperature and concentration are imposed. Problem subject to low Reynolds number and long wavelength are constructed. Numerical approach (called shooting method with the combination of Runge-Kutta Fehlberg algorithm) is employed to find the solutions. Behavior of velocity, temperature and concentration for sundry parameters is plotted. Graphical results reveal that velocity and temperature have opposite behavior for their respective slip parameters (i.e. velocity and thermal). Aspects of chemical reaction (for both constructive and destructive cases) on concentration are quite prominent. • Peristalsis of tangent hyperbolic liquid in a curved channel is considered. • Chemical reaction is accounted. • Multiple slip conditions are imposed at the boundary. • Problem subject to long wavelength and low Reynolds number are constructed. [ABSTRACT FROM AUTHOR]

This paper studies the influence of an inclined magnetic field on peristaltic transport of incompressible Bingham plastic fluid in an inclined symmetric channel with heat transfer and mass transfer. Slip conditions for heat transfer and concentration are employed. The formulation of the problem is presented through, the regular perturbation technique for small Bingham number is used to find the final expression of stream function, the flow rate, heat distribution and concentration distribution. The numerical solution of pressure rise per wave length is obtained through numerical integration because its analytical solution is impossible. Also the trapping phenomenon is analyzed. The effect of the physical parameters of the problem are discussed and illustrated graphically. [ABSTRACT FROM AUTHOR]

Abstract Here mixed convective MHD peristalsis of Jeffrey material in porous space with non-Darcy resistance is discussed. Symmetric flow configuration is chosen. Hall effects are considered for higher magnetic field effects. Heat and mass transfer coupled with thermo-diffusion and diffusion-thermo aspects are studied. First order chemical reaction with activation energy is also accounted. First, the problem is modelled with the help of conservation laws and then it is simplified through lubrication technique. Numerical solution of non-dimensional system of resulting equations is undertaken through NDSolve command in Mathematica. Discussion is presented through graphs for velocity, temperature and concentration. It is observed that by increasing the permeability parameter, velocity is enhanced. Increase in Dufour and Soret effects corresponds to velocity increase as a results in amplification in temperature is observed. Concentration has opposite response for activation energy and chemically reactive parameter. [ABSTRACT FROM AUTHOR]

Oscillatory pressure-driven MHD flow in a vertical rotating channel has been explored in the present article. Emphasis has been given to velocity slip effects along with Hall current and periodic thermal boundaries. Casson fluid model has been incorporated to examine viscoplastic effects. Heat transfer analysis has been performed in the presence of thermal radiation. The current problem has been modeled in a rotating frame. Equations are formulated in the Cartesian coordinate system and simplified by means of suitable non-dimensional variables. Furthermore, closed- form exact solutions are derived for velocity and temperature fields. The effects of pertinent parameters are studied through graphs. [ABSTRACT FROM AUTHOR]

The present study is related to indicating the several effects of the relaxation time, dynamic behaviour of wall properties and slip conditions at the boundaries on the peristaltic locomotion of viscous non-Newtonian Maxwell fluid flow through a two-dimensional (2D) horizontal flexible sinusoidal wave-shaped channel. An approximated theoretical model is constructed. The solution of the governing equations is developed using the perturbation method. Small amplitude ratio "ratio between amplitude of the wave and half channel width" for the wavy transport is considered for describing the velocity and pressure distributions. Different factors of wall features such as damping force coefficient, wall tension parameter, wall bending coefficient and spring stiffness factor in addition to various flow parameters such as the compressibility factor, Reynolds number, slip coefficient and also the main parameter of interest relaxation time are involved in the mathematical calculations and discussed through graphical representation. Graphs for mean axial velocity, perturbation function and velocity at the wall distributions using the previous coefficients are plotted and then discussed in detail. Results indicate that wall properties, compressibility factor and relaxation time in the presence of peristaltic transport have a significant effect on velocity distributions. The damping factor, wall tension, slip parameter and relaxation time are reducing the mean axial velocity and raising the reversal flow but, the wall elasticity factor enhances the mean axial velocity. Also, the liquid compressibility has a strong effect on the dynamics of the flow. [ABSTRACT FROM AUTHOR]

