Magnetically driven chemically reactive Casson nanofluid flow over curved surface with thermal radiation

During this exploration, Casson nanofluid is taken over a sheet that is curved and stretching in nature and its flow equations are analyzed. Radiation and slip provisions are also taken into consideration. A magnetic field of uniform rate is provided. Convective heat and mass transference extract dominant conclusions from the system. The Brownian migration together with thermophoresis is also included in the flow structure. Moreover, the chemical reaction of higher-order within the nanoingredients also generates interest. Guiding equations furnished by the selected model are resettled to ordinary differential equations of nonlinear type by significant similarity transformation. We have worked on MAPLE-19 software to work out this with a suitable accuracy rate. Upshots are shown with diagrams and tables. Corresponding physical consignment such as Nusselt number has been analyzed. Determination of skin friction and moreover Sherwood's number is also in the area of interest. Magnificent advancement in heat sifting is dealt with by magnetic and Brownian motion specification. The graphs prescribed the upshots of thermophoresis and slip parameters. Outcomes convey that temperature together with concentration are reduced for stretching parameters but velocity lines are enhanced. Heat transport goes up for magnetic and Brownian motion framework but elevated outcomes are spotted for radiative flow in contrast to nonradiative flow. Mass transfer is reduced for chemical reaction components but the rate of augmentation is elevated for higher-order chemically reactive flow. Mass Biot number and temperature Biot number both increase the concentration and temperature transport, respectively.     

Radiative CNT-based hybrid magneto-nanoliquid flow over an extending curved surface with slippage and convective heating

This study concentrates on the hydrothermal prominence of a mixed convective flow of a hybrid nanoliquid over a convectively heated extending curved surface under the influence of a uniform transverse magnetic field. Two types of carbon nanotubes (CNTs), namely single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs), and magnetite nanoparticles are dispersed in the host liquid (water) to simulate the hybrid nanoliquid flow model. First- and second-order velocity slip conditions and nonlinear radiative heat flux are incorporated in this model. First, the system of governing partial differential equations is changed into nonlinear ordinary differential equations through the utilization of appropriate transformations and computed numerically via MATLAB built-in function bvp4c based on the three-stage Lobatto IIIA technique. The consequences of physical and geometrical parameters pertinent to this analysis on the dimensionless physical quantities of interest are deliberated using requisite graphs and tables. Our simulation communicates that the first-order velocity slip parameter decreases the velocity profile, whereas the second-order velocity slip parameter is found to be augmented. The suspension of CNTs in the magnetite nanoliquid improves the local surface drag force but diminishes the local heat flux. Moreover, it is examined that SWCNTs have greater impacts than MWCNTs.     

Physical aspects on unsteady MHD‐free convective stagnation point flow of micropolar fluid over a stretching surface

The unsteady magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid across a vertical stretching surface with second‐order velocity slip is the main concern of the present paper. The influence of electrical energy, temperature‐dependent thermal conductivity, thermal radiation, Joule heating, and heat sink/source is investigated. The basic partial differential equations are changed into ordinary differential equations with the help of appropriate similarity variables and then solved by the fourth‐order Runge‐Kutta–based shooting technique. The impact of physical parameters on the velocity, microrotation, and temperature as well as friction factor, couple stress, and local Nusselt number is thoroughly explained with the support of graphs and tables. The results divulge that the heat source/sink and thermal radiation parameters have a propensity to enhance the fluid temperature. The distribution of velocity is an increasing function of an electric field and unsteadiness parameter. The numerical results are also compared with the results available in the literature.     

