Unsteady squeezed Casson nanofluid flow by considering the slip condition and time-dependent magnetic field

The present flow problem investigates the incompressible and squeezed flow between two parallel plates. The mathematical formulation includes the constitutive equations of Casson nanofluid, which is treated as a lubricant. Brownian movement, slip condition, and thermophoretic mechanisms are also considered. The formulated model is tackled by Runge-Kutta-Fehlberg fourth- and fifth-order numerical scheme joint with shooting criteria. Momentum, thermal, and mass species behavior is executed by plots of distinct physical constraints values. It is found that the velocity component is boosted for the larger squeezed parameter whereas the temperature component shows the same behavior for Brownian motion and thermophoresis parameter. Near the lower half of the plate, velocity increases for the slip parameter whereas it decreases for magnetic and Casson parameters.     

Magnetic field and viscous dissipation effect on bioconvection in a permeable sphere embedded in a porous medium with a nanofluid containing gyrotactic micro‐organisms

Micro‐organisms play a vital role to understand the ecological system and therefore it is very important to understand the behavior of micro‐organism due to different parameters. In the present paper, we investigated the bioconvection about a permeable sphere with constant surface temperature embedded in a porous medium filled with a water‐based nanofluid containing gyrotactic micro‐organisms. The convection and movement of the micro‐organisms are constrained or assisted by thermophoresis, viscous dissipation effects, and an applied magnetic field. First, we have used the similarity transformation to simplify the governing equations. Then, we have solved the governing nonlinear partial differential equations numerically using a recent spectral relaxation method. The effects of the significant parameters on the local density of the gyrotactic micro‐organisms have been determined and discussed. It is observed that by introducing the magnetic field in the system, the skin friction, local nanoparticle Sherwood number, and the local density of the micro‐organism decrease, while the last two governing parameters show a positive response with increase in the viscous dissipation.     

Non-Newtonian fluid flow with the influence of induced magnetic field through a curved channel under peristalsis

In this study, we investigated the influence of the induced magnetic field on the Jeffrey fluid under peristalsis through the curved channel. The governing equations, such as the continuity equation, momentum equation, and magnetic force functions, are formulated. The lengthy equations are shortened by considering the approximations of the tiny Reynolds number and the long wavelength. From the resulting reduced equations, the exact solution is determined. Graphs are used to explain the graphical results of the impact of important parameters of velocity, magnetic force function, current density, induced magnetic field, pressure rise, and stream functions.     

Radiative flow of Maxwell nanofluid containing gyrotactic microorganism and energy activation with convective Nield conditions

On the account of industrial and technological applications, the enhancement of energy by inserting nanoparticles is a hot topic in the present century. Therefore, the current analysis presents a theoretical analysis regarding the flow of electrically conducted Maxwell nanofluid over a stretching surface in the presence of the gyrotactic microorganism. In addition, the influence of thermal conductivity and Arrhenius activation energy are considered. By using the apposite transformation, the system of contemporary partial differential expressions is first converted into nonlinear ordinary differential system. The set of these transmuted equations is solved with the help of the shooting method. Reliable results are obtained for the velocity profile, temperature, motile microorganism density and concentration. It is evaluated that by increasing the value of bioconvection Peclet and Lewis numbers, the microorganism distribution exhibited diminishing behavior. These results may be useful in improving the efficiency of heat transfer devices and microbial fuel cells.     

Numerical investigation of ferromagnetic liquid film flow over an unsteady stretching surface in the presence of radiation and aligned magnetic field

An investigation of the two-dimensional unsteady flow of a thin layer of ferromagnetic liquid past a stretching sheet is performed. The flow is exposed to an external magnetic field in the axial direction along with the thermal radiation effect. Relevant Maxwell's equations are considered together with the conservation laws of fluid dynamics to model the problem. The mathematical model is constructed using a system of partial differential equations with relevant boundary conditions, which are transformed into two-point boundary value problem (BVP) using similarity transformations. The resultant BVP is numerically solved by a shooting technique that involves Runge–Kutta–Fehlberg (RKF45) method to integrate the initial value problem and the Newton–Raphson method to refine the guessed initial values. The influence of the dimensionless parameters on the flow and heat exchange characteristics is graphically analyzed. It is found that the thickness of the film increases for higher values of the thermal radiation parameter. The thermal profile shows increasing behavior with the radiation parameter and reverse effect with the Prandtl number.     

