Search

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.

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...

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.

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.

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.

Marangoni convection flow of Carreau liquid by an inclined porous surface is addressed. Magnetic field is taken inclined. Non-linear thermal radiation effects are incorporated considering the Rosseland?s approximation. Runge-Kutta-Fehl?berg fourth fifth order scheme is utilized to solve the non-linear equations subject to non-linear convective boundary conditions. Non-linear expression of Nusselt number is derived. Concrete graphical description is present out for flow velocity, temperature and Nusselt number. Numerical treatment of non-linear Nusselt number is performed and analyzed.

Purpose The purpose of this study is to examine the simultaneous effects of Hafnium particles and partially submerged metallic particles for the flow of bi-phase coupled stress fluid over an inclined flat plane. Design/methodology/approach An unflinching free stream flow that stretches far from the surface of the plane with the possibility of containing some partially submerged metallic particles is considered. Innovative model has been proposed and designed using Runge–Kutta–Fehlberg method. Findings The findings show that the drag force resists the couple stress fluid, whereas the Newtonian flow is supported by increasing the velocity. For both types of flows, movement of the particle is retarded gradually against the drag force coefficient. Originality/value To the best of the authors’ knowledge, this model is reported for the first time.

This paper reports multiple slip effects on MHD unsteady flow heat and mass transfer over a stretching sheet with Soret effect; suction/injection and thermal radiation are numerically analyzed. We consider a time-dependent applied magnetic field and stretching sheet which moves with nonuniform velocity. Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved numerically by applying an implicit finite difference method with quasi-linearization technique. The influences of the various parameters on the velocity temperature and concentration profiles as well as on the skin friction coefficient and Sherwood and Nusselt numbers are discussed by the aid of graphs and tables.

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 present work concentrates on the two-dimensional steady incompressible flow of an Oldroyd-8 constant fluid between vertical plates influenced by a magnetic field. The cross diffusive and second-order chemical reactions are incorporated into the study. The homotopy analysis method (HAM) is used to obtain the series solutions of the transformed system of nonlinear equations. The effects of these parameters on the dimensionless velocity, temperature, concentration, skin friction, and Nusselt and Sherwood numbers are also investigated for various values of relevant parameters affecting the flow and heat transfer phenomena. The most relevant outcomes of the present study are that enhancement in magnetic field strength undermines the flow velocity, temperature, and concentration establishing thinner related boundary layer. Another important outcome is that an increase in the Dufour parameter upsurges the rate of heat transfer at the wall y = 0 while peters out at y = 1. Finally, the second-order chemical reaction parameter reduces the concentration distribution. The novel outcomes of this investigation will be helpful in the field of the aerosol technology.

This article deals with the analytical study of MHD flow and heat transfer over a permeable stretching sheet via homotopy analysis method (HAM). The effect of thermal radiation is included in the energy equation, while velocity and thermal slips are included in the boundary conditions. The governing boundary layer equations are transformed into a set of ordinary differential equations by means of similarity transformations. The effects of different parameters on the flow field and heat transfer characteristics are examined. The results obtained were shown to compare well with the numerical results and for some special cases with the published data available in the literature, which are in favorable agreement. Keywords: MHD; Slip flow; Stretching sheet; Thermal radiation; Homotopy analysis method

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.

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.

This research study explores the effects of entropy generations on the pulsatile blood flow through a w-shape curved stenosed channel. The mathematical formulations of this physical problem are derived from the couple equations of momentum and energy. These equations are first normalized, and then solved numerically using the explicit finite difference technique. Subsequently, the solutions of these equations are utilized in the calculation of the Bejan number (Be) and entropy generations (NG). To simplify this problem, a few assumptions are taken into consideration; for instance, a mild stenotic condition is assumed in order to reduce the order of differential equations. The results are based on various velocity graphs sketched under the influence of the curvature (Rc) and magnetic (M) parameters. The magnitude of velocity as well as streamline profiles are highly affected due to the curvature effects of channel wall. The results demonstrate that the value of Bejan (Be) number is highly influenced by increasing the value of curvature parameter (Rc) as depicted in the graphs. Similarly, the shape of velocity profile reduces to symmetric in the unbent vessel. Moreover, it is also observed that the magnitude of velocity has decelerated in the presence of magnetic field.

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.

Several boundary layer flowswith heat and mass transfer problems do arise from a pebble bed nuclear reactor system. In this study, we examine the combined effects of variable thermal conductivity, thermal diffusion, diffusion thermo, heat source, chemical reaction and fluid rotation on hydromagnetic mixed convective flow with heat and mass transfer over a vertical plate embedded in porous medium. The governing partial differential equations have been transformed into a system of ordinary differential equations by employing the similarity transformation and solved numerically using the Runge–Kutta–Fehlberg method with a shooting technique. Pertinent results obtained are presented graphically and in tabular form with respect to variation in various thermophysical parameters. A comparison of the special case of this study with the previously published work shows excellent agreement.

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.