Numerous non-Newtonian fluid models are formulated as an alternative to Newton's Law of viscosity, which describes absolute viscous sources as a function of shear rate rather than constantly. In this paper, the Reiner-Philippoff fluid (RPF) model is considered out of many existing models since it can capture certain non-Newtonian characteristics in certain cases. An adopted underlying mathematical model employs a partial differential system, which is reduced to the system of ordinary differential system with the help of suitable similarity variables. The resultant system is computed with the Runga-Kutta-Fehlberg (RK-F) method to boost-up the confidence of its accuracy. It is found that the porosity and Darcy-Forchheimer parameters improve the flow rate of RPF. On the other hand, heat transfer is positively affected by thermal slip in contrast to the outcomes of radiation parameter, which, however, are inauspicious. Furthermore, the mass diffusion rate is noticed to be significantly influenced by the Schmidt number along with the chemical reaction parameter. In conclusion, all the results are expected to benefit numerous transport phenomena of industrial, biomedical, and thermal sciences. [ABSTRACT FROM AUTHOR]

This article examines the magneto-hydrodynamic (MHD) flow of nanofluid bounded by a stretching surface. The slip conditions are utilized in the present analysis. The involved differential systems are solved for the velocity, temperature and mass fraction. Graphical and numerical results are reported for the analysis of various parameters of interest entering into the modeled problems. Combined effects of thermal and concentration jump are analyzed. Various tables are constructed to show the rheological effects of different physical parameters. Streamlines are plotted showing the rheology for the slip and no slip flow regime. Plots of skin friction are also prepared for the slip and magnetic field effects.

The peristaltic motion of a third order fluid due to asymmetric waves propagating on the sidewalls of a inclined asymmetric channel is discussed. The key features of the problem includes longwavelength and low-Reynolds number assumptions. A mathematical analysis has been carried out to investigate the effect of slip condition, variable viscosity and magnetohydrodynamics (MHD). Followed by the nondimensionalization of the nonlinear governing equations along with the nonlinear boundary conditions, a perturbation analysis is made. For the validity of the approximate solution, a numerical solution is obtained using the iterative collocation technique.

The objective of this paper is to examine the flow of a non-Newtonian Maxwell fluid induced by a permeable stretching sheet in motion within a porous medium. The research incorporates the Cattaneo-Christov heat flux model to study the heat transfer process. The utilization of the Cattaneo-Christov heat flux approach becomes relevant in scenarios involving materials with high thermal conductivity or during short time intervals. Consequently, the current investigation holds significant importance. It is assumed that the viscosity of the Maxwell fluid changes exponentially as the temperature changes. The modeling of the physical phenomena being investigated takes into account the effects of a magnetic field, thermal radiation, velocity, and thermal slip conditions. In this study, the viscous dissipation phenomenon is taken into account because it can have notable impacts on the temperature and viscosity of the fluid, and is known to play a crucial role in fluid flow phenomena. The equations developed to model fluid flow are transformed into nonlinear ordinary differential equations through the use of appropriate similarity transformations. The focus of the research revolves around investigating the numerical solution of ordinary differential equations accompanied by boundary conditions using the shooting technique. The findings are then showcased via tables and graphs and scrutinized in order to arrive at conclusions. Furthermore, the precision of the present findings was evaluated by contrasting the heat transfer rate with outcomes that were previously published. Based on the obtained outcomes, it can be concluded that both the Eckert number and thermal radiation have a comparable enhancing influence, whereas the thermal relaxation parameter and thermal slip parameter exhibit opposing effects., Competing Interests: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Sara I. Abdelsalam reports travel was provided by Fundación Mujeres Por África., (© 2023 The Authors.)

Highlights • Numerical approach for peristalsis of Williamson fluid in the presence of porous medium is established. • Modified Darcy’s law is utilized. • Influences of Soret and Dufour effects are analyzed. • Slip conditions for both heat and mass transfer are present. • Effect of MHD is investigated. Abstract Objective of present investigation is to study peristaltic flow of MHD Williamson fluid in a planar symmetric channel. An incompressible fluid occupies the porous medium in a channel. Unlike the traditional approach, the modified Darcy’s law of Williamson fluid is utilized in the modeling. Numerous attempts for this aspect in non-Newtonian fluids have been made just by employing classical Darcy’s law of viscous fluid which is not correct. Heat and mass transfer equations are studied in the presence of Soret and Dufour effects. The walls of channel are flexible. In addition effects of slip are not ignored. The relevant problem formulation has been made and then simplified under long wavelength and low Reynolds number consideration. The effects of different embedded parameters on velocity, temperature, concentration and heat transfer rate are plotted numerically. Velocity, temperature and heat transfer rate are seen increasing when porosity parameter is enhanced. A decreasing effect of both Soret and Dufour numbers is observed for concentration profile. [ABSTRACT FROM AUTHOR]