Nonlinear convection flow of dissipative Casson nanofluid through an inclined annular microchannel with a porous medium

The nonlinear convection study on the flow of a dissipative Casson nanofluid through a porous medium of an inclined micro-annular channel is presented. The cylindrical surfaces were conditioned to temperature increase and velocity slip effects. A uniform magnetic field strength was applied perpendicular to the cylinder surface. The heat source and Darcy number influence are explored in the examination of the blood rheological model (Casson) through the annular cylinder. Appropriate dimensionless variables are imposed on the dimensional equations encompassing Casson nanofluid rheology through an annular microchannel. The resulting systems of equations were solved and computed numerically via Chebyshev-based collocation approach. Thus, the solutions of flow distributions, volumetric flow rate, and other flow characteristics were obtained. The result shows that both nonlinear convection parameters decrease the nanoparticle volume fraction, whereas they increase the energy and momentum distributions. Moreover, the volumetric flow rate is upsurged significantly by a wider porous medium, annular gap, a higher Casson parameter, and nonlinear convection influence.     

Numerical solution for Sisko nanofluid flow through stretching surface in a Darcy–Forchheimer porous medium with thermal radiation

The heat transfer assessments in a Sisko nanofluid flow over a stretching surface in a Darcy–Forchheimer porous medium with heat generation and thermal radiation are studied. The numerical analysis technique is used to assess the governing nonlinear equations of the model. The influence of Forchheimer number, porosity, heat generation, radiation, and material parameters is examined. The outlines of Nusselt number and skin friction coefficient corresponding to pertinent parameters are revealed. The comparison of Nusselt number outlines of working fluid and Newtonian fluid is depicted. From the analysis, it has been examined that with the increase in Forchheimer number and material parameter values, heat transfer function decreases, whereas heat transfer characteristics of Sisko nanofluid increase with heat generation and material parameters. Moreover, working fluid velocity outlines depreciate when there is an increase in porosity parameter for both shear-thinning and shear-thickening. The comparison of this study with previous research has been conducted.     

Numerical simulation of turbulent natural convection of nanofluid with thermal radiation inside a tall enclosure under the influence of magnetohydrodynamic

In the present study, the natural convective heat transfer in the turbulent flow of water/CuO nanofluid with volumetric radiation and magnetic field inside a tall enclosure has been numerically investigated. The thermophysical properties of nanofluid have been considered variable with temperature and the effects of Brownian motion of nanoparticles have been considered. The main objective of this work is an investigation of the effect of using water/CuO nanofluid and presence of magnetic field on turbulent natural convection in three types of enclosures (vertical, inclined, and horizontal) by considering the volumetric radiation. The governing equations on turbulent flow domain under the influence of the magnetic field and by considering the combination of volumetric radiation and natural convection have been solved by a coupled algorithm. For validating the present research, a comparison has been carried out with the laminar natural convection flow under the influence of the magnetic field and radiation effects and also, the natural turbulent convection flow of previous studies and a proper coincidence has been achieved. The results indicated that by increasing volume fraction and Hartmann number the average Nusselt number enhances and reduces, respectively. By adding 1% CuO nanoparticles to the base fluid, heat transfer improves from 10.59% to 17.05%. However, by increasing the volume fraction from 1% to 4%, heat transfer improves from 1.35% to 4.90%. By increasing Hartmann number from 0 to 600, heat transfer reduces from 9.29% to 22.07%. Also, the results show that the ratio of deviation angle of the enclosure to the horizontal surface has considerable effects on heat transfer performance. Therefore, in similar conditions, the inclined enclosure with a deviation angle of 45° compared to the vertical and horizontal enclosure has better thermal performance.     

