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In this paper, we present a detailed mathematical model of the unsteady hybrid blood through the curved overlapping stenosed vessels in the presence of the applied external magnetic field. The governing differential equations of this model are derived from the generic laws of conservation of momentum and energy. These derived differential equations are then rendered dimensionless by incorporating the normalization parameters, which are subsequently followed by the implementation of mild stenotic supposition. The parabolic equations are solved numerically by using the explicit finite difference technique. After that, these numerical calculations are used to simulate several flow characteristics such as velocity, impedance, and wall shear stress using the set of emerging parameters taken from literature. The influence of these emerging parameters on the flow characteristics reveals that the velocity of the hybrid blood flow stream decelerates due to the presence of an induced magnetic field having the inclusion of nanoparticles. Finally, the global behavior of hybrid blood flow within the curved stenosed channels is sketched and analyzed by using various streamline plots.

The influence of thermal radiation and Joule heating on the entropy inception by triple diffusion over the permeable plate is examined, as well as its influence on other physical aspects of the pro...

The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study. The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon. The conventional models for heat and mass flux, i.e., Fourier and Fick models, are modified using the Cattaneo-Christov (CC) model for the more accurate modeling of the process. The boundary layer equations that govern this problem are solved using the apt similarity variables. The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg (RKF) scheme. The graphical visualizations of the results are discussed with the physical significance. The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters. The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid. The external magnetism is observed to decrease the velocity field. Also, more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles. The heat transport is enhanced by the stretching of the rotating disk.

Current study investigates the incompressible hydromagnetic flow of Maxwell nanofluid. The fluid motion is caused by the stretchable rotating disk. Buongiorno model of nanofluid theory is acquired in flow model. Cattaneo-Christov double-diffusive theory along with temperature dependent thermal conductivity is main features of the constitutive equations. The governing equations are influenced by Stefan blowing and mass convection effects. The dimensionalized form of flow equations is obtained by elaborating appropriate similarity functions. The solution of resultant governing system is obtained by Runge-Kutta-Fehlberg (RKF) shooting technique. The results of dimensionless quantities are discussed on flow, concentration and temperature quantities. The graphical representation of Nusselt and Sherwood numbers is also presented against selected physical variables. The numerical results predicted that an increment in Deborah number has the tendency to reduce the radial curves. Temperature field is declined due to enlarge values of thermal relaxation time parameter. Increased thermophoretic parameter resulted into a decrement of Sherwood number. Excellent comparison is established through tabular description to validate the adopted numerical procedure.

This numerical study elaborates on the impacts of non-linear thermal radiation, Ohmic heating quadratic chemical reaction, an applied magnetic field on thermal characteristics of an axisymmetric fl...

Purpose This study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source. Design/methodology/approach This study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios. Findings The significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes. Originality/value This study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.

The essence of the present investigation is to reveal the hydrothermal variations of viscoelastic nanofluid flow in a porous medium over a stretchable surface. A higher-order chemical reaction is incorporated with thermophoresis and Brownian motion. Similarity conversions reduce the resulting equations into their dimensionless form and then solved using Runge-Kutta-Fehlberg (RKF) based shooting procedure. The effects of underlying factors on the flow are discussed through various graphs and tables. Computational results for noteworthy skin friction and heat and mass transport are presented and reviewed with sensible judgment. The study reveals that the fluid velocity reduces with incremental values of the viscoelastic parameter [Formula: see text] and magnetic strength. The temperature reduces for the suction parameter with the existence of stretchable but enhances with thermophoresis and Brownian motion effects. Heat transfer rate amplifies for [Formula: see text] but declines for [Formula: see text]. Mass transfer rate increases with the increase in Brownian parameter and Schmidt number. A comparative analysis shows a better agreement with previous results in limiting scenarios.

