Hydromagnetic Mixed Convective Nanofluid Slip Flow past an Inclined Stretching Plate in the Presence of Internal Heat Absorption and Suction

The steady two-dimensional mixed convective boundary layer flow of nanofluid over an inclined stretching plate with the effects of magnetic field, slip boundary conditions, suction and internal heat absorption have been investigated numerically. Two different types of nanoparticles, namely copper and alumina with water as the base fluid are considered. Similarity transformations are employed to transform the governing nonlinear partial differential equations into coupled non-linear ordinary differential equations. The influence of pertinent parameters such as magnetic interaction parameter, angle of inclination, volume fraction, suction parameter, velocity slip parameter, thermal jump parameter, heat absorption parameter, mixed convection parameter and Prandtl number on the flow and heat transfer characteristics are discussed. A representative set of results are displayed graphically to illustrate the issue of governing parameters on the dimensionless velocity and temperature. Numerical values of skin friction coefficient and the Nusselt number are shown in tabular form. A comparative study between the previously published work and the present results in a limiting sense reveals excellent agreement between them

Unsteady reactive magnetic radiative micropolar flow, heat and mass transfer from an inclined plate with joule heating: a model for magnetic polymer processing

Magnetic polymer materials processing involves many multi-physical and chemical effects. Motivated by such applications, in the present work a theoretical analysis is conducted of combined heat and mass transfer in unsteady mixed convection flow of micropolar fluid over an oscillatory inclined porous plate in a homogenous porous medium with heat source, radiation absorption and Joule dissipation. A first order homogenous chemical reaction model is used. The transformed non-dimensional boundary value problem is solved using a perturbation method and Runge-Kutta fourth order numerical quadrature (shooting technique). The emerging parameters dictating the transport phenomena are shown to be the gyro-viscosity micropolar material parameter, magnetic field parameter, permeability of the porous medium, Prandtl number, Schmidt number, thermal Grashof number, species Grashof number, thermal radiation-conduction parameter, heat absorption parameter, radiation absorption parameter, Eckert number, chemical reaction parameter and Eringen coupling number (vortex viscosity ratio parameter). The impact of these parameters on linear velocity, microrotation (angular velocity), temperature and concentration are evaluated in detail. Results for skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are also included. Couple stress is observed to be reduced with stronger magnetic field. Verification of solutions is achieved with earlier published analytical results

Finite element computation of magnetohydrodynamic nanofluid convection from an oscillating inclined plate with radiative flux, heat source and variable temperature effects

The present work describes finite element computations for radiative magnetohydrodynamic convective Newtonian nanofluid flow from an oscillating inclined porous plate with variable temperature. Heat source/sink and buoyancy effects are included in the mathematical model. The problem is formulated by employing Tiwari-Das nanofluid model and two water - based nanofluids with spherical shaped metal nano particles as copper and alumina are considered. The Brinkman and Maxwell-Garnetts models are used for the dynamic viscosity and effective thermal conductivity of the nanofluids respectively. An algebraic flux model, the Rosseland diffusion approximation is adopted to simulate thermal radiative flux effects. The dimensionless, coupled governing partial differential equations are numerically solved via the finite element method with weak variational formulation by imposing initial and boundary conditions with a weighted residual scheme. A grid independence study is also conducted. The finite element solutions are reduced to known previous solutions in some limiting cases of the present investigation and are found to be in good agreement with published work. This investigation is relevant to electromagnetic nanomaterial manufacturing processes operating at high temperatures where radiation heat transfer is significant

Transpiration effects on stagnation flow towards a stretching sheet with induced magnetic field

In this study, we analyzed the effect of suction/injection on stagnation-point flow towards a stretching sheet with heat source/sink and induced magnetic field. The nonlinear partial differential equations are transformed into a set of nonlinear ordinary differential equations using self-suitable transformations, which are then solved numerically using bvp4c Matlab package. The effects of various physical parameters like magnetic field parameter , heat source/sink parameter and stretching ratio  etc. on velocity, induced magnetic field and temperature profiles are presented and discussed with the help of graphs. It is found that rising values of heat source/sink parameter declines the temperature filed. Key words: Induced magnetic field, suction/injection, heat source/sink, stretching sheet

Radiative heat transfer in MHD mixed convection flow of nanofluids along a vertical channel