In this paper, the steady three-dimensional magnetohydrodynamic (MHD) mixed convection flow of nanofluids over a permeable vertical stretching/shrinking sheet with slip conditions is investigated in a numerical manner. As such, two types of nanofluids, Cu-water and Ag-water, had been considered. A similarity transformation was employed to reduce the governing equations to ordinary differential equations, which were then solved numerically using the MATLAB (Matlab R2015a, MathWorks, Natick, MA, USA, 1984) programme bvp4c. The numerical solutions derived from the ordinary differential equations subjected to the associated boundary conditions, were obtained to represent the values of the mixed convection parameter. Dual (upper and lower branch) solutions were discovered in the opposing flow region of the mixed convection parameter. A stability analysis was carried out to prove that the upper branch solution was indeed stable, while the lower branch solution was unstable. The significant effects of the governing parameters on the reduced skin friction coefficients, the reduced local Nusselt number, as well as the velocity and temperature profiles, were presented graphically and discussed in detail. [ABSTRACT FROM AUTHOR]

This article addresses thermally stratified stagnation point flow of viscous fluid induced by a non-linear variable thicked Riga plate. Velocity and thermal slip effects are incorporated to disclose the flow analysis. Solar thermal radiation phenomenon is implemented to address the characteristics of heat transfer. Variations of different physical parameters on the horizontal velocity and temperature distributions are described through graphs. Graphical interpretations of skin friction coefficient (drag force at the surface) and Nusselt number (rate of heat transfer) are also addressed. Modified Hartman number and thermal stratification parameter result in reduction of temperature distribution. [ABSTRACT FROM AUTHOR]

This study addresses mixed convection on peristaltic flow in an inclined channel. The relevant flow problem is developed for MHD Johnson-Segalman nanofluid. Hall current and thermal radiation are discussed. Channel boundaries are compliant in nature. Slip effects for velocity, temperature and concentration are examined. Long wavelength concept is employed. Variations for prominent parameters in velocity, temperature, concentration, heat transfer coefficient and streamlines are obtained via built-in numerical approach. Velocity shows significant decline for larger local temperature Grashof number. Heat transfer slows down for increasing thermophoresis and thermal slip parameters. Increase in bolus is reported for higher Weissenberg number. [ABSTRACT FROM AUTHOR]

Here axisymmetric mixed convective, stagnation point flow of electrically conducting nanofluid by a permeable cylinder is examined. Magnetic field in transverse direction is applied. The Darcy-Forchheimer relation is accounted to specify the flow nature in porous medium. Formulation of mathematical model is given by using Tiwari-Das nanofluid model. The velocity and thermal slip conditions.are taken. This whole communication comprises water as a base fluid with nano-sized particles (Aluminum oxide, Copper and Titanium Oxide). The nonlinear coupled ordinary differential equations are obtained after using appropriate transformations. The convergent series solution of nonlinear system is accomplished by homotopic approach. The nondimensional velocity and temperature curve are examined under the impact of physical parameters like the nanoparticle volume fraction, permeability parameter, curvature parameter, the magnetic parameter and the mixed convection parameter. Numeric values of coefficient of skin friction and Nusselt number are analyzed. [ABSTRACT FROM AUTHOR]

This paper aims to examine the Darcy–Brinkman flow over a stretching sheet in the presence of frictional heating and porous dissipation. The governing equations are modeled and simplified under boundary layer approximations, which are then transformed into system of self-similar equations using appropriate transformations. The resulting system of nonlinear equations was solved numerically under velocity and thermal slip conditions, by fourth-order Runge–Kutta method and built-in routine bvp4c in Matlab. Under special conditions, the obtained results were compared with the results available in the literature. An excellent agreement was observed. The variation of parameters was studied for different flow quantities of interest and results are presented in the form of tables and graphs.