In the current paper, numerical study is carried out to investigate the peristaltic propulsion of Eyring–Powell fluid in a vertical symmetric channel with electro-kinetic pumping and transvers Lorentz force. The mass, momentum and energy equations for non-Newtonian fluid are formulated and simplified using suitable transformations and dimensionless variables. The governing equations in dimensionless form are solved numerically by implicit finite difference scheme for stream function and temperature profile in computational software Mathematica 9. The impact of several parameters of interest is analyzed and discussed for both values of Helmholtz–Smoluchowski velocity UHS and Joule heating parameter through graphs. An entropy generation analysis is also considered and observed for various values of involved parameters. The nonlinear dimensionless equations are also solved by another numerical technique which is built in routine in MATLAB which is commonly known as bvp4c. The results for velocity and temperature are compared by both techniques. The Joule heating parameter also increases the size and number of isothermal bolus. The entropy of the system can be controlled for assisting pumping, i.e., UHS 0.

Micropolar fluid model is considered to discuss the microrotational inertial effects of fluid particles. The fluid movement is initiated through stretchable disk, which is engulfed into porous space. Porous medium is characterized in numerous engineering processes, geophysics, petroleum technology and biological tissues. The generalized Fourier’s law that is the Cattaneo–Christov model is utilized for to study the heat transfer mechanism. Moreover, the thermophoresis phenomenon is reflected in flow phenomenon. The constitute model is initially consists upon the system of partial differential equations, which is then converted to ordinary one by making use of appropriate similarity variables. Runge–Kutta–Fehlberg procedure is then used to obtain the numerical solutions. The determined physical parameters are discussed through graphical way and tabular description.

Flow and heat transportation in hybrid nanofluid impinging obliquely on a vertical cylinder are investigated numerically in this communication. Silver A g and aluminum oxide A l 2 O 3 nanoparticl...

The present work concentrates on two-dimensional unsteady incompressible flow of a micropolar cross nanofluid past a linear stretching/shrinking sheet with a magnetic field. The Cattaneo–Christov diffusion theory with heat and mass fluxes is incorporated into the study. Famous Buongiorno model featured by Brownian motion and thermophoresis accounting for nanoparticle diffusion is included. The shooting method is employed to obtain numerical solutions of the transformed system of non-linear equations. The influence of the governing parameters on the dimensionless velocity, temperature, micro-rotation, nanoparticle concentration, skin friction, heat and mass transfer rates, entropy generation rate, Bejan number, irreversibility ratio, streamlines and finally isotherms are incorporated. The significant outcomes of the current investigation are that increment in micropolar parameter uplifts flow velocity, microrotation, while that peters out fluid temperature. Irreversibility ratio augments due to increment in stretching/shrinking strength parameter. Streamlines/Isotherms diverge/converge more and more from/to an origin accordingly.

In this study, the problem of carbon nanotubes (CNTs) suspended in water between two stretchable rotating disks is discussed. This problem is vital in the industry due to several applications, incl...

This study communicates stagnation-point flow in magneto-Williamson nanofluid along a convectively heated nonlinear stretchable material in a porous medium. The impacts of Joule heating, thermophoresis together with Brownian motion are also checked in this investigation. In addition, thermodynamic second law is applied to develop entropy generation analysis of crucial parameters with identification of parameters capable of minimizing energy loss in the system. The transport equations are simplified into ordinary differential equations and then integrated numerically using Runge-Kutta-Fehlberg with shooting technique. The effects of the emerging parameters on the dimensionless velocity, temperature, concentration and entropy generation number are publicized through tables and graphs with appropriate discussions. In the limiting conditions, the results are found to conform accurately with published studies in the literature. It is found that the viscous drag can be reduced by lowering the magnitude of Weissenberg number, magnetic field and Darcy parameters while heat transfer at the surface improves in the presence of surface convection, temperature ratio and thermal radiation parameters. Besides, the analysis reveals that entropy generation can be minimized by lowering the magnitude of magnetic field, Schmidt number and surface convection parameters. The reduction in these parameters will promote efficient performance of thermal devices. More so, the results obtained in this study can be useful for the construction of appropriate thermal devices for use in energy and electronic devices.