Over the past few decades, nanofluids have emerged as a promising technology for the enhancement of the intrinsic thermophysical properties of many convectional heat transfer fluids such as water and oil. Many researchers have been investigated the merits of dispersing nanometer-sized particles into base fluids to enhance heat transfer, thermal conductivity and viscosity of the fluids. Therefore, this research focused on radiative heat transfer in magnethohydrodynamics mixed convection flow in a channel filled with nanofluids containing different type of nanoparticles. Five types of nanoparticles (Al2O3, 3 4Fe O , Cu, 2 TiO , and Ag) with five different shapes (platelet, blade, cylinder, brick and spherical) were used in water 2 (H O) and ethylene glycol 2 6 2 (C H O), as conventional base fluid. An important subtype of nanofluids called ferrofluids 3 4 (Fe O in water based nanofluids) was also studied. Four different problems were modelled as partial differential equations with physical boundary conditions. In the first three problems, the channel walls were taken rigid, while the fourth problem the walls were chosen permeable where suction or injection was taking place. Perturbed type analytical solutions for velocity and temperature were obtained and discussed graphically in various graphs. Results for skin friction and Nusselt number were also computed and presented in tabular forms. This study showed that 2 6 2 C H O was the better convectional base fluid compared to 2 H O because of the higher viscosity and thermal conductivity. Ag nanoparticles had the highest thermal conductivity and viscosity compared to other type of nanoparticles. Increasing nanoparticles size had caused variation in velocity. It was also observed that, variation in velocity for Ag nanoparticles was obtained at low volume concentration, whereas for 2 3 Al O nanoparticles, this variation was observed only at high volume concentration. Velocity increases with increasing Grashof number, radiation, heat generation and permeability parameters, but decreases with increasing magnetic parameter and volume fraction of nanoparticles. However, the effects of these parameters were quite different in the case of suction and injection. Results had also shown that, temperature increases with increasing radiation and heat generation parameters. In this study, the temperature of ferrofluids was found smaller when compared to the temperature of nanofluids

Chebyshev collocation computation of magneto-bioconvection nanofluid flow over a wedge with multiple slips and magnetic induction

In this paper the steady two dimensional stagnation point flow of a viscous incompressible electrically conducting bio-nanofluid over a stretching/shrinking wedge in the presence of passively control boundary condition, Stefan blowing and multiple slips is numerically investigated. Magnetic induction is also taken into account. The governing conservation equations are rendered into a system of ordinary differential equations via appropriate similarity transformations. The reduced system is solved using a fast, convergent Chebyshev collocation method. The influence of selected parameters on the dimensionless velocity, induced magnetic field, temperature, nanoparticle volume fraction and density of motile microorganisms as well as on the local skin friction, local Nusselt number, local Sherwood number and density of motile microorganism numbers are discussed and presented graphically. Validation with previously published results is performed and an excellent agreement is found. The study is relevant to electromagnetic manufacturing processes involving bionano-fluids

Mathematical models for heat and mass transfer in nanofluid flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The behaviour and evolution of most physical phenomena is often best described using mathematical models in the form of systems of ordinary and partial differential equations. A typical example of such phenomena is the flow of a viscous impressible fluid which is described by the Navier-Stokes equations, first derived in the nineteenth century using physical approximations and the principles of mass and momentum conservation. The flow of fluids, and the growth of flow instabilities has been the subject of many investigations because fluids have wide uses in engineering and science, including as carriers of heat, solutes and aggregates. Conventional heat transfer fluids used in engineering applications include air, water and oil. However, each of these fluids has an inherently low thermal conductivity that severely limit heat exchange efficiency. Suspension of nanosized solid particles in traditional heat transfer fluids significantly increases the thermophysical properties of such fluids leading to better heat transfer performance. In this study we present theoretical models to investigate the flow of unsteady nanofluids, heat and mass transport in porous media. Different flow configurations are assumed including an inclined cylinder, a moving surface, a stretching cone and the flow of a polymer nanocomposite modeled as an Oldroyd-B fluid. The nanoparticles assumed include copper, silver and titanium dioxide with water as the base fluid. Most recent boundary-layer nanofluid flow studies assume that the nanoparticle volume fraction can be actively controlled at a bounding solid surface, similar to temperature controls. However, in practice, such controls present significant challenges, and may, in practice, not be possible. In this study the nanoparticle flux at the boundary surface is assumed to be zero. Unsteadiness in fluid flows leads to complex system of partial differential equations. These transport equations are often highly nonlinear and cannot be solved to find exact solutions that describe the evolution of the physical phenomena modeled. A large number of numerical or semi-numerical techniques exist in the literature for finding solutions of nonlinear systems of equations. Some of these methods may, however be subject to certain limitations including slow convergence rates and a small radius of convergence. In recent years, innovative linearization techniques used together with spectral methods have been suggested as suitable tools for solving systems of ordinary and partial differential equations. The techniques which include the spectral local linearization method, spectral relaxation method and the spectral quasiliearization method are used in this study to solve the transport equations, and to determine how the flow characteristics are impacted by changes in certain important physical and fluid parameters. The findings show that these methods give accurate solutions and that the speed of convergence of solutions is comparable with methods such as the Keller-box, Galerkin, and other finite difference or finite element methods. The study gives new insights, and result on the influence of certain events, such as internal heat generation, velocity slip, nanoparticle thermophoresis and random motion on the flow structure, heat and mass transfer rates and the fluid properties in the case of a nanofluid