Oscillatory slip flow of Fe3O4 and Al2O3 nanoparticles in a vertical porous channel using Darcy's law with thermal radiation

The heat transfer phenomena and oscillatory flow of an electrically conducting viscous nanofluid (NF) in a channel with porous walls and saturated porous media exposed to the thermal radiation are studied. The nanoparticles (NPs) Fe₃O₄ and Al₂O₃ are taken with water as base fluid along with nonuniform temperature and velocity slip at the wall of channel (y′ = 0). The basic laws of momentum and energy conservation are converted into the dimensionless system of the partial differential equations (PDEs) using similarity variables. Closed‐form solutions of these coupled PDEs are constructed for all values of time by taking the oscillatory pressure gradient. The physical insight of involved parameters on the fluid velocity, temperature profile, heat transfer rate, and surface friction is studied and analyzed graphically. It is noted from this study that the fluid velocity shows a decreasing behavior with the volume fraction of NPs. Furthermore, the amplitude of the oscillatory motion in case of skin friction decreases for a large magnetic field.     

Entropy generation minimization and nonlinear heat transport in MHD flow of a couple stress nanofluid through an inclined permeable channel with a porous medium,thermal radiation and slip

Irreversible losses and heat transport in a magnetohydrodynamic flow of a viscous, steady, incompressible, and fully developed couple stress Al₂O₃–water nanofluid through a sloping permeable wall channel with porous medium and under the effect of radiation heat flux and slip were analyzed. The fundamental equations were solved numerically by using Runge-Kutta together with the shooting technique and the results were in qualitative agreement with an exact solution obtained for a limit case. The impacts of couple stress, Darcy number, solid nanoparticle concentrations, conduction-radiation parameter, Hartmann number and hydrodynamic slip on flow, temperature, heat transport, and entropy production were examined. It was possible to achieve values of minimum entropy production not yet reported in previous studies. In this way, optimal values of couple stress and slip were obtained. The heat transport was also explored and optimal values of slip flow and conduction-radiation parameter with maximum heat transfer were found. Finally, in addition to the alumina, the distributions of velocity, temperature, and entropy generation in TiO₂–water and Cu–water were presented for different solid nanoparticle concentrations. It was obtained that the local entropy of TiO₂–water was lower than Cu–water and Al₂O₃–water in the channel bottom region while it was greater in the upper region.     

Thermal radiation and magnetic field effects on squeezing motion analysis for Cu–kerosene and Cu–water nanofluids

This article examines the squeezing motion of Cu–kerosene and Cu–water nanofluids with thermal radiation and magnetic field between two parallel sheets. By appropriate transformation, the governing nonlinear partial differential equations are converted into ordinary differential equations and then solved numerically by the Runge–Kutta technique. The motion characteristics have been examined with graphs by relevant parameters. It is observed that fluid temperature reduces if squeezing parameter, thermal radiation, and Hartmann number increases, but fluid temperature improves if nanoparticle volume fraction, Eckert number, and Prandtl number increases and it is observed that liquid momentum improves if the squeezing parameter increases, but fluid velocity reduces if nanoparticle volume fraction and Hartmann number increases.     

Mutual effects of chemical reaction and thermal radiation on MHD peristaltic transport of Jeffrey nanofluids: Tumor tissues treatment

As thermal radiation is one of the fundamental means of heat transfer, therefore, this study analyzes the impacts of thermal radiation and magnetic field on the peristaltic transport of a Jeffrey nanofluid in a nonuniform asymmetric channel. Further, Two models of viscosity are debated: Model (I), in which all parameters dependent on viscosity behave as a constant (as treated before in nanofluid research); Model (II), in which these known parameters are considered to vary with the temperature of the flow. Under the condition of long wavelength and low Reynolds number, the problem is rearranged. The resulting system of partial differential equations (PNE) is solved with aid of Mathematica 11. Furthermore, the streamline graphs are presented by significance of trapping bolus phenomenon. To emphasize the quality of solutions, comparisons between the previous results and recent published results by Reddy et al. have been made and signified. The comparisons are shown in Table 1 and are found to be in good agreement. As the thermal radiation increases, the diameter of nanoparticles rises (thermal radiation is a diminishing function of temperature, and with a decrease in the temperature, the diameter of the nanoparticles increases, that is, the size of nanoparticles increases and they become more active near malignant tumor tissues). Therefore, its work as agents for radiation remedy, produce limited radiation quantities, and selectively target malignant tumor for controlled mutilation (radiotherapy of oncology). Such a model is appropriate for the transportation of physiological flows in the arteries with heat and mass transfer (blood flow models).     

