Non-Similar Computational Solutions for Free Convection Boundary-Layer Flow of a Nanofluid from an Isothermal Sphere in a Non-Darcy Porous Medium

Prasad, V. Ramachandra; Gaffar, S. Abdul; Bég, O. Anwar

doi:10.1166/jon.2015.1149

Cited by 25 publications

(17 citation statements)

References 2 publications

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“…(12), the boundary layer Eqs. (5) - (7) reduce to the following coupled, parabolic, nonlinear, dimensionless partial differential equations for momentum, energy and mass for the regime:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The mathematical models in non-Newtonian fluids are more complicated and relate the shear stresses to the velocity field [1]. Few non-Newtonian transport modeling include Casson non-Newtonian fluids [2], oblique micropolar stagnation flows [3], Walter's viscoelastic flows [4], Jeffrey's viscoelastic boundary layers [5], magnetized Williamson fluids [6], nanofluid transport from a sphere [7], Maxwell fluids [8] Eyring-Powell fluid [9], Tangent Hyperbolic fluid [10] and Jeffery Nano fluid [11][12].…”

Section: Introductionmentioning

confidence: 99%

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Radiative and magnetohydrodynamics flow of third-grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

Gaffar¹,

Prasad

Bég

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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R a di a tiv e a n d m a g n e t o hy d r o dy n a mi c s flo w of t hi r d g r a d e vis c o el a s ti c flui d p a s t a n iso t h e r m al inv e r t e d c o n e in t h e p r e s e n c e of h e a t g e n e r a tio n/ a b s o r p tio n ABSTRACT A mathematical analysis is presented to investigate the nonlinear, isothermal, steady-state, free convection boundary layer flow of an incompressible third grade viscoelastic fluid past an isothermal inverted cone in the presence of magnetohydrodynamic, thermal radiation and heat generation/absorption. The transformed conservation equations for linear momentum, heat and mass are solved numerically subject to the realistic boundary conditions using the second-order accurate implicit finite-difference Keller Box Method. The numerical code is validated with previous studies. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low-density polymer materials processing.

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“…(12), the boundary layer Eqs. (5) - (7) reduce to the following coupled, parabolic, nonlinear, dimensionless partial differential equations for momentum, energy and mass for the regime:…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Radiative and magnetohydrodynamics flow of third-grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

Gaffar¹,

Prasad

Bég

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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“…However external boundary layer convection flows also find applications in many technological systems including enrobing polymer coating processes, heat exchanger design, solar collector architecture etc. Prasad et al (2015) studied two-dimensional nanofluid boundary layer flow from a spherical geometry embedded in porous media with a finite difference scheme. Mahesh and Reddy (2015) studied natural convection flow of a non-Newtonian nanofluid past a sphere.…”

Section: Frontiers In Heat and Mass Transfermentioning

confidence: 99%

Mathematical Study of Non-Newtonian Nanofluid Transport Phenomena From an Isothermal Sphere

Nagendra¹,

Amanulla²,

Reddy³

et al. 2017

Frontiers in Heat and Mass Transfer

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In this article, the heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from an isothermal sphere surface is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. Casson fluid parameter (β), Buoyancy ratio parameter (N), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le) and Prandtl number (Pr) on velocity, temperature and nano-particle concentration distributions are illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tridiagonal method has been included.

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“…A transverse static uniform strength magnetic field is applied, which is sufficiently weak to negate magnetic induction and Hall current effects. The nanofluid is dilute and comprises a homogenous suspension of equallysized nanoparticles in thermal equilibrium [35]. The sheet is stretched in the plane 0 y  .…”

Section: Mathematical Flow Modelmentioning

confidence: 99%

Magneto-nanofluid flow with heat transfer past a stretching surface for the new heat flux model using numerical approach

Akbar

Bég

Khan

2017

HFF

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Sheet processing of magnetic nanomaterials is emerging as a new branch of smart materials manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, herein we develop a mathematical model for steady, laminar, magnetohydrodynamic, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant strength magnetic field is applied transverse to the plane of the stretching flow. The Buonjiornio nanofluid model is employed to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo-Christov) model is deployed to simulate thermal conduction effects of which the Fourier model is a special case when thermal relaxation effects are neglected. The governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth order Runge-Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nano-particle concentration distributions is investigated. A strong elevation in temperature accompanies an increase in Brownian motion parameter whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nano-particle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model.

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Non-Similar Computational Solutions for Free Convection Boundary-Layer Flow of a Nanofluid from an Isothermal Sphere in a Non-Darcy Porous Medium

Cited by 25 publications

References 2 publications

Radiative and magnetohydrodynamics flow of third-grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

Radiative and magnetohydrodynamics flow of third-grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

Mathematical Study of Non-Newtonian Nanofluid Transport Phenomena From an Isothermal Sphere

Magneto-nanofluid flow with heat transfer past a stretching surface for the new heat flux model using numerical approach

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