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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.

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.

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...

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.

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.

Numerical analysis is performed for magnetohydrodynamics (MHD) couple stress nanofluid flow over a stretching sheet with melting and nonlinear radiation. The second law of thermodynamics is also incorporated with first-order slip. Nanofluid characteristics for thermophoresis and Brownian moments are encountered. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved numerically through the Runge–Kutta–Fehlberg fourth-fifth (RKF-45) order technique. The physical parameters, which emerges from the derived system are discussed in graphical format. The significant outcomes of the current investigation are that the velocity field decays for a higher magnetic parameter. Another, important outcome of the study is both temperature and concentration are increasing functions of the first-order slip. Nusselt and Sherwood numbers are decreasing with an increase in magnetic strength. Further, Bejan number augment due to enhancement in the first-order slip and couple stress fluid parameters whereas a differing tendency is shown for magnetic and radiation parameters.

The inherent irreversibility in boundary-layer flow of a radiating water/functionalized carbon nanotubes nanofluid over a convectively heated moving wedge and a horizontal/vertical plates is examined. The water-based nanofluid contains two types of carbon nanotubes, namely SWCNTs and MWCNTs. Using a suitable similarity transformation, the model partial differential equations are reduced to ordinary differential equations along with the corresponding boundary conditions. Solutions are obtained for the nanofluid velocity and temperature profiles analytically via optimal homotopy asymptotic method and numerically via shooting method with Runge–Kutta–Fehlberg integration scheme. Entropy generation analysis is conducted based on second law of thermodynamic, and the Bejan number is determined. Results are presented in graphical and tabular forms in order to scrutinize the effects of various geometrical, dynamical and thermophysical parameters on velocity, temperature, skin friction, Nusselt number, entropy generation rate and Bejan number. Generally, it is found that the entropy production can be minimized by reducing the convection through boundaries, moving the obstacle at the same velocity and direction as the flow (λoptimal = 1) and controlling the penetration of viscous dissipation, while increasing nanoparticles rate and thermal radiation has influence to increase the entropy generation. In addition, horizontal plate corresponding to the wedge angle value m = 0 is the optimum geometry to reduce entropy production.

The current study is modelled to evaluate numerous flow applications in applied sciences espeically in nuclear reacting cooling, geothermal reservoirs, chemical engineering and thermal oil recovery. The present research investigates the magnetohydrodynamic transport of non-Newtonian Casson Nano fluid past due to stretching permeable cylinder by employing Buongiorno's mathematical model. Unlike the frequently used constant temperature and concentration boundary conditions, the present study employed convective boundary conditions. The influences of important sundary parameters like an inclination of magnetic field, joule heating, viscous dissipation, thermophoresis, Brownian motion, Arrhenius activation energy, and chemical reaction are taken into account. The physical flow phenomenon is modelled and after that transformed into a non-dimensional form by incorporating suitable similarity transforms. For solution purpose, Runge-Kutta-Fehlberg fourth-fifth order (RKF45) numerical integrating procedure along with shooting algorithm is adopted. Impacts of several emerging parameters on the velocity distribution, temperature distribution, and concentration distribution, coefficient of skin friction, Sherwood number, and Nusselt number are clarified via graphical and tabular results. It seems to establish that with the rise of chemical reaction parameter chemical reaction parameter the nanoparticles concentration distributions decline while the contrasting trend is perceived for activation energy parameter.

Steady flow of non-Newtonian nanofluid impinging on a vertical lubricated surface is numerically investigated. The rheological behaviour of the base fluid is characterized by the constitutive equation of third-grade fluid and the power-law fluid model is used for lubricant. Higher-order chemical reaction and nonlinear radiative heat flux are also taken into account. The governing nonlinear partial differential equations are simplified using the Prandtl boundary layer theory and similarity transformations. An efficient and accurate implicit finite difference method is applied to approximate the resulting nonlinear coupled differential equations with complicated boundary conditions for several values of parameters of interest. The velocity, temperature, nanoparticles concentration profiles Nusselt number, and streamlines are illustrated through graphs for full slip and no–slip case as well as assisting and opposing flow cases. The temperature and concentration profiles are also described for linear and non-linear thermal radiation and for different order chemical reactions. The numerical results are compared with the existing literature and found good agreement. It is found that heat and mass transfer rates reduces over the lubricated surface compared with the rough surface.