Exploration of recent developments of hybrid nanofluids

Over the past two decades, research on hybrid nanofluids has developed at a breakneck pace. Hybrid nanofluids are the potential fluids that outperform conventional nanofluids heat transfer fluids regarding thermophysical characteristics and thermal performance. Hybrid nanofluids are traditionally prepared by emulsifying each nanoparticle into the base fluid independently or diffusing both particles as a composite form into the base fluid. Despite the popularity and broad application of hybrid nanofluids in industrial/manufacturing processes, the review article classifying the mathematical models and categorization of the various hybrid nanofluids is limited in the scientific community. In light of this, this study examines recent and past research articles on deterministic hybrid nanofluid flow problems by exploiting different categorizations and metrics (method to solve the differential equation, the geometry of choice and thermophysical effects that have been employed as well as the nano-particle types). Researchers will be able to use the findings of this study for a future research proposal. Essentially, it is to fill in the gaps in the literature, particularly regarding the mathematical model for hybrid nanofluid flow problems and determining the geometry, thermophysical properties, and nanoparticle type

Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions

Energy conversion under conduction, convection, diffusion and radiation has been studied for MHD free convection heat transfer of a steady laminar boundary-layer flow past a moving permeable non-linearly extrusion stretching sheet. The nonlinear Rosseland thermal radiation flux model, velocity slip, thermal and mass convective boundary conditions are considered to obtain a model with fundamental applications to real world energy systems. The Navier slip, thermal and mass convective boundary conditions are taken into account. Similarity differential equations with corresponding boundary conditions for the flow problem, are derived, using a scaling group of transformation. The transformed model is shown to be controlled by magnetic field, conduction-convection, convection-diffusion, suction/injection, radiation-conduction, temperature ratio, Prandtl number, Lewis number, buoyancy ratio and velocity slip parameters. The transformed non-dimensional boundary value problem comprises a system of nonlinear ordinary differential equations and physically realistic boundary conditions, and is solved numerically using the efficient Runge-Kutta-Fehlberg fourth fifth order numerical method, available in Maple17 symbolic software. Validation of results is achieved with previous simulations available in the published literature. The obtained results are displayed both in graphical and tabular form to exhibit the effect of the controlling parameters on the dimensionless velocity, temperature and concentration distributions. The current study has applications in high temperature materials processing utilizing magnetohydrodynamics, improved performance of MHD energy generator wall flows and also magnetic-microscale fluid devices

Numerical solution of the stagnation point flow and heat transfer with several effects

Problems related to boundary layer flow and heat transfer is important due to its various practical applications in engineering and industrial area. Cooling systems, nuclear reactor, electronic, hydrodynamics process, paper production and the boundary layer in liquid film condensation process are some of the example of various applications related to boundary layer flow and heat transfer. Present thesis solved numerically three problems of boundary layer flow on stagnation point over a stretching by considering the Newtonian fluid (viscous fluid) and non-Newtonian fluid (Williamson fluid). Besides, this thesis concern of the influence of slip flow, thermal radiation, magnetohydrodynamic (MHD) and viscous dissipation effects associated with constant wall temperature as boundary conditions. All gorvening equations in the form partial differential equations are transformed into ordinary differential equations by employing the suitable similarity transformation. The transformed ordinary differential equations obtained are solved numerically using a Shooting method in Maple software. Numerical solutions are obtained for the local Nusselt number and skin friction coefficient as well as the temperature and velocity profiles. The features of the flow and heat transfer characteristics for various values of eight pertinent parameters which are the Prandtl number, the stretching parameter, the Eckert number, the velocity slip parameter, the thermal slip parameter, the radiation parameter, the magnetic parameter and the nonNewtonian Williamson fluid parameter are analyzed and discussed. The comparison is also done by verifying through existing research so that the results obtained are a good agreement and reliable. As conclusion, the increases of Prandtl number, stretching parameter, dimensionless thermal and velocity slip parameter result to the decreasing in the wall temperature and also thermal boundary layer thickness. Meanwhile, increasing the non-Newtonian Williamson fluid parameter and thermal radiation parameter, the thermal boundary layer also increases