Influence of nanofluids on mixed convective heat transfer over a horizontal backward‐facing step

Predictions are reported for laminar mixed convection using various types of nanofluids over a horizontal backward‐facing step in a duct, in which the upstream wall and the step are considered adiabatic surfaces, while the downstream wall from the step is heated to a uniform temperature that is higher than the inlet fluid temperature. The straight wall that forms the other side of the duct is maintained at constant temperature equivalent to the inlet fluid temperature. Eight different types of nanoparticles, Au, Ag, Al₂O₃, Cu, CuO, diamond, SiO₂, and TiO₂, with 5% volume fraction are used. The conservation equations along with the boundary conditions are solved using the finite volume method. Results presented in this paper are for a step height of 4.9 mm and an expansion ratio of 1.942, while the total length in the downstream of the step is 0.5 m. The Reynolds number is in the range of 75 ≤ Re ≤ 225. The downstream wall was fixed at a uniform wall temperature in the range of 0 ≤ ΔT ≤ 30 °C which is higher than the inlet flow temperature. Results reveal that there is a primary recirculation region for all nanofluids behind the step. It is noticed that nanofluids without secondary recirculation region have a higher Nusselt number and it increases with Prandtl number decrement. On the other hand, nanofluids with secondary recirculation regions are found to have a lower Nusselt number. Diamond nanofluid has the highest Nusselt number in the primary recirculation region, while SiO₂ nanofluid has the highest Nusselt number downstream of the primary recirculation region. The skin friction coefficient increases as the temperature difference increases and the Reynolds number decreases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20344     

Second law analysis for mixed convection nanofluid flow in an inclined channel with convectively heated walls

In this study, entropy generation analysis for Cu–water nanofluid mixed convective flow in an inclined channel occupied with a saturated porous media with Navier slip and convective boundary conditions is explored. The governing equations composed of equations of velocity and temperature are nondimensionalized and then solved utilizing the technique of homotopy analysis. Temperature and velocity profile expressions are acquired, which are then used to calculate the entropy produced in the scheme. The impacts of the corresponding fluid parameters are addressed in‐depth on velocity, temperature, entropy generation, Bejan number, Nusselt number, skin friction, volume flow rate, and heat carried out by the fluid for nanofluid concentration. Entropy has been observed to be minimal in all cases just above the channel center and maximum at the channel's bottom wall. Fluid friction‐generated entropy has been discovered to have a higher influence on entropy generation. We also provide a comparative study with existing literature to validate our current results.     

Steady MHD mixed convection flow of a viscoelastic fluid over a magnetized convectively heated vertical surface with Hall current and induced magnetic field effects

In this paper, the steady magnetohydrodynamic mixed convection flow of a viscoelastic fluid over a magnetized vertical surface embedded in a uniform porous material with rotation is considered. The Hall and induced magnetic field effects are also considered in this investigation. The regular perturbation technique is used to find the solutions of flow governing equations. To analyze the consequences of flow-influencing parameters to the flow variables, numerical computation has been performed and the results are illustrated in graphical and tabular forms. It is interesting to note that magnetic diffusion leads to the increase of the fluid flow. It brings a decrement in the induced magnetic field in the vicinity of the magnetized vertical surface.     

Analysis of a boundary layer flow over moving an exponentially stretching surface with variable viscosity and Prandtl number

Boundary layer flow phenomenons on a stretching sheet find numerous applications in industrial processes such as manufacture and extraction of rubber and polymer sheets. The current study focuses on two‐dimensional water boundary layer flow on exponential stretching surface with a vertical plate for variable physical properties of fluid such as viscosity and Prandtl number. The Quasilinearization technique has been used on governing equations to transform nonlinear to linear equations and these equations are discretized by finite difference techniques to get numerical solutions. The effect of buoyancy parameters (λ), velocity ratio parameter () and streamwise coordinator (ξ) on velocity profiles (F), temperature profiles (θ), local skin‐friction coefficient (C_fx(Re_Lξexp(ξ)^)1/2) and the local Nusselt number (Nu_x(Re_Lξexp(ξ)^)?1/2) has been analyzed graphically based on numerical outcome. The magnitude of velocity profiles increases and temperature profile decreases approximately by 4% and 16% with increases the buoyancy parameter from λ = 1 to λ = 3 at = 0.5 and ξ = 1.0. The skinfriction and heat transfer coefficient increases approximately by 22% and 27% with an increase in ξ from 0.5 to 1.0 at fixed = 0.5 and λ = 1.0. The variations of velocity profiles and temperature profiles have more impact with as compared to ξ and λ. The benchmark studies were carried out to validate the current results with previously published work and found to be in excellent agreement.     