In this paper, steady 2-D MHD free convective boundary-layer flows of an electrically conducting nanofluid over a non-linear stretching sheet taking into account the chemical reaction and heat source/sink are investigated. The governing equations are transformed into a system of non-linear ODE using suitable similarity transformations. Analytical solution for the dimensionless velocity, temperature, concentration, skin friction coefficient, heat and mass transfer rates are obtained by using homotopy analysis method. The obtained results show that the flow field is substantially influenced by the presence of chemical reaction, radiation, and magnetic field.

Bioconvection with gyrotactic microorganisms has a significant role in biotechnology and biosensors. This paper communicates a theoretical numerical investigation regarding the transient bioconvection flow of chemically reactive cross nanofluid over a permeable cylinder under the impact of nonlinear radiation and binary chemical reactions. Additionally, Arrhenius activation energy influences are taken into account. Further, revise model of nanoparticles is considered in present investigation. Boundary layer theory is invoked to develop the basic PDEs of microorganisms field, nanoparticles concentration, energy, momentum and mass for bioconvection flow of cross nanofluid in cylindrical coordinate system and then altered into nonlinear ODEs by utilizing the transforming variables. Numerical solutions of obtained highly nonlinear ODEs system are achieved through shooting Fehlberg approach for both the cases of stretching cylinder aw well as shrinking cylinder. Numerical computations for surface drag force, mass transfer rate, density number of microorganisms and heat transfer rate are executed. It is interesting to found that the density number of microorganisms is depreciated for higher estimation of Peclet number, microorganisms difference parameter and bioconvection Rayleigh number in both cases of stretching cylinder as well as shrinking cylinder. Furthermore, nanoparticles concentration is accelerated for the augmented values of activation energy parameter in shrinking as well as stretching cylinder. For the authenticity of considered study, we have also made a comparative analysis with existing study and noticed to be in excellent agreement.

In this paper, the non-Newtonian Casson flow of nanofluid past a thin needle is considered. The effect of combined nonlinear thermal radiation and internally generated heat on porous embedded fluid flow, heat transfer and volume concentration are studied. This study investigates the transport phenomena for flow over fixed needle and moving needle through stationary fluid. As the mechanics describing fluid dynamics are highly successive and nonlinear. The Runge-Kutta-Fehlberg forth-fifth (RKF-45) numerical method with shooting scheme is applied to obtain the approximate solution. Analysis obtained from approximate solution were utilized to investigate the parametric effect on fluid transport and heat transfer. Results obtained reveals enhanced fluid heat generation during transport improves fluid temperature at a high rate within 0 ≤ η ≤ 10 for moving fluid phenomena, while for moving needle fluid temperature slightly increases within0 ≤ η ≤ 4. Similarly, radiation effect on moving fluid shows high rate of heat transfer while for moving needle flow, rate of heat transfer improves slightly has radiation parameter is varied between 0.2 ≤ R ≤ 0.4. Obtained results compared with literatures shows good agreement. This study provides useful insight to practical applications including aircraft technology, manufacturing, medicine and solar nanofluids systems amongst others.

The model based upon the Poiseiulle flow of hybrid nanofluid within a micro channel for the inclusion of varying viscosity and thermal conductivity. The suggested model is designed for the use of variable properties of the hybrid nanofluid embedding with the metal and oxide nanoparticles such as Cu and Al2O3 submerged in the base fluids i.e. water and Ethylene glycol (EG). For the preparation nanofluid the base fluid contains a combination of 20% water and 80% of EG. In addition to that, the interpretation of entropy generation due to the thermal irreversibility process of the system is conducted. The suitable choice of the similarity transformation is used for the dimensional form of the present problem to distort into non-dimensional form. Further, the numerical treatment is made employing Runge-Kutta-Fehlberg technique for the solution of the set of transformed equations. The physical behavior of the contributing parameters on the flow phenomena along with the Entropy and Bejan number are presented through graphs. The tabular result depicts the numerical results of the rate coefficients for these parameters. Finally, the comparative study is carried out to validate the current result with the earlier work that shows a greater concurrency.

The flow, heat and mass transfer of water-based nanofluid are examined between two horizontal parallel plates in a rotating system. The effects of Brownian motion, thermophoresis, viscosity and Hall current parameters are considered. The governing partial differential equations are reduced to ordinary differential equations that are then solved numerically using the Runge–Kutta–Fehlberg method. Validation of numerical solution is achieved with an exact solution of primary velocity and found to be in good agreement. Results show that both surfaces experience opposite behavior regarding skin friction, Nusselt and Sherwood numbers in both primary and secondary flows. These physical quantities depend upon dimensionless parameters and numbers.