Carbon nanotubes (CNTs) are inevitable due to its tremendously high thermal and electrical conductivities, strength, stiffness, and toughness characteristics. The utilization of both porous media and nanofluids with CNTs as nanoparticles can augment the thermal efficiency of typical physical systems significantly. In view of such advantages, the present study is intended to convey the influence of entropy minimization and nonlinear thermal radiation on the electromagnetic flow of nanofluids with single wall carbon nanotubes (SWCNTs) and multiwall carbon nanotubes (MWCNTs) nanoparticles suspensions past the surface of thin needle. In addition, the famous Darcy Forchheimer flow and Cattaneo-Christov heat flux models are implemented. The required numerical solution is devised pragmatically via bvp4c in MATLAB for the system of highly nonlinear ordinary differential equations. It is found that the porous matrix and local Forchheimer parameter are detrimental to the regular flow of nanofluids. Thermal fields magnify in respect of hiked porosity and temperature ratio parameters and diminish due to rise in electric and thermal relaxation parameters. Entropy minimization due to porous irreversibility is prominent for MWCNTs than SWCNTs. Bejan number upsurges due to rise in volume fraction and porosity parameter for both SWCNT-water and MWCNT-water nanofluids.

The current research is conducted to investigate the slip effect and to analyze entropy production in both hybrid nanofluids, and common nanofluids flow past a convectively heated three-dimensional stretching sheet placed in a porous medium. The slip flow is considered in a Darcy-Forchheimer’s scheme by incorporating the nonlinear thermal radiation. Water is taken as base fluid, while Copper and Titanium dioxide nanoparticles are considered. The governing models are overset into dimensionless variables using similarity transformation, and the solution is acquired numerically. The impacts of pertinent factors on the flow, heat transfer, and entropy generation rates are explored. Additional plot portraying the streamlines and isotherms for both nanofluids are presented to examine the hydrothermal behavior. Skin friction and heat transport are discussed with sensible judgment. A comparison with earlier studies is unwrapped to ensure the model’s validity. The results communicate that temperature is enhanced with porosity, whereas velocity is found to be decelerated. Bejan number is decreasing with an increase in the nanoparticle volume fraction of nanoparticles. Furthermore, hybrid nanofluids generate less entropy than common nanofluids.

In this paper, the boundary layer analysis of three-dimensional Prandtl nanofluid flow over a convectively heated sheet in a porous material is addressed. Nonlinear radiation and high-order chemical reaction analysis are featured in this work. Nonlinear differential equations representing flow expressions are numerically solved by shooting technique. Features of Brownian motion and thermophoresis accounting for nanoparticle diffusion are taken into account. Then, a complete discussion of the influences of the flow regime on several thermofluidic parameters is presented. The outcome of the present study is that velocity field lines are grown due to the strengthening of Prandtl fluid numbers [Formula: see text] and [Formula: see text] while a reverse trend takes place for temperature profile. Furthermore, it is shown that when the magnetic strength is improved, the skin friction coefficient and heat transfer rate triggers considerable evolution. The obtained results of this model closely match with those available in the literature as a limiting situation.

The enhancement of heat transfer in a new kind of hybrid nanofluid is more than that of a single nanoparticle. Also, the thermal conductivity of diamond, silver and gold is more than that of copper, titanium oxide and alumina. Hence, an attempt is made to study the influence of hybrid nanoparticles (diamond and silica) with ethylene glycol as a base fluid in a diverging/converging channel. Using similarity analysis, the governing system of equations is transformed to a set of nonlinear ODEs. The resulting system is evaluated computationally by using the most powerful shooting procedure with the support of MATLAB software. The influence of (diamond and silica-ethylene glycol) hybrid nanomaterial on various thermofluidic parameters in a Jeffery–Hamel channel is investigated. The outcomes of this work conclude that (1) the fluid flow velocity decreases in divergent channels with increasing Reynolds number and nanoparticle volume fraction. (2) The skin friction coefficient is found to be a rising function of diamond nanoparticles in the presence of the ethylene glycol-based fluid for divergent channel.