Influence of multiple slips on magnetically driven nanofluid flow over an externally heated stretching cylinder

In this article, we have inspected multiple slippery consequences along a stretching cylinder. Brownian migration along with thermophoresis is clutched together with an external heat source. Magnetic influence is considered perpendicular to the cylinder. Standard flow systems are transfigured to ordinary differential equations by well-qualified similarity transformations. They are solved by the Runge–Kutta scheme of the fourth-order (shooting technique) method with the assistance of MAPLE software. The entire simulation is done with a proper accuracy rate and the upshots are portrayed by graphs and tables. All results are compared under no slip and with slip provisions. Augmentation in Reynolds number and magnetic parameter uprise the velocity lines and the slip effect reduces the magnitude decently. The thermal jump effect reduces the magnitude of the heat transfer rate. The solutal slip effect decreases the concentration boundary layer for magnetic and Brownian migration specifications. Approximately 6.69% and 6.79% drop in Nusselt number is spotted for Brownian migration and thermophoresis parameters. The external heat source parameter brings out 14.98% inflation in the Nusselt number significantly.     

Second law analysis in radiative mixed convective squeezing flow of Casson fluid between parallel disks with Soret and Dufour effects

The present communication deals the entropy generation by cause of heat and mass transform in an unsteady mixed convective radiative squeezing flow of a Casson fluid confined between two parallel disks in the presence of diffusion‐thermo and thermal‐diffusion effects and temperature jump. The lower disk is taken to be porous and the upper one is impermeable. The governing PDE is converted as nonlinear ordinary differential equations (ODE) by using well‐established similarity transformations; then, the reduced nonlinear ODE are solved by shooting method with Runge‐Kutta fourth‐order approach. The influence of distinct nondimensional fluid and geometric‐related parameters on the velocity profiles, temperature, concentration, entropy generation number, and Bejan number are studied in detail and represented in the form of graphs. The entropy of the Casson fluid is increased with the Eckert number, whereas the concentration profile is decreased by squeezing Reynolds number. The current results are correlated with existing results for the viscous case and found to be in better agreement.     

Effects of variable thermophysical properties on mixed convection slip flow over a wedge

This paper reveals the characteristics of mixed convection slip flow of an electrically conducting fluid over a wedge subject to temperature dependent viscosity and thermal conductivity variations. The system of dimensionless nonsimilar governing equations has been solved by an implicit finite difference method. We also use stream‐function formulation to reduce the governing equations into a convenient form, which are valid for small and large time regimes. These are solved employing the perturbation method for small time and the asymptotic method for large time. Numerical solutions yield a good agreement with the series solutions. Because of the increase in the mixed convection parameter, the peak of the velocity profile increases whereas the maximum temperature decreases. In contrast, the local skin‐friction coefficient and local Nusselt number are found to increase with the mixed convection parameter. For higher values of the velocity slip and temperature jump conditions, the local skin‐friction coefficient and the local Nusselt number are found to increase. The viscosity parameter enhances the local skin friction and the local Nusselt number. But the converse characteristic is observed for the thermal conductivity parameter. The results could be used in microelectromechanical systems, fabrication, melting of polymers, polishing of artificial heart valves, etc.     

Fluid flow and heat transfer of mixed convection adjacent to vertical heated plates placed in uniform horizontal flow of air

Experiments have been carried out for mixed convective flows of air adjacent to the vertical heated plates in uniform horizontal forced flows to investigate relationships between the flow and the heat transfer. The experiments cover the ranges of the Reynolds and modified Rayleigh numbers: Re_L = 160 to 2300 and Ra_L^* = 4.3 × 10⁵ to 2.0 × 10⁸. The flow fields over the plates are visualized with particles and smoke. The results show that a stagnation point moves downward away from the center of the plate when the surface heat flux is beyond a critical value. The condition where the stagnation point begins to move is expressed with non‐dimensional parameters as: Gr_L^*/Re_L^2.5 = 0.15. Profiles of measured local heat transfer coefficients are smooth even at the stagnation points in all the cases examined. When buoyancy effect is sufficiently weak, the coefficients agree well with those of the wedge flow. With increasing the surface heat flux, the coefficients are augmented to approach asymptotically the boundary layer solution of natural convection along a vertical heated plate. Finally, forced, mixed, and natural convection regimes are classified by the non‐dimensional parameter (Gr_L^*/Re_L^2.5). © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20256     