The magnetohydrodynamic (MHD) stagnation point flow of Casson nanofluid over a nonlinear stretching sheet in the presence of velocity slip and convective boundary condition is examined. In this analysis, various effects such as velocity ratio, viscous dissipation, heat generation/absorption and chemical reaction are accentuated. Possessions of Brownian motion and thermophoresis are also depicted in this study. A uniform magnetic field as well as suction is taken into account. Suitable similarity transformations are availed to convert the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations and then series solutions are secured using a homotopy analysis method (HAM). Notable accuracy of the present results has been obtained with the earlier results. Impact of distinct parameters on velocity, temperature, concentration, skin friction coefficient,Nusselt number and Sherwood number is canvassed through graphs and tabular forms.

The present study particularizes the effects of nonlinear thermal radiation and the novel accepts of activation energy in the axisymmetric rotational stagnation point flow of hybrid fluid. Thermophysical properties of water and CWCNT/MWCNT are used for base fluid and nanoparticles respectively. The modeled partial differential equations are reduces to system of ordinary differential equations. The resulting equations are integrated numerically and the impact of involved parameters on velocity, temperature and nanoparticle concentration presented graphically. The tabular values for local Nusselt numbers in case of linear and nonlinear thermal radiation and the Sherwood number with and without activation energy are documented. It is observed that concentration of nanoparticles reduces with activation energy and increasing the solid volume fraction of SWCNT as well as MWCNT nanoparticles. Moreover the axial velocity increases while secondary velocity decreases by increasing the rotation parameter.

In this paper, a generalized Newtonian nanofluid in a bio-microfluidics channel due to combined effects of peristalsis and external applied electric field in the presence of thermal radiation and Joule heating is considered. The Poisson and Nernst-Planck equations are taken into account. The obtained non-linear coupled ordinary differential equations are simulated numerically. The impacts of several parameters under the applied electric field on velocity, temperature, concentration, trapping isothermal lines, Nusselt, and Sherwood numbers are presented graphically. It is observed that the number of isothermal lines increases with the electro-osmotic parameter thermophoresis parameter and Brownian motion parameter while perter out with thermal radiation. The results are helpful to design the micro pumps/chips used in medical engineering and improved the thermal efficiency and the durability of microchip cooling devices.

In this study, the stability of flowing viscous hybrid nanofluid over a stretching surface under uniform magnetic effect and radiation are investigated. The mechanics governing the system of coupled momentum and energy equations are formulated using the Navier Stokes model, which is transformed from the partial form of differential equations into an ordinary form of differentials adopting suitable transforms. As this model is highly non-linear, the Runge-Kutta Fehlberg numerical method is utilized as a suitable method of analysis. Significant parameters such as radiation, magnetic, and volume concentration effects are studied amongst other pertinent parameters. The result presented graphically reveals a numeric increase of radiation parameter enhances thermal distribution, this connotes an improved heat transfer rate. While the volume concentration-effect reveals velocity decrease with an enhanced nanoparticle concentration. Moreover, it is seen that the velocity decreases with the magnetic parameter but increases with the suction/injection parameter. The fluid temperature enhances with the radiation and Eckert number. The result compared with suitable literature shows good agreement with the present study. Applications of the study include heat exchanger, lubrication, microelectronics, air conditioning, and refrigeration amongst others.

The fluid flow through inclined plates has several applications in magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics. Inspired by these applications, the rate of entropy production in a bio-convective flow of a magnetohydrodynamic Williamson nanoliquid over an inclined convectively heated stretchy plate with the influence of thermal radiation, porous materials and chemical reaction has been deliberated in this paper. The presence of microorganisms aids in stabilizing the suspended nanoparticles through a bioconvection process. Also, the thermal radiation assumed an optically thick limit approximation. With the help of similarity transformations, the coupled partial differential equations are converted to nonlinear ordinary differential equations and the resulting model is numerically tackled using the shooting method. The influences of the determining thermo-physical parameters on the flow field are incorporated and extensively discussed. The major relevant outcomes of the present analysis are that the upsurge in values of Schmidt number decays the mass transfer characteristics, but the converse trend is depicted for boost up values of the thermophoresis parameter. Enhancement in bioconvection Peclet and Schmidt numbers deteriorates the microorganism density characteristics. Further, the upsurge in the Williamson parameter declines the Bejan number and irreversibility ratio.

