Viscous Dissipation and Thermal Radiation Effects on Mixed Convection from a Vertical Plate in a Non-Darcy Porous Medium

Narayana, Mahesha; Khidir, Ahmed A.; Sibanda, Precious; Murthy, P. V. S. N.

doi:10.1007/s11242-012-0096-8

Cited by 9 publications

(14 citation statements)

References 25 publications

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“…Utilizing the Oberbeck‐Boussinesq approximation, continuity, momentum, and nanoparticle concentration equations can be written as (Kairi and Murthy, Narayana et al, and Murthy et al)

\frac{\partial}{\partial x} (r^{m} u) goodbreakinfix+ \frac{\partial}{\partial y} (r^{m} v) goodbreakinfix= 0,

\frac{\partial u}{\partial y} + \frac{c \sqrt{K_{normalp}}}{μ / ρ_{f}} \frac{\partial u^{2}}{\partial y} = \frac{(1 - C_{\infty}) g ρ_{f} K_{p} β \cos γ}{μ} \frac{\partial T}{\partial y} - \frac{(ρ_{normalp} - ρ_{normalf}) g K_{p} \cos γ}{μ} \frac{\partial C}{\partial y},

u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α \frac{\partial^{2} T}{\partial y^{2}} + τ [D_{normalB} {(\frac{\partial T}{\partial y})}^{2} + \frac{D_{T}}{T_{\infty}} true(\frac{\partial T}{\partial y} \frac{\partial C}{\partial y} true)] + \frac{μ}{ρ_{f} K C_{p}} u (u + \frac{ρ_{normalf} c K}{μ} u^{2}) - \frac{1}{ρ c_{p}} \frac{\partial q_{r}}{\partial y},

…”

Section: Problem Formulationmentioning

confidence: 99%

“…The respective temperature and nanoparticle concentrations in the ambient medium are defined as ∞ T and ∞ C , respectively. Utilizing the Oberbeck-Boussinesq approximation, continuity, momentum, and nanoparticle concentration equations can be written as (Kairi and Murthy, 5 Narayana et al, 25 and Murthy et al 36 ) where components of the velocity along x-and y-directions are defined as u and v, respectively. The empirical constant (c) is a function of Forchheimer porous inertia term, K p is the permeability, μ ρ and f are defined as the viscosity and density of the nanofluid, respectively, g is the acceleration due to gravity, ∞ C is the ambient concentration of the nanoparticle, γ is the half angle of the cone with the vertical axis, β is defined by the volumetric thermal expansion coefficient of the nanofluid, τ ε ρc ρc = ( ) /( ) p f , D B and D T are the Brownian diffusion coefficient and the thermophoresis diffusion coefficient, respectively, C p is the specific heat at constant pressure, and ∞ T is the ambient temperature.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The impact of viscous dissipation is also very important in free convective flows at large Rayleigh numbers (Kairi and Murthy and Ishak). Recently, Narayana et al studied the mixed convective Newtonian nanofluid flow over a vertical plate in the presence of thermal radiation and viscous dissipation by considering a vertical plate immersed in a non‐Darcy porous medium. Viscous dissipation can influence the bioconvection due to the presence of gyrotactic microorganisms (Shaw et al).…”

Section: Introductionmentioning

confidence: 99%

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Nanofluid flow over three different geometries under viscous dissipation and thermal radiation using the local linearization method

Shaw

Motsa

Sibanda

2019

Heat Trans. Asian Res.

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This study deals with the transfer of mass and heat of nanofluid flow over three different geometries of the non‐Darcy permeable vertical cone/wedge/vertical plate. Influence of the Brownian motion and thermophoresis takes place due to the nanofluid. Boundary condition on the temperature is introduced at the surface where the thermal conductivity of the fluid obeys a linear relation with the temperature. The local linearization method is introduced for solving the governing equations, and is based on spectral discretization. To verify the numerical scheme, we compared our results with those in the existing literature. The impact of the governing parameters on the fluid velocity, temperature distribution, and concentration distribution of nanoparticles along with the Nusselt number and Sherwood number is discussed. Some important outcomes of the present study are that the Nusselt number is higher for the plane plate than that for the vertical cone and it significantly decreases with introduction of the radiation parameter. The nanofluid Lewis number decreases the diffusivity of mass of the nanofluid, and as a result it helps enhance the Sherwood number.

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“…Utilizing the Oberbeck‐Boussinesq approximation, continuity, momentum, and nanoparticle concentration equations can be written as (Kairi and Murthy, Narayana et al, and Murthy et al)

\frac{\partial}{\partial x} (r^{m} u) goodbreakinfix+ \frac{\partial}{\partial y} (r^{m} v) goodbreakinfix= 0,

\frac{\partial u}{\partial y} + \frac{c \sqrt{K_{normalp}}}{μ / ρ_{f}} \frac{\partial u^{2}}{\partial y} = \frac{(1 - C_{\infty}) g ρ_{f} K_{p} β \cos γ}{μ} \frac{\partial T}{\partial y} - \frac{(ρ_{normalp} - ρ_{normalf}) g K_{p} \cos γ}{μ} \frac{\partial C}{\partial y},

u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α \frac{\partial^{2} T}{\partial y^{2}} + τ [D_{normalB} {(\frac{\partial T}{\partial y})}^{2} + \frac{D_{T}}{T_{\infty}} true(\frac{\partial T}{\partial y} \frac{\partial C}{\partial y} true)] + \frac{μ}{ρ_{f} K C_{p}} u (u + \frac{ρ_{normalf} c K}{μ} u^{2}) - \frac{1}{ρ c_{p}} \frac{\partial q_{r}}{\partial y},

…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nanofluid flow over three different geometries under viscous dissipation and thermal radiation using the local linearization method

Shaw

Motsa

Sibanda

2019

Heat Trans. Asian Res.

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“…Indeed, it has been emphasized by Rees and Magyari and Nield that a mixed or forced‐convection boundary‐layer flow generates heat everywhere when the viscous dissipation is present, including the free stream region outside the boundary layer. For an exhaustive discussion of the mixed convective flow due to a vertical plate immersed in a non‐Darcy porous medium saturated with a Newtonian fluid in the presence of viscous dissipation, the reader is referred to the works of Narayana and colleagues (also see the references cited therein).…”

Section: Introductionmentioning

confidence: 99%

“…Comparison of Dimensionless Similarity Functions θ′(η) for Mixed Convection Along a Vertical Flat Plate in Non-Darcy Porous Medium with Nb → 0, Nt = Nr = 0, ε = 0.1, χ 2 = 1, Re * = 1, and S(η) → 0 (Narayana and colleagues[17]) Effects of modified Reynolds number Re * on (a) velocity, (b) temperature, and (c) volume fraction profiles.…”

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confidence: 99%

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

Rashad

Chamkha

RamReddy

et al. 2013

Heat Trans. Asian Res.

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In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library (http://wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21083

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Mixed Convection

Nield¹,

Bejan²

2017

Convection in Porous Media

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Viscous Dissipation and Thermal Radiation Effects on Mixed Convection from a Vertical Plate in a Non-Darcy Porous Medium

Cited by 9 publications

References 25 publications

Nanofluid flow over three different geometries under viscous dissipation and thermal radiation using the local linearization method

Nanofluid flow over three different geometries under viscous dissipation and thermal radiation using the local linearization method

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

Mixed Convection

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