An Equation for Laminar Flow Heat Transfer for Constant Heat Flux Boundary Condition in Ducts of Arbitrary Cross-Sectional Area

Yılmaz, Tuncay; Cihan, Ertuğrul

doi:10.1115/1.2822644

Cited by 21 publications

(6 citation statements)

References 6 publications

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“…The equations for converting between w k and w k [Equation (28)] and between c k and w k [Equation (29)] are used extensively in subsequent sections.…”

Section: Quadratic Spline Interpolationmentioning

confidence: 99%

“…The evaluated boundary integral equation in equation (32) contains three vectors of unknowns, w k , w k and c k . The latter two, however, can be expressed in terms of w k by using the quadratic spline relations of equations (28) and (29). By applying equation (32) to each boundary node, we arrive at a system of equations in matrix form…”

Section: Regular Integrationmentioning

confidence: 99%

See 1 more Smart Citation

A complex‐variable boundary element approach to fully developed flow and heat transfer in ducts of general cross‐section

Fisher

Torrance

1999

Int. J. Numer. Meth. Engng.

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SUMMARYThe complex-variable boundary element method (CVBEM) is used to analyse forced convection in cooling passages with general, convex cross-sections. Quadratic spline interpolation is employed for the modelling of coupled velocity and temperature ÿelds. The method is well-suited for ducts with curved surfaces and high geometric aspect ratios. The method is illustrated for ducts with rounded rectangular, elliptical and rounded diamond cross-sections. General correlations are presented for the fully developed Nusselt number and Moody friction factor, and the Hagenbach entrance region factor.

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“…The equations for converting between w k and w k [Equation (28)] and between c k and w k [Equation (29)] are used extensively in subsequent sections.…”

Section: Quadratic Spline Interpolationmentioning

confidence: 99%

Section: Regular Integrationmentioning

confidence: 99%

A complex‐variable boundary element approach to fully developed flow and heat transfer in ducts of general cross‐section

Fisher

Torrance

1999

Int. J. Numer. Meth. Engng.

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“…The BGK model automatically considers the gas slip effects [12]. Investigations on flows in an unconventional porous medium utilize the same procedure, and the Velocity slips are considered only at object surfaces [11,[13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

Zhang

Cai

2019

Fluids

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This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

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“…The Leveque solution was combined by Churchill and Ozoe [16,17]. For the Graetz problem, and in order to predict the thermal characteristics in an arbitrary form of the tube, models have been developed by Yilmaz and Cihan [18,19]. These two authors developed models for uniform wall flow conditions (H) and a uniform wall temperature (T) in order to predict the fully developed number of Nusselt.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution and numerical approaches of the generalized LevÃ¨que equation to predict the thermal boundary layer

Belhocine

Omar

2019

ACI

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In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge-Kutta fourth order (RK4) method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail.

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An Equation for Laminar Flow Heat Transfer for Constant Heat Flux Boundary Condition in Ducts of Arbitrary Cross-Sectional Area

Cited by 21 publications

References 6 publications

A complex‐variable boundary element approach to fully developed flow and heat transfer in ducts of general cross‐section

A complex‐variable boundary element approach to fully developed flow and heat transfer in ducts of general cross‐section

Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

Analytical solution and numerical approaches of the generalized LevÃ¨que equation to predict the thermal boundary layer

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