Free convection on an arbitrarily inclined plate with uniform surface heat flux

Lin, Heng-Kuang; Yu, W. S.; Yang, Shih-Cheng

doi:10.1007/bf01590018

Cited by 15 publications

(14 citation statements)

References 11 publications

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“…In this figure, small and large results are obtained from the relations given in (19) and (20), respectively, whereas the curves for the intermediate region are obtained through (18). It is anticipated from the figure below that small, large, and all curves matches well for precise range of locally varying parameter .…”

Section: Resultsmentioning

confidence: 78%

“…The dimensionless boundary layer equations are transformed into suitable form for numerical integration. An efficient It is worthy to mention that present numerical results are also compared with Samanta and Guha [14], Mehrizi et al [15], Deswita et al [16], Raju et al [17], and Lin et al [18] for = 0.0 and = 0.0 and are entered in Tables 1 and 2. These tables contain the comparison of (0) and (0) for different Prandtl number, Pr.…”

Section: Resultsmentioning

confidence: 99%

“…Rest of the analysis is done by taking results from the relations (18). In Figure 3 the effect of phase shift parameter, , is shown on the coefficients of local skin friction and local Nusselt numbers.…”

Section: Resultsmentioning

confidence: 99%

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Natural Convection Flow over Wavy Horizontal Surface

Siddiqa

Hossain

2013

Advances in Mechanical Engineering

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In this paper boundary layer analysis is performed over a heated horizontal wavy surface. The governing boundary layer equations are transformed into parabolic partial differential equations with the help of appropriate coordinate transformation. Parabolic partial differential equations are then solved numerically with finite difference scheme, seeking details of the momentum and energy fields.Step by step computations are done for the upstream, downstream, and entire regimes. The numerical results are thoroughly discussed in terms of local skin friction and local Nusselt number coefficients for various parameters, like phase shift parameter, , and amplitude of the wavy surface, . In addition, streamlines and isotherms are also drawn in order to visualize velocity and temperature distributions, respectively, within the boundary layer region.

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Section: Resultsmentioning

confidence: 78%

Section: Resultsmentioning

confidence: 99%

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Natural Convection Flow over Wavy Horizontal Surface

Siddiqa

Hossain

2013

Advances in Mechanical Engineering

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“…It may be noted to this end that important contributions to the problem of free convection from arbitrarily inclined plate in a viscous (non-porous) fluid were made by Yu and Liu [8], Lin et al [9], and Umemura and Law [10].…”

Section: Introductionmentioning

confidence: 98%

Free convection from an arbitrarily inclined plate in a porous medium

Pop

1996

Heat and Mass Transfer

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A mathematical model for the flow and heat transfer in the free convection from an arbitrary inclined isothermal flat plate embedded in a porous medium is presented, in which the Darcy-Boussinesq approximation is adopted to account for bouyancy force. A novel inclination parameter is proposed such that all cases of the horizontal, inclined and vertical plates can be described by a single set of transformed boundary layer equations. Moreover, the similarity equations for the limiting cases of the horizontal and vertical plates are recovered from the transformed equations by setting :0 and :1, respectively. Detailed results for the skin friction coefficient and Nusselt number as well as for the dimensionless velocity and temperature profiles are presented for a wide range of the parameter. A comparison with similarity solution shows excellent agreement.

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“…Experimental and numerical studies of laminar natural convection from a finite, isothermal horizontal plate have been presented by Fujii and Imura [7], Goldstein and Lau [8] and Clifton and Chapman [9]. Numerical study of laminar free convection heat transfer above an upward facing semi-infinite horizontal heated plate was provided by Yu and Lin [10], Lin et al [11] and Pretot et al [12]. Mahajan and Gebhart [13], Pera and Gebhart [14] and Afzal [15] have considered higher order boundary layer effects of natural convection flow over horizontal surfaces.…”

Section: Introductionmentioning

confidence: 99%

Closed-Form Analytical Solutions for Laminar Natural Convection on Horizontal Plates

Guha¹,

Samanta

2013

Journal of Heat Transfer

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A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T¯w(x¯)-T¯∞=ax¯n whereas the heat flux is assumed to vary according to qw(x¯)=bx¯m. Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr ≤ 1 or Pr ≈ 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.

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Free convection on an arbitrarily inclined plate with uniform surface heat flux

Cited by 15 publications

References 11 publications

Natural Convection Flow over Wavy Horizontal Surface

Natural Convection Flow over Wavy Horizontal Surface

Free convection from an arbitrarily inclined plate in a porous medium

Closed-Form Analytical Solutions for Laminar Natural Convection on Horizontal Plates

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