Heatline visualization of forced convection laminar boundary layers

Morega, Alexandru M.; Bejan, Adrian

doi:10.1016/0017-9310(93)90146-w

Cited by 77 publications

(35 citation statements)

References 11 publications

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“…The duct flow and boundary layer flow versions of this formulation are simpler, because these flow regions are slender [1], and as a consequence v is small when compared with u. In 1993 we showed [7] that Eqs. (3)- (6) are replaced by…”

Section: Heatlinesmentioning

confidence: 94%

“…(3)- (6). Instead, they used the simpler version, from my 1993-1