Free Convection Boundary Layer Flow from a Heated Upward Facing Horizontal Flat Plate Embedded in a Porous Medium Filled by a Nanofluid with Convective Boundary Condition

Uddin, Md. Jashim; Khan, Waqar A.; Ismail, Ahmad Izani Md.

doi:10.1007/s11242-011-9938-z

Cited by 50 publications

(18 citation statements)

References 32 publications

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“…We solve the system of non-linear boundary value problem that is given in Equations (8)-(11) numerically by applying the finite element method (FEM) subjected with the boundary conditions (12)- (16). The FEM is extremely effectual and has been applied to study different problems in fluid mechanics, CFD, mass transfer, heat transfer, solid mechanics, and also in many other fields.…”

Section: Finite Element Methods Solutionsmentioning

confidence: 99%

Finite Element Analysis of Thermo-Diffusion and Multi-Slip Effects on MHD Unsteady Flow of Casson Nano-Fluid over a Shrinking/Stretching Sheet with Radiation and Heat Source

et al. 2019

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In this article, we probe the multiple-slip effects on magnetohydrodynamic unsteady Casson nano-fluid flow over a penetrable stretching sheet, sheet entrenched in a porous medium with thermo-diffusion effect, and injection/suction in the presence of heat source. The flow is engendered due to the unsteady time-dependent stretching sheet retained inside the porous medium. The leading non-linear partial differential equations are transmuted in the system of coupled nonlinear ordinary differential equations by using appropriate transformations, then the transformed equations are solved by using the variational finite element method numerically. The velocity, temperature, solutal concentration, and nano-particles concentration, as well as the rate of heat transfer, the skin friction coefficient, and Sherwood number for solutal concentration, are presented for several physical parameters. Next, the effects of these various physical parameters are conferred with graphs and tables. The exact values of flow velocity, skin friction, and Nusselt number are compared with a numerical solution acquired with the finite element method (FEM), and also with numerical results accessible in literature. In the end, we rationalize the convergence of the finite element numerical solution, and the calculations are carried out by reducing the mesh size. Appl. Sci. 2019, 9, 5217 2 of 21 partial velocity slip can occur on the stretching boundary. In an assortment of industry procedures, the influences of slip can crop-up at the boundary of pipes, surfaces, and walls. The Navier Stoke velocity slip conditions are customary to approach in the study of slip phenomenon.There are hundreds of applications in industries and engineering, and magneto-hydrodynamic fluid flows through stretching sheet have achieved much importance in recent days, according to Mabbod et al. [3]. Applications as well as the liquid coating on the photographic films, boundary layers throughout the liquid film in the concentration procedure, and the aerodynamic excrescence of plastic sheets exist. With this, the extensive range of applications of magnetohydrodynamic flow that can be found in copious fields like in electronic cooling process, in boilers, heat lagging, and metal extrusion, geothermal system, nuclear process, micro-magnetohydrodynamic pumps, underground water system, in energy storage units, biological conveyance, and in the thermal energy procedure has played a very important role. Unsteady flow due to the stretching sheet has been scrutinized by Pop and Na [4]. Afterward, Sheridan et al. [5] investigated the significance of variable wall temperature and variable heat flux in the boundary layer flow over the unsteady stretching surface with similarity transformation. An unsteady stagnation point flow of the viscous fluid caused by a stretching sheet under the influence of slip condition has been reported by Bhattacharyya et al. [6]. The impact of the magnetic field on the two-dimensional flow of nano-fluid with and without slip condition was conferred b...

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Section: Finite Element Methods Solutionsmentioning

confidence: 99%

Finite Element Analysis of Thermo-Diffusion and Multi-Slip Effects on MHD Unsteady Flow of Casson Nano-Fluid over a Shrinking/Stretching Sheet with Radiation and Heat Source

et al. 2019

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“…The nonlinear two-point boundary value problem is solved using MAPLE17 which uses the Runge-Kutta-Fehlberg fourth-fifth order numerical algorithm (RKF45). This approach has been extensively implemented in a diverse array of nonlinear multi-physical flow problems in chemical and materials engineering sciences including entropy minimization in magnetic materials processing [39], viscoelastic petroleum flows [40], annular magnetohydrodynamics [41], nano-structural mechanics [42], nanofluid convection flows [43,44] and thermo-capillary convection [45]. The robustness and stability of this numerical method is therefore well established.…”

Section: Numerical Solution By Maple 17mentioning

confidence: 99%

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

Uddin

Bég

Uddin

2016

Energy

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Energy conversion under conjugate conduction, magnetoconvection, diffusion and nonlinear radiation over a nonlinearly stretching sheet with slip and multiple convective boundary conditions Uddin AbstractEnergy 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.

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“…Sohaib et al [32] investigated the multislip impacts of a magneto-hydrodynamic mixed convection unsteady flow of micropolar nanofluid through a stretching sheet on radiation and the heat source. Uddin et al [33] deliberated whether free convective boundary layer flow of nanofluid through an infiltrate would be able to ascend a horizontal plate in permeable medium under thermal convective boundary conditions. Sarafraz et al [34] explored the thermal conductivity, viscosity, and boiling heat transfer coefficient of a biologically produced nano-coolant.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Analysis of Variable Viscosity Impact on MHD Flow and Heat Transfer of Nanofluid Using the Cattaneo–Christov Model

2020

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In this mathematical study, magnetohydrodynamic, time-independent nanofluid flow over a stretching sheet by using the Cattaneo-Christov heat flux model is inspected. The impact of the thermal, solutal boundary and gravitational body forces with the effect of double stratification on the mass flow and heat transfer phenomena is also observed. The temperature-dependent viscosity impact on heat transfer through a moving sheet with capricious heat generation in nanofluids have studied, and the viscosity of the fluid is presumed to deviate as the inverse function of temperature. With the appropriate transformations, the system of partial differential equations is transformed into a system of nonlinear ordinary differential equations. By applying the variational finite element method, the transformed system of equations is solved. The properties of the several parameters for buoyancy, velocity, temperature, stratification, and Brownian motion parameters have examined. The enhancement in the concentration and thermal boundary layer thickness of the nanofluid sheet due to the increment in the viscosity parameter, also increased the temperature and concentration of nanoparticles. Moreover, the fluid temperature declined with the increasing values of thermal relaxation parameter. This displays that the Cattaneo-Christov heat flux model provides a better assessment of temperature distribution. Moreover, confirmation of the code and precision of the numerical method has inveterate with the valuation of the presented results with previous studies.

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Free Convection Boundary Layer Flow from a Heated Upward Facing Horizontal Flat Plate Embedded in a Porous Medium Filled by a Nanofluid with Convective Boundary Condition

Cited by 50 publications

References 32 publications

Finite Element Analysis of Thermo-Diffusion and Multi-Slip Effects on MHD Unsteady Flow of Casson Nano-Fluid over a Shrinking/Stretching Sheet with Radiation and Heat Source

Finite Element Analysis of Thermo-Diffusion and Multi-Slip Effects on MHD Unsteady Flow of Casson Nano-Fluid over a Shrinking/Stretching Sheet with Radiation and Heat Source

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

Finite Element Analysis of Variable Viscosity Impact on MHD Flow and Heat Transfer of Nanofluid Using the Cattaneo–Christov Model

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