In this paper simultaneous effects of Coriolis forces, Brownian motion and thermophoresis on the peristaltic motion of Newtonian fluid are incorporated. The governing nonlinear flow equations with appropriate conditions are converted into non-dimensional form, afterward, they were solved numerically by the Keller box procedure. Also, another numerical method is used to solve these transformed equations and by tabular data, we made a comparison of the numerical values of velocities, temperature and concentration profiles. A parametric investigation was conducted and the influence of various parameters on primary and secondary velocities is conducted for both slip and no-slip flow cases. The obtained results are compared with the existing literature as a particular case and found with an excellent agreement. Furthermore graphical results for temperature and nanoparticle concentration profiles are reported for both rotating and non-rotating frames. It is worth mentioning that the effects of Nt and Nb are the dominant in rotating frame as compared to the non-rotating frame of reference and the magnitude of temperature distribution is small for slip flow.

Three-dimensional unsteady magnetohydrodynamic stagnancy flow of hybrid nanoliquid, with nonlinear radiation and uneven heat rise/sag, is studied hypothetically. We considered Fe3O4/graphene nanopa...

In this paper, we have investigated thermally stratified MHD flow of an Oldroyd-B fluid over an inclined stretching surface in the presence of heat generation/absorption. Similarity solutions for the transformed governing equations are obtained. The reduced equations are solved numerically using the Runge–Kutta Fehlberg method with shooting technique. The influences of various involved parameters on velocity profiles, temperature profiles, local skin friction, and local Nusselt number are discussed. Numerical values of local skin friction and local Nusselt number are computed. The significant outcomes of the study are that the velocity decreases when the radiation parameter $$R_{d}$$ R d is increased while the temperature profile is increased for higher values of radiation parameter $$R_{d}$$ R d in case of opposing flow, moreover, growth in Deborah number $$\beta_{2}$$ β 2 enhance the velocity and momentum boundary layer. The heat transfer rate is decrease due to magnetic strength but increase with the increased values of Prandtl and Deborah numbers. The results of this model are closely matched with the outputs available in the literature.

The pioneer motivations for current flow model are to study the rheological aspects of chemical reactive Williamson nano-material with utilization of gyrotactic microorganisms. The peak theme of activation energy and variable thermal conductivity are also incorporated. Unlike typical investigations, current flow model is formulated with employment of slip consequences with higher order relations. The induced flow is caused by a porous stretched surface additionally impact by magnetic force. The flow equations are transmuted into dimensionless form first for which numerical simulations are performed using famous finite difference approximations. The results are verified for limiting cases by comparing with various investigations and found excellent accuracy. The physical insight of all flow parameters are graphically underlined with interesting physical appliances. Furthermore, the numerical calculation for heat transfer enhancement, change in mass flux and motile density simulations are also evaluated in tabular form. The stream line and contour plots are also prepared.

A new attempt has been made to analyze the different combinations of Water and Ethylene Glycol with hybrid nanoparticles. A comparative analysis has been performed using two distinct fluids namely ...

The pivotal aim of this research is to address the boundary layer analysis of two-dimensional unsteady hybrid nanofluid flow over a flat/slendering stretching surface. Thermal radiation and magnetohydrodynamic analysis are featured in this work. The transformed nonlinear ordinary differential equations are resolved using Runge–Kutta–Fehlberg technique. Then, a complete discussion of the influences of the flow regime on several thermofluidic parameters is presented. The significant outcome of the current investigation is that the increment in magnetic field and nanoparticle volume fraction parameters declines the skin friction. Furthermore, it is shown that when the radiation and the nanoparticle volume fraction are improved, the heat transfer rate triggers considerable evolution. The obtained results of this model closely match with those available in the literature as a limiting situation.

The current paper on carbon nanotubes suspended magnetohydrodynamics micropolar dusty nanofluid impinging on a permeable extending sheet placed in a porous regime. The Darcy–Forchheimer scheme with heat source/sink and thermal radiation is taken into account. The shooting method is instrumental for obtaining numerical solutions of the transformed-converted system of nonlinear equations. The prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions are used. The impact of governing parameters on velocity, temperature, skin friction coefficient, Nusselt number, entropy generation rate and Bejan number are incorporated. The significant outcomes of the current investigation are that increment in the suction parameter decline the flow velocity and temperature (for both PST and PHF cases) while the injection uplift them. An enhancement in magnetic strength, the skin friction and heat transfer rate show the opposite trend for both SWCNT and MWCNT. Bejan number is increasing with the increase in nanoparticle volume fraction $$\phi$$ for both SWCNT and MWCNT.