In this article, the semi-analytical/numerical technique known as the homotopy analysis method (HAM) is employed to derive solutions for partial slip effects on the heat transfer of nanofluids over a stretching sheet. An accurate analytical solution is presented which depends on the Prandtl number, slip factor, Lewis number, Brownian motion number, and thermophoresis number. The variation of the reduced Nusselt and reduced Sherwood numbers with Brownian motion number, and thermophoresis number for various values Prandtl number, slip factor, Lewis number is presented in tabular and graphical forms. The results of the present article show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and reduced Sherwood number are strongly influenced by the slip parameter. It is found that hydrodynamic boundary layer decreases and thermal boundary layer increases with slip parameter. Comparison of the present analysis is made with the previously existing literature and an appreciable agreement in the values is observed for the limiting case.

A mathematical model has been developed using Tiwari-Das model to study the MHD stagnation-point flow and heat transfer characteristics of an electrically conducting nanofluid over a vertical permeable shrinking/stretching sheet in the presence of viscous dissipation. Formulated partial differential equations are converted into a set of ordinary differential equations using suitable similarity transformation. Runge-Kutta-Fehlberg method with shooting technique is applied to solve the resulting coupled ordinary differential equations. The profiles for velocity, temperature, skin friction coefficient and local Nusselt number for various parameters are displayed through graphs and tabular forms. In this problem, we considered two types of nanoparticles, namely, copper (Cu) and Alumina (Al2O3) with water as base fluid. Keywords: Nanofluid, Stagnation-point flow, Shrinking/stretching sheet, Viscous dissipation

A numerical investigation has been conducted to investigate the steady forced convection boundary layer nanofluid flow past a horizontal circular cylinder placed in water-based copper (Cu) and alumina (Al 2 O 3 ) nanofluids. Using appropriate transformations, the system of partial differential equations is converted into an ordinary differential system of three equations, which is solved numerically using Keller box and Newton-Raphson methods. The effects of thermal and solutal convective boundary conditions are taken into account which makes the present analysis practically applicable. Numerical results are obtained for the dimensionless velocity, temperature and concentration as well as the skin-friction, Nusselt and Sherwood numbers for specific values of the governing parameters with fixed Prandtl number ( Pr = 6.2) and Schmidt number ( Sc = 0.68) for water. It is shown that, for a regular fluid ( ϕ = 0), a very good agreement exists between the present numerical results and those reported in open literature.

Hydromagnetic Couette-Poiseuille flow of variable viscosity nanofluids with heat and mass transfer between two parallel plates in a rotating permeable channel is investigated numerically. The model nonlinear problem which incorporates thermophoresis, Brownian motion, viscous dissipation, Joule heating and Hall effects are obtained and tackled numerically using a fourth order Runge–Kutta–Fehlberg integration scheme with shooting technique. The effects of various thermophysical parameters on nanofluid velocity, temperature, concentration, skin friction coefficient, and Nusselt and Sherwood numbers are discussed thoroughly and analyzed through graphs. The results show that Hall current significantly affects the flow system. Results for some special cases of the present analysis are in good agreement with the existing literature.

An analysis is carried out to obtain analytical solution of an unsteady two-dimensional MHD nanofluid flow with heat and mass transfer over a heated surface. The governing partial differential equations are reduced to system of nonlinear ordinary differential equations using suitable transformations. The resulting nonlinear coupled system subject to the boundary conditions is solved using homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided. A detailed study illustrating the influences of the magnetic, unsteady, suction/injection and nanofluid parameters, on the dimensionless velocity, temperature, concentration as well as on the skin friction coefficient, the reduced Nusselt and Sherwood numbers is conducted. It is found out that the flow field is substantially influenced due to unsteadiness, transpiration and magnetic field.

This study investigates the combined effects of thermal radiation, thermophoresis, Brownian motion, magnetic field and variable viscosity on boundary layer flow, heat and mass transfer of an electrically conducting nanofluid over a radially stretching convectively heated surface. The stretching velocity is assumed to vary linearly with the radial distance. Using similarity transformation, the governing nonlinear partial differential equations are reduced to a set of nonlinear ordinary differential equations which are solved numerically by employing shooting method coupled with Runge-Kutta Fehlberg integration technique. Graphical results showing the effects of various pertinent parameters on the dimensionless velocity, temperature, nanoparticle concentration, local skin friction, local Nusselt and local Sherwood numbers are presented and discussed quantitatively. Comparisons with the earlier results have been made and good agreements are found. The present results reveal that the heat transfer rate is reduced with viscosity and nanofluid parameters whereas the mass transfer rates is enhanced with Brownian motion parameter and Lewis number.