Thermal performance of straight porous fin with variable thermal conductivity under magnetic field and radiation effects

The present numerical study reports the thermal performance of the straight porous fin with temperature-dependent thermal conductivity, radiation, and magnetic field effects. The heat transfer model comprising the Darcy's law for simulating flow with solid-fluid interactions in porous medium, Rosseland approximation for heat transfer through radiation, Maxwell equations for magnetic field effect and linearly varying temperature dependent thermal conductivity, results into highly nonlinear ordinary differential equation. The governing equation is solved using a finite difference scheme with suitable boundary conditions. The obtained solutions are physically interpreted by considering the impact of different nondimensional parameters on thermal performance, efficiency, and effectiveness of the system through plotted graphs. A detailed result with regard to the Nusselt number at the fin base is calculated. The results obtained are observed to be in excellent agreement with previous studies. From the study, it is observed that there is a significant effect on the thermal performance of the fin in the presence of porous constraints; also, results reveal that the nonlinear thermal conductivity parameter strengthens the thermal performance, efficiency, and effectiveness of the fin. Furthermore, the results of the study reveal that the rate of heat transfer of the fin increases with the increase in the magnetic parameter and radiation parameter.     

Barycentric rational interpolation method for numerical investigation of magnetohydrodynamics nanofluid flow and heat transfer in nonparallel plates with thermal radiation

In this study, the problem of heat transfer in the steady two‐dimensional flow of an incompressible viscous magnetohydrodynamics nanofluid from a sink or source between two shrinkable or stretchable plates under the effect of thermal radiation has been studied. The governing differential equations have been solved numerically using a collocation method based on the barycentric rational basis functions. This method employs the derivative operational matrix of the barycentric rational bases and the weights that were introduced by Floater and Hormann. The influence of some embedding parameters, such as the solid volume fraction , the Reynolds number , the Hartmann number , the Prandtl number , the radiation parameter , the stretching‐shrinking parameter, , and the angle of the channel on the temperature distribution and velocity profile has been illustrated by graphs and tables. Numerical results reveal the efficiency and high accuracy of the proposed scheme compared to the previously existing solutions. Furthermore, the implementation of the proposed method is fast and the run time is short.     

MHD boundary layer flow of SWCNT‐water and MWCNT‐water nanofluid over a vertical cone with heat generation/absorption

The analysis is carried out to investigate the magneto hydro dynamics (MHD) boundary layer flow, heat and mass transfer characteristics of two carbon nanotubes, namely, single‐wall carbon nanotubes (SWCNTs) and multiwall carbon nanotubes (MWCNTs), with water as the base fluid by taking thermal radiation and chemical reaction into consideration. Suitable similarity conversions are employed to reduce nonlinear partial differential equations into the system of ordinary differential equations, and these equations together with boundary conditions are solved numerically using the finite element method. Velocity, temperature, and concentration distributions as well as skin friction coefficient, Nusselt number, and Sherwood number for diverse values of influencing parameters are examined in detail, and the results are displayed graphically and in tabular form. It is found that the rate of heat transfer is remarkably higher in water‐based MWCNTs than the SWCNTs as the value of the nanoparticle volume fraction parameter rises in the boundary layer regime.     