Magnetohydrodynamic flow of a nanofluid due to a non‐linearly curved stretching surface with high order slip flow

This article numerically scrutinizes magnetohydrodynamic flow of a nanofluid due to a nonlinearly curved stretching surface with third order slip flow conditions. The third order slip flow condition has not yet been discussed in fluid dynamics research. The mathematical modeling of the flow problem is given in partial differential equation form. The governing partial differential equations are transformed to high order ordinary differential equations using the similarity transformation and then solved numerically using a boundary value problem solver, bvp4c from Matlab software. The effect of the governing parameters on the flow of the velocity profile, concentration, and heat transfer characteristics are studied. Also graphs of the skin friction coefficient, local Nusselt number, and Sherwood number are drawn and their numerical values are tabulated. The numerical results of the study are compared with previously published articles in the limiting condition. The velocity of the flow field is reduced as the third order slip parameter and the first order slip parameter rises, but the velocity grows as the values of the second order slip flow parameter are elevated. The findings also indicate that the local Nusselt number is depreciated but local Sherwood numbers are elevated when the Soret and Dufour numbers are larger.     

Fluid flow and heat transfer of opposing mixed convection adjacent to vertical heated plates

Opposing mixed convective flows induced around heated vertical plates were investigated experimentally. The experiments have been carried out with air and test plates of 100 mm and 200 mm long. The flow fields over the heated plates were visualized and the local heat transfer coefficients of the plates were measured for a wide range of Reynolds and Rayleigh numbers; Re_L = 7 × 10²−1.5 × 10⁴, Ra = 9 × 10⁶−8 × 10⁸. The visualization experiments showed that the separation of the boundary layer appears first at the trailing edge of the plate when the non‐dimensional parameter of (Gr/Re) = 0.35, and that the separation point reaches the leading edge when (Gr_L^*/Re_L^2.5) = 1.0. The heat transfer experiments showed that the above flow separation retards the heat transfer significantly from that of pure forced convection. It was also revealed that the flows over the heated plates can be categorized into forced, natural, and combined convection using the above parameter, (Gr/Re), as (Gr/Re) < 0.2, (Gr/Re) > 3 and 0.2 < (Gr/Re) < 3, respectively. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(8): 595–607, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20080     

Micropolar nanoliquid flow via mixed convective over an orthogonal cylinder

The intent of the current investigation is to explore the axisymmetric flow of the micropolar nanoliquid past an orthogonal cylinder in the existence of mixed convection impact. Suitable similitude changes produce joined nonlinear differential schemes, which were explicated via fourth-order finite difference style. The authenticity of the results was emphasized by contrasting them with previous results with some limited presumptions and uncovered to be in excellent agreement. Performance of numerous physical parameters on velocity components and temperature distributions alongside the physical quantities of interests were revealed graphically and in tabular forms. It was shown that the skin friction and heat transport rate boost with rising in the volume fraction nanoparticle and the buoyancy, while they decline with the increase of micropolar parameter. This investigation intends to improve on an intuitive understanding of similar patterns by confirming the physical debates and may be applicable in the field of biomechanics, polymer processing, production of aerosol deposition, and thermal treatment.     