An incompressible flow of Casson-Maxwell fluids over stretchable disk rotating with constant angular speed is demonstrated in this research. Buongiorno theory of nanomaterials is utilized in the flow model to reveals the impacts of Brownian movement and thermophoresis. Cattaneo-Christov heat diffusion theory along with variable thermal conductivity is elaborated in the energy equation. The convective boundary condition for thermal analysis is imposed at the disk surface. The governing equations are normalized by means of similarity functions. Numerical approach is adopted to solve the complex non-linear system by Runge–Kutta-Fehlberg (RKF) procedure. The influence of dimensionless variables on velocity, thermal and concentration fields is illustrated through graphs, while the numerical values of thermal and concentration rates are explained in tabular way.

A boundary layer analysis of three dimensional electromagnetic flows of single and multi walls carbon nanotubes over the surface of a thin needle is addressed. Both single wall (SWCNTs) and multi wall (MWCNTs) are considered as nanoparticles whereas water is considered as base liquid. The energy equation is modeled by using non-linear thermal radiation because it has a major impact on the solar energy absorption capacity of nanofluid. Because of such solar energy utilization at greater scale, global warming/pollution levels can be controlled. Homogeneous-heterogeneous reactions are taken into consideration as they find their applications in catalysis, biochemical systems, combustion, batteries, corrosion phenomenon and electrolytic cells. Xue model describing the augmentation of thermal conductivity of carbon nanotubes is invoked. Entropy generation model is adopted because its minimization prevents the loss of available energy which in turn boosts the efficiency of thermal systems. Nonlinear differential equations representing flow expressions are numerically solved by shooting technique. The outcome of the present study is that velocity field lines are grown due to strengthening of electric field parameter in the flow of SWCNT-water and MWCNT-water nanofluids. Brinkman number uplifts the entropy generation.

Oblique stagnation point flow of incompressible Maxwell nanofluid past a stretching cylinder with active and passive controlled nanoparticles concentration condition is discussed numerically. The suitable coordinate decomposition reduce the governing boundary layer equations into the system of nonlinear ordinary differential equations which are approximated by Keller box procedure for several values of pertinent parameters. The Numerical results are compared and validated with existing ones as particular cases and found to be an excellent agreement. Velocity profile and lines of flow are sketched to discuss the Obliqueness of the flow. The temperature and concentration profiles drawn to illustrate the influence of involved parameters also variations in local Nusselt and Sherwood numbers are presented through tabular data. It is observed that the behavior of tangential velocity for the viscoelastic fluid and concentration of nanoparticles against thermophoresis diffusion over the cylinder are quite opposite when compared with the results over flat sheet. The temperature distribution and concentration of nanoparticles decreases with elasticity of the fluid.

This study elaborates on the flow of viscoelastic nanofluid consisting of gyrotactic microorganism over a rotating stretching disk along with convective boundary and zero mass flux conditions. Using the similarity transformations the nonlinear coupled partial differential equations regulating the present problem are converted into a set of ordinary differential equations which are approximated numerically by the Keller Box method. The numerically obtained results are verified with the available existing literature for particular values of the involved parameters which are limiting cases of the present analysis. Variation of heat and mass transfer and density numbers are presented graphically and the influence of various parameters on both radial and azimuthal velocities, temperature, concentration, and density of motile-microorganisms for convective and non-convective surfaces is shown through various plots and discussed.

This communication provides an innovative idea of entropy generation optimization and activation energy aspects on transient axisymmetric flow of Williamson nanofluid due to moving radiallysurface with the effects of binary chemical reactions. A revised model of nanofluid is adopted for the suspension of nanoparticles. Moreover, nonlinear thermal radiation is considered. Impact of Joule heating, MHD and viscous dissipation enhances the importance of this investigation for entropy generation optimization. Two more realistic surface conditions, zero nanoparticles normal flux and velocity slip are utilized at the radially moving surface. The fundamental equations of entropy generation rate, nanoparticles concentration, Bejan number, thermal energy as well as momentum for the Williamson nanofluid in axisymmetric case are modeled with the help of boundary layer analysis. Highly nonlinear ODEs are received from leading PDEs with the help of nondimensional transformation and then solved numerically through shooting Fehlberg approach. Surface drag force and Nusselt number are also computed. Fabulous numerical outcomes are achieved and compared with the existing study and found to be in outstanding agreement. It is important to find that entropy generation rate grows for larger estimation of Brinkmann number. Moreover, Bejan number is depressed for escalating Eckert number. Furthermore, nanoparticles concentration is a growing function of activation energy parameter.