The present investigation is devoted to the peristalsis of hyperbolic tangent fluid with nanoparticles. The study is carried out under the effect of thermal radiation and Joule heating. The Buongiorno model is employed to the nanofluid flow in a channel with compliant walls. Effect of Hall current is also considered. The boundaries of the channel satisfy slip conditions. The involved equations are simplified using long wavelength and low Reynolds number approximation. The consequences of Hall current, thermal radiation, Hartman number, Brownian motion, thermophoresis and slip parameters are examined numerically. It is notable that Hartman number and Hall parameter shows similar behavior on temperature but opposite behavior on the velocity. [ABSTRACT FROM AUTHOR]

In this paper, we examine the combined effects of magnetic field, thermal radiation, heat source, velocity slip and thermal jump on peristaltic transport of an electrically conducting Walters-B fluid through a compliant walled channel. Using small wave number approach, the nonlinear model differential equations are obtained and tackled analytically by regular perturbation method. Expressions for the stream function, velocity, temperature, skin-friction coefficient and heat transfer coefficient are constructed. Pertinent results are presented graphically and discussed quantitatively. It is found that the velocity distribution depresses while the fluid temperature rises with an increase in Hartmann number. The trapping phenomenon is observed and the size of trapped bolus increases with an increase in Hartmann number. [ABSTRACT FROM AUTHOR]

This article intends to relate the significance of porous medium by modified Darcy's law in peristaltic flow of Sisko fluid. Curvature in modeling is considered. Such effects have particular significance in ureteral peristalsis and arterial blood flows. Radial magnetic field is applied to regulate the flow. Mathematical description of problem highlights the viscous dissipation and chemical reaction characteristics. The curved boundaries of channel are subject to wall's slip and compliant properties. The resulting coupled system has been executed numerically to plot various effects graphically. The drawn results approved decreasing response of magnetic field and increasing impact of Darcy number on fluid velocity and temperature. [ABSTRACT FROM AUTHOR]

In this paper, we examine the combined effects on peristaltic movement of an electrically conducting Walters-B fluid through a compliant walled channel. Using small wave number move towards, the nonlinear model differential equations are obtained and tackled analytically by regular perturbation method. Expressions for the stream function, velocity, temperature, skin-friction coefficient and heat transfer coefficient are constructed. Pertinent results are presented graphically and discussed quantitatively. It is found that the velocity distribution depresses while the fluid temperature rises with an increase in Hartmann number. The trapping phenomenon is observed and the size of trapped bolus increases with an increase in Hartmann number. [ABSTRACT FROM AUTHOR]

This article is intended to investigate the influence of Hall current on peristaltic transport of conducting Eyring–Powell fluid in an inclined symmetric channel. Energy equation is modeled by taking Joule heating effect into consideration. Velocity and thermal slip conditions are imposed. Lubrication approximation is considered for the analysis. Fundamental equations are non-linear due to fluid parameter A . Regular perturbation technique is employed to find the solution of systems of equations. The key roles of different embedded parameters on velocity, temperature and heat transfer coefficient in the problem are discussed graphically. Trapping phenomenon is analyzed carefully. [ABSTRACT FROM AUTHOR]

Outcome of entropy generation in peristalsis of Casson fluid in a rotating frame is intended. Formulation is based upon thermal radiation, viscous dissipation and slip conditions of velocity and temperature. Lubrication approach is followed. The velocity components, temperature and trapping are examined. Specifically the outcomes of Taylor number, fluid parameter, slip parameters, Brinkman, radiation and compliant wall effects are focused. In addition entropy generation and Bejan numbers are examined. It is observed that entropy is controlled through slip effects. [ABSTRACT FROM AUTHOR]

An analysis has been carried out for thermal radiation effects on peristaltic activity of couple stress fluid in a non-uniform rotating channel. The velocity and thermal slip effects at the channel boundaries are considered. Heat transfer with non-uniform heat generation/absorption effect is also taken into consideration. System of ordinary differential equations is obtained from the governing nonlinear partial differential equations. Small Reynolds number and large wavelength approximations are employed. Numerical technique is applied to solve the non-linear system. The influences of the various fluid and geometric parameters on velocities and temperature profiles have been presented and analyzed. [ABSTRACT FROM AUTHOR]