Studying the effect of radiation on thin‐film sprayed nanofluid flow with heat transfer

In this paper, we discuss thin‐film nanofluid sprayed in non‐Darcian, magnetohydrodynamic, embedding in a porous medium flow and thermal radiation with heat transfer generation on a stretching cylinder. The spray rate is a function of film size. A comparative study is made for the nanoparticles, namely, copper oxide , alumina oxide (), and iron oxide . The governing continuity, momentum, and energy equations of the nanofluid are reduced using similarity transformation and converted into a system of nonlinear ordinary differential equations, which are solved numerically. Numerical solutions are obtained for the velocity and temperature fields as well as for the skin‐friction coefficient and Nusselt number. The pressure distribution and spray rate are also calculated. The results are presented in graphical forms to study the effects of various parameters.     

Influence of magnetic field and thermal radiation on peristaltic motion with double‐diffusive convection in Jeffery nanofluids

A theoretical study is conducted to examine the peristaltic pumping with double‐diffusive convection in Jeffery nanofluids through a two‐dimensional infinite asymmetric channel. The flow is examined in a wave casing of orientation that moves pace with the velocity of the wave. The peristaltic wave train on the walls that have different amplitude and phase is chosen to form channel irregularity. Rosseland approximation is noticed in the modeling of the transmission radiation heat transfer and temperatures of the walls are recognized constants. The replica has a great impact in discovering nanofluid dynamic influences on peristaltic motion, in biological vessels as symbolized by transportation of heat in blood flow, food molecules, hormones, novel pharmacodynamics pumps, and engineered gastrointestinal motility enhancement. Peristaltic motion has applications in physiology, such as transport of urine, transport of food bolus through gastrointestinal tract, and transport of blood through small blood vessels. Analytical results have been established for stream function, axial velocity, temperature, and absorption and nanoparticle volume fraction. The effect of the principal hydrodynamic parameters (thermophoresis, Brownian motion, Dufour, and Soret) and Grashof numbers (concentration, thermal, nanoparticle) on peristaltic transport patterns with double‐diffusive convection are deliberated with the support of computational outcomes found. The pictorial investigation is done to investigate the possessions of miscellaneous limitations on flow quantities of curiosity.     

Quadratic mixed convective nanofluid flow past a moving yawed cylinder in the presence of thermal radiation and diffusive liquids

The fluid flow around a yawed cylinder helps to understand the practical implications for undersea applications, such as managing transference, separating the boundary layer above submerged blocks, and suppressing recirculating bubbles. As many authors such as Roy, Chiu and Lienhard, Roy and Saikrishnan, and Revathi et al. have analyzed a boundary layer flow over a yawed cylinder, and their work sticks to only forced convection, we are interested to work on mixed convection flow. Therefore, the work of these researchers has stimulated us to work on the present article. As a result, we have examined the work on triple diffusion quadratic mixed convective nanofluid flow over a moving yawed cylinder. The impact of yaw angle, which exists due to the inclination of a vertically moving cylinder away from the origin, is mathematically investigated in the present paper by converting the governing equations into a compatible form using appropriate nonsimilar transformations and the quasilinearization technique. Nanofluids have crucial usages in science and technology, marine engineering, and applications in industries such as plastic, polymer industries, cancer home therapy, and building sciences. Many processes in new engineering areas occur at high temperatures, and knowledge of radiation heat transfer becomes very important for designing the pertinent equipment. Nuclear power plants, gas turbines, and the various propulsion devices for aircraft, missiles, satellites, and space vehicles are examples of such engineering areas. The finite difference approximation is employed to solve the resulting equations. Enhancing the magnitude of thermal radiation enhances the temperature of the liquid and the energy transport strength. However, liquid hydrogen and liquid oxygen species concentration patterns are reduced in nanofluid compared to traditional liquids. At the same time, the outcomes behave conversely in the case of their wall gradients. Furthermore, the temperature of the liquid enhances the enhancing values of Brownian motion and thermophoresis characteristics. Moreover, nanoparticle mass transport augments with enhancing yaw angle and Lewis number values. Both species' concentration profiles decrease for increasing values of yaw angle. The velocity profiles increase for increasing values of velocity ratio parameter in the spanwise and chordwise directions.