Nonlinear convection at a porous flat plate with application to heat transfer from a dike

Vajravelu, K.; Cannon, John R.; Leto, J.; Semmoum, R.; Nathan, S. Sendhil; Draper, Matthew; Hammock, D.

doi:10.1016/s0022-247x(02)00634-0

Cited by 54 publications

(23 citation statements)

References 6 publications

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“…In nonlinear convection, the density temperature relation is nonlinear which causes a nonlinear convective heat transfer. Further, the nonlinear variation in buoyancy may effect on the flow and heat transfer characteristics (for more details see Barrow and Rao [17] and Vajravelu et al [18]). This physical concept has a wide range of applications in geothermal and engineering such as pore water convection near salt domes, cooling of electric equipment, and the residual warm water discharged from a geothermal power plant.…”

Section: Introductionmentioning

confidence: 99%

Spectral Quasi-linearization Method for Homogeneous-Heterogeneous Reactions on Nonlinear Convection Flow of Micropolar Fluid Saturated Porous Medium with Convective Boundary Condition

RamReddy

Pradeepa

2016

Open Engineering

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Based on the nonlinear variation of density with temperature (NDT) in the buoyancy term, the mixed convection flow along a vertical plate of a micropolar fluid saturated porous medium is considered. In addition, the effect of homogeneous-heterogeneous reaction and convective boundary condition has been taken into account. Using lie scaling group transformations, the similarity representation is attained for the system of partial differential equations, prior to being solved by a spectral quasilinearization method. The results show that in the presence of aiding and opposing flow situations, both the species concentration and mass transfer rate decreases when the strength of homogeneous and heterogeneous reaction parameters are enhanced.

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Section: Introductionmentioning

confidence: 99%

Spectral Quasi-linearization Method for Homogeneous-Heterogeneous Reactions on Nonlinear Convection Flow of Micropolar Fluid Saturated Porous Medium with Convective Boundary Condition

RamReddy

Pradeepa

2016

Open Engineering

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“…Using a parabolic temperature-density relationship, Korovkin and Andrievskii [17] investigated a fully developed free-convective flow above a horizontal linear heat source and on a flat impermeable vertical semi-infinite plate for three types of thermal boundary conditions, namely, an adiabatic surface, a constant temperature, and a constant heat flux on the surface. Vajravelu et al [18] studied the problem of free convection flow at a vertical flat plate embedded in a saturated porous medium in the presence of heat sources (or sinks) with nonlinear density temperature variation. Fluid flow problems involving the nonlinear density temperature variation have been investigated by [19][20][21][22] among others.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Nanofluid Flow over Heated Vertical Surface with Sinusoidal Wall Temperature Variations

Motsa

Awad

Khumalo

2014

Abstract and Applied Analysis

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The nonlinear density temperature variations in two-dimensional nanofluid flow over heated vertical surface with a sinusoidal wall temperature are investigated. The model includes the effects of Brownian motion and thermophoresis. Using the boundary layer approximation, the two-dimensional momentum, heat, and mass transfer equations are transferred to nonlinear partial differential equations form and solved numerically using a new method called spectral local linearisation method. The effects of the governing parameters on the fluid properties and on the heat and nanomass transfer coefficients are determined and shown graphically.

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“…Another physical phenomenon is the case in which the temperature difference between the plate and the ambient fluid may be appreciably large. The nonlinear density temperature variation in the buoyancy force term (for details, see Barrow and Rao 1971;Vajravelu and Sastri 1977;Vajravelu et al 2003) may exert a strong influence on the flow and heat transfer characteristics. This physical concept has number of geothermal and engineering applications.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This is a generalization of Vajravelu et al (2003) to study fluid flow and heat transfer in a porous medium with variable fluid properties. Because of the complexity, unlike in Vajravelu et al (2003) the momentum and energy equations are coupled and highly nonlinear. To reduce the number of independent variables, these coupled nonlinear partial differential equations are reduced to a system of nonlinear ordinary differential equations by a similarity transformation, and the system is solved numerically by an implicit finite difference method known as Keller-Box method.…”

Section: Introductionmentioning

confidence: 99%

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Free Convection Boundary Layer Flow Past a Vertical Surface in a Porous Medium with Temperature-Dependent Properties

et al. 2011

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Numerical solutions for the free convection heat transfer in a viscous fluid at a permeable surface embedded in a saturated porous medium, in the presence of viscous dissipation with temperature-dependent variable fluid properties, are obtained. The governing equations for the problem are derived using the Darcy model and the Boussinesq approximation (with nonlinear density temperature variation in the buoyancy force term). The coupled non-linearities arising from the temperature-dependent density, viscosity, thermal conductivity, and viscous dissipation are included. The partial differential equations of the model are reduced to ordinary differential equations by a similarity transformation and the resulting coupled, nonlinear ordinary differential equations are solved numerically by a second order finite difference scheme for several sets of values of the parameters. Also, asymptotic results are obtained for large values of | f w |. Moreover, the numerical results for the velocity, the temperature, and the wall-temperature gradient are presented through graphs and tables, and are discussed. It is observed that by increasing the fluid variable viscosity parameter, one could reduce the velocity and thermal boundary layer thickness. However, quite the opposite is true with the non-linear density temperature variation parameter.123 978 K. Vajravelu et al.

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Nonlinear convection at a porous flat plate with application to heat transfer from a dike

Cited by 54 publications

References 6 publications

Spectral Quasi-linearization Method for Homogeneous-Heterogeneous Reactions on Nonlinear Convection Flow of Micropolar Fluid Saturated Porous Medium with Convective Boundary Condition

Spectral Quasi-linearization Method for Homogeneous-Heterogeneous Reactions on Nonlinear Convection Flow of Micropolar Fluid Saturated Porous Medium with Convective Boundary Condition

Nonlinear Nanofluid Flow over Heated Vertical Surface with Sinusoidal Wall Temperature Variations

Free Convection Boundary Layer Flow Past a Vertical Surface in a Porous Medium with Temperature-Dependent Properties

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