Natural convection flow of second-grade fluid along a vertical heated surface with variable heat flux

Mustafa, Naeem; Asghar, S.; Hossain, M. A.

doi:10.1016/j.ijheatmasstransfer.2010.07.060

Cited by 20 publications

(6 citation statements)

References 24 publications

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“…The boundary layer flows of non-Newtonian fluids in the presence of heat transfer have relevance in food engineering, petroleum production, power engineering and in industrial processes including polymer melt and polymer solutions used in the plastic processing industries. Some recent studies on the topic can be seen in Labropulu et al (2010), Sahoo (2011), Mustafa et al (2010), , , , Makinde and Aziz (2011), Sahoo and Poncet (2011), Abbas et al (2010), Hsiao (2011) and . It is noted that most studies in the literature discussed the two-dimensional boundary layer flows when heat transfer characteristics are restricted to two boundary conditions of either prescribed temperatures or heat flux at the surface.…”

Section: Introductionmentioning

confidence: 99%

Study on three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions

Hayat¹

2012

Int. J. Phys. Sci.

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Three-dimensional flow of non-Newtonian fluid induced by a stretching surface has been studied. The constitutive equations of Maxwell fluid are used. The surface possesses convective boundary conditions. Computations have been carried out for the non-linear problem. Convergence of the obtained solutions is discussed. Impact of the influential parameters involved in the heat transfer analysis is emphasized. Comparison with the previous results is shown. It is found that effects of Deborah and Biot parameters on the Nusselt number are opposite. The Prandtl and Biot numbers have qualitative similar impact on the Nusselt number.

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Section: Introductionmentioning

confidence: 99%

Study on three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions

Hayat¹

2012

Int. J. Phys. Sci.

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“…They have noted that the effect of elasticity on Nusselt number depends on the value of Weissenberg number. Also, a set of studies [7][8][9][10] have been done for viscoelastic second-grade fluids in different geometries. It has been noticed that the elasticity is considered as a resistance force, which trends to depreciate heat transfer within the flow and decelerate the fluid motion.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Natural Convection for Generalized Second-Grade Fluids Confined in a Square Cavity Subjected to Horizontal Heat Flux

Daghab¹,

Kaddiri²,

Raghay³

et al. 2021

IJHT

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Two-dimensional steady laminar natural convection of a viscoelastic fluid represented by generalized second-grade fluid model in a square enclosure is studied. The cavity is submitted at its vertical sides to a uniform density of heat flux while the horizontal walls are insulated, without slipping conditions at all the solid boundaries. The governing conservation and constitutive equations with the corresponding boundary conditions are solved by finite volume method in a collocated grid system. The contributions of shear rate dependent and elastic characteristics of the viscoelastic fluid are investigated on momentum and heat transport. The effects of elastic number (E) in the range 0 - 1 on heat transfer and fluid motion are interpreted for a power-law index (n) in the range 1.4 - 0.6 and nominal values of Rayleigh number (Ra) range of 103 to 105.

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“…Tsai and Huang [32] obtained the solutions for heat and mass transfer from steady natural convection flow along a vertical surface with variable heat fluxes embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. Mustafa, Asghar, and Hossain [33] studied the effects of steady natural convection flow of a viscoelistic second-grade fluid along vertical plate with a spatially varied heat flux. Palani and Kim [34] carried out a numerical study to examine the heat transfer characteristics of the unsteady natural convection past a vertical cone subjected to variable surface heat flux under the combined effects of magnetic field and thermal radiation.…”

Section: Introductionmentioning

confidence: 99%

Scalings for unsteady natural convection boundary layers on an evenly heated plate with time-dependent heating flux

Lin

Armfield

2013

Phys. Rev. E

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It is of fundamental significance, especially with regard to application, to fully understand the flow behavior of unsteady natural convection boundary layers on a vertical plate heated by a time-dependent heat flux. Such an understanding is currently scarce. In this paper, the scaling analysis by Lin et al. [Phys. Rev. E 79, 066313 (2009)] using a simple three-region structure for the unsteady natural convection boundary layer of a homogeneous Newtonian fluid with Pr>1 under isothermal heating was substantially extended for the case when the heating is due to a time-varying sinusoidal heat flux. A series of scalings was developed for the thermal boundary thickness, the plate temperature, the viscous boundary thicknesses, and the maximum vertical velocity within the boundary layer, which are the major parameters representing the flow behavior, in terms of the governing parameters of the flow, i.e., the Rayleigh number Ra, the Prandtl number Pr, and the dimensionless natural frequency f(n) of the time-varying sinusoidal heat flux, at the start-up stage, at the transition time scale which represents the ending of the start-up stage and the beginning of the transitional stage of the boundary-layer development, and at the quasi-steady stage. These scalings were validated by comparison to 10 full numerical solutions of the governing equations with Ra, Pr, and f(n) in the ranges 10(6)≤Ra≤10(9), 3≤Pr≤100, and 0.01≤f_{n}≤0.1 and were shown in general to provide an accurate description of the flow at different development stages, except for high-Pr runs in which a further, although weak, Pr dependence is present, which cannot be accurately predicted by the current scaling analysis using the simple three-region structure, attributed to the non-boundary-layer nature of the velocity field with high-Pr fluids. Some scalings at the transition time scale and at the quasi-steady stage also produce noticeable deviations from the numerical results when f(n) is reduced, indicating that there may be a further f(n) dependence of the scalings which also cannot be accurately predicted by the current scaling analysis.

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Natural convection flow of second-grade fluid along a vertical heated surface with variable heat flux

Cited by 20 publications

References 24 publications

Study on three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions

Study on three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions

Numerical Study of Natural Convection for Generalized Second-Grade Fluids Confined in a Square Cavity Subjected to Horizontal Heat Flux

Scalings for unsteady natural convection boundary layers on an evenly heated plate with time-dependent heating flux

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