Differential transformed approach of unsteady chemically reactive nanofluid flow over a bidirectional stretched surface in presence of magnetic field

This study investigates the consequences of steady and unsteady nanofluid flow over a bidirectional stretching sheet. Herein, the magnetic field is working in the normal direction. The Brownian motion together with thermophoresis is taken into consideration. Moreover, the chemical reaction within the nanoingredients also occupies a novel corner in this study. The leading equations of the considered model are transferred to nonlinear ordinary differential equations (ODEs) by an appropriate similarity transformation. The differential transformation method is used to solve the set of ODEs. We have used MAPLE‐17 software to solve this with the desired accuracy rate. Results are portrayed with graphs and tables. The corresponding physical consignments such as the Nusselt number, skin friction, and the Sherwood number are exhibited. Excellent improvement in heat and mass transport is observed, which can be visualized through tables. Outcomes reveal that both the temperature and x‐direction velocity are reduced for the stretching parameter. Heat transport escalates for stretching factor, but higher outcomes are marked for the unsteady flow as compared with the steady flow. The mass transfer also increases for the chemical reaction factor, but the rate of increment is higher for the unsteady flow.     

Impact of Soret and Dufour on MHD mixed convective flow of non-Newtonian fluid over a coagulated surface

In the present study, we investigated the steady, two-dimensional mixed convective stagnation point flow of an electrically conducting micropolar fluid due to stretching of a variable thicked surface in the attendance of viscous dissipation. The flow is incompressible and laminar. The combined heat and mass transfer features are investigated. Convective and diffusion conditions are considered. The nonlinear thermal radiation, thermo-diffusion, and diffusion thermal effects are considered. The governing partial differential equations are converted to ordinary differential equations by using the appropriate similarity transformations. The obtained nonlinear and coupled ordinary differential equations are elucidated numerically using the fourth-order Runge–Kutta based shooting technique. The influence of various nondimensional parameters on the flow field like velocity, microrotation, temperature, and concentration is examined with the assistance of graphs. Results indicate that the Dufour number has a proclivity to increase the distributions of concentration and temperature correspondingly. Also, fluid temperature and concentration enhance for increasing values of the wall thickness parameter.     

Fluid flow and heat transfer of opposing mixed convection adjacent to downward‐facing,inclined heated plates

Experimental investigations were carried out for opposing mixed convective flows of air adjacent to downward‐facing, inclined heated plates. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers from Re_L=400 to 4600 and Ra_L^*=1.0×10⁷ to 5.4×10⁸, and the inclination angles from θ=15 to 75^° from horizontal. The flow fields over the plates were visualized with smoke. The results showed that a separation of forced boundary layer flow occurs first at the bottom edge of the plate, and then the separation point shifts toward upstream with increasing wall heat flux, and finally, reaches the top edge of the plates. It was found that the separations at the bottom and top edges are predicted with a non‐dimensional parameter (Gr_Lθ^*/Re_L^2.5)=0.35 and 1.0, respectively. The local heat transfer coefficients of the inclined plates were also measured and the results showed that the minimum coefficients appear in the separation region. Moreover, it was revealed that forced, natural, and combined convective flows can be classified by the non‐dimensional parameter (Gr_Lθ^*/Re_L^2.5). © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Pub‐ lished online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20233     

Numerical simulation of mixed convective 3D flow of a chemically reactive nanofluid subject to convective Nield's conditions with a nonuniform heat source/sink

The present investigation aims to explore the influence of a mixed convection and nonuniform heat source/sink on unsteady flow of a chemically reactive nanofluid driven by a bidirectionally expandable surface. Convective heat transport phenomenon is used to maintain the temperature of the surface. Moreover, zero mass flux is also accounted at the surface such that the fraction of nanomaterial maintains itself on strong retardation. The governing nonlinear set of partial differential equations is transformed into a set of ordinary differential equations via a suitable combination of variables. The Keller‐Box scheme has been incorporated to make a numerical inspection of the transformed problem. The spectacular impacts of the pertinent constraints on thermal and concentration distributions are elucidated through various plots. Graphical outcomes indicate that the thermal state of nanomaterial and nanoparticles concentration are escalated for elevated amounts of Biot number, porosity parameter and nonuniform heat source/sink constraints. Furthermore, it is also seen that escalating amounts of unsteady parameter, temperature controlling indices, Prandtl number, and expansion ratio parameter reduce the thermal and concentration distributions. Numerical results for the rate of heat transference have been reported in tabular form. The grid independence approach is used to verify the convergence of the numerical solution and the CPU run time is also obtained to check the efficiency of the numerical scheme adopted for finding the solution.