The present investigation concentrates on the hydrothermal features of both hybrid nanofluid and usual nanofluid flow over a slippery permeable bent structure. The surface has also been considered to be coiled inside the circular section of radius R. Ferrous and graphene nanoparticles along with the host fluid water are taken to simulate the flow. The existence of heat sink/source and thermal radiation are incorporated within the system. Resulting equations are translated into its non-dimensional form using similarity renovation and solved by the RK-4 method. The consequence of pertinent factors on the flow profile is explored through graphs and tables. Streamlines and isotherms for both hybrid nanofluid and usual nanofluid are depicted to show the hydrothermal variations. The result communicates that temperature is reduced for curvature factor, whereas velocity is found to be accelerated. Heat transfer is intensified for thermal Biot number, and the rate of increment is higher for hybrid nanosuspension. Velocity and temperature are intensified for enhanced nanoparticle concentration. The heat transport process is decreased for the heat source parameter, but the reduction rate is comparatively slower for hybrid nanofluid.

Transportation of heat and mass for the bio-convective magneto-hydrodynamic flow of Eyring-Powel nanofluid flowing over a rotating disk is inspected in the current exploration which has applications in different industries. i.e. To enhance the thermal performance of the system, mixture of bioconvective is used along with nanofluids. Flow is produced due to the stretching of rotating disk. Phenomenon of heat and mass are developed by using traditional Fourier and Fick's laws respectively. Viscous dissipation is included in the thermal transport expression. Buongiorno model is considered to capture the involvement of Brownian motion and thermophoresis aspects by the presence of nanofluid. Boundary layer approximation is used to develop the expressions for the momentum, heat, mass and swimming gyrotactic microorganism's profiles. The derived boundary layer equations are converted into set of ordinary differential equations by engaging an appropriate transformation. These converted equations are solved numerically with the help of shooting method. Various graphs are prepared in order to inspect the bearing of influential parameters. Moreover, skin friction, heat transfer, mass transfer and density of motile microorganism are presented with the help of graphs and tables.

We have investigated the influence of hybrid nanoparticles on various physical quantities in a water-based hybrid nanofluid involved in a steady and fully developed forced convective flow generated over a stretched surface. Nonlinear thermal radiation and melting heat transfer analysis are featured in this work. To obtain the solution of the governing equations, a standard transformation and numerical procedure are implemented. Then, a comprehensive discussion of the effects of the flow regime on several governing parameters is presented. The results indicated that increasing magnetic strength $$M$$ and nanoparticle volume fraction $$\phi_{1}$$ lead to a thicker thermal boundary layer. A similar trend takes place with increasing nonlinear thermal radiation while the reverse is noticed for Eckert number. The entropy generation rate increases with the increase in Brinkman number and Bejan number reduces with increasing Eckert number. The obtained results of this model closely match with those available in the literature as a limiting situation. It is demonstrated that hybrid nanofluids exhibit lower entropy generation rates. The results of this study are of importance in the assessment of the effect of some essential design parameters on heat transfer and, consequently, in the optimization of industrial processes.

The aim of the present investigation is framing the effect of thermal radiation and slip on a magnetohydrodynamic (MHD) Casson nanofluid flow over a stretching surface under the influence of variable viscosity and convective boundary condition. First, non-dimensionally developed boundary layer equations are deduced with suitable transformations. Then they are solved numerically by the Runge–Kutta–Fehlberg method with the shooting technique for different values of parameters. The most relevant result of the present study is the fact that the augmented magnetic field strength, Casson fluid parameter, and the inclined angle undermine the flow velocity, establishing thinner hydrodynamics boundary layer, while the thermal slip and radiation parameters show the opposite trend. Another most important outcome is the fact that increase in the Prandtl number, radiation, viscosity, thermal slip, and radiation upsurges the fluid temperature, leading to improvement in the thermal boundary layer. The effects of different natural parameters on the skin friction coefficient and the Nusselt and Sherwood numbers are examined graphically. For a limiting case of the present model, the obtained solution was found to be in excellent agreement with the existing literature.