Aneurysm or stenosis in an artery is not very common, but it is becoming increasingly recognized due to its high incidence in pediatric and young adult patient. In the present study, a fractional second-grade fluid model with ternary nano-particles (Cu, Ag, CuO) is implemented to investigate the effects of electroosmotic forces (EMHD) through an oblique stenosed aneurysmal artery. The mild stenotic supposition is used to normalize and reduce the two directional momentum equations to the unidirectional flow. Closed-form solutions are calculated for the situation of mild stenosis and aneurysm by solving the governing equations for the suggested paradigm. Graphs are used to illustrate the effects of nanoparticles and aneurysm on blood flow rate, wall shear stress, and impedance. The results of ternary nanoparticles (Cu-Ag-CuO /blood), hybrid nanoparticles (Cu-Ag/blood), and copper (Cu) nanoparticles have also been compared, and this comparison suggests that ternary nanoparticles (Cu-Ag-CuO/blood) are more effective at attenuating hemodynamic factors (such as wall shear stress and impedance) than hybrid and copper (Cu) nanoparticles. Through the streamlines for various emerging parameters, the general behaviour of the blood flow patterns is also seen. The present study findings are particularly helpful for drug transportation and biomedical research. • The fractional second-grade, EMHD, ternary (modified) nanofluid model is utilized in this paper to investigate blood flow characteristics in stenosed and aneurysmal arterial segments. Exact solutions are found, and the impact of the important parameters is investigated. Comparisons are made for aneurysm and stenosis instances. The highlights of the paper are described as follows. • Ternary nanofluid has a higher hemodynamic velocity than hybrid nanofluid. • Resistance impedance is lower in aneurysm segments than in stenosis segments. • This model is appropriate to the drug dispersal system and also effective for physiological conversion in which nanoparticles have an important role. [ABSTRACT FROM AUTHOR]

• Rate of heat transfer is noted to be maximum for enhanced Debye length parameter. • Heat transfer rate enhances due to prominent viscous dissipation effects within the fluid. • The study is applicable to electrophoresis in electrohydrodynamic therapy, biomimetic electro-osmotic pumps and in hematology. In this article, we have investigated a non-Newtonian Jeffrey fluid model, which shows the role of cilia generated metachronal waves in a vertical tube. Electroosmosis effects, a viscous dissipation term is also adopted in this current analysis. The partial differential equations that govern the flow are transformed into a non-dimensional form by considering a low wavelength and small Reynolds number approximations. The obtained set of coupled ordinary differential equations is further solved by using Mathematica solver to get the required flow properties. The current model's output has important heat transfer rate applications in the ciliated channel due to the enhanced viscous dissipation effects, which can be used for the analysis of various areas of biological transport processes such as to design artificial cilia and for the operation of some mechanical devices. [ABSTRACT FROM AUTHOR]

In this paper, the steady three-dimensional magnetohydrodynamic (MHD) mixed convection flow of nanofluids over a permeable vertical stretching/shrinking sheet with slip conditions is investigated in a numerical manner. As such, two types of nanofluids, Cu-water and Ag-water, had been considered. A similarity transformation was employed to reduce the governing equations to ordinary differential equations, which were then solved numerically using the MATLAB (Matlab R2015a, MathWorks, Natick, MA, USA, 1984) programme bvp4c. The numerical solutions derived from the ordinary differential equations subjected to the associated boundary conditions, were obtained to represent the values of the mixed convection parameter. Dual (upper and lower branch) solutions were discovered in the opposing flow region of the mixed convection parameter. A stability analysis was carried out to prove that the upper branch solution was indeed stable, while the lower branch solution was unstable. The significant effects of the governing parameters on the reduced skin friction coefficients, the reduced local Nusselt number, as well as the velocity and temperature profiles, were presented graphically and discussed in detail.

The magneto hydrodynamics (MHD) boundary layer flow and heat transfer of a nanofluid with boundary slip condition for velocity second order, thermal slip, solutal slip, and suction, thermal radiation have been investigated numerically over a nonlinear stretching sheet with viscous dissipation. The profiles for the velocity, temperature and nanoparticle concentration depends on parameters viz. thermal radiation parameter R, suction parameter s, velocity first and second order slip parameters A and B, respectively, thermal slip parameter C, concentration slip parameter D, power-law parameter N, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, Eckert number Ec, and magnetic parameter M. Similarity transformation is used to convert the governing non-linear boundary-layer equations into coupled higher order non-linear ordinary differential equations. These equations are numerically solved by using an implicit finite difference method known as Keller-Box method. An analysis has been carried out to reveal the effects of governing parameters corresponding to various physical conditions. Numerical results and Graphical representation are obtained for distributions of velocity, temperature and concentration, as well as, for the skin friction, local Nusselt number and local Sherwood number for several values of governing parameters. The result reveals that velocity decreases with increase of first and second order velocity slip, suction and increases with increase of power-law parameter. Temperature decreases with the increase of thermal slip, suction, concentration slip but increases with thermal radiation, second order velocity slip. Nanoprticle concentration decreases with increase of concentration slip, suction, thermal radiation, thermal slip but increase with increase of second order velocity slip. A comparison with previous results available in the literature has been done and we found a good conformity with it. The numerical values of skin friction, Nusselt number and Sherwood number are presented in tables. [ABSTRACT FROM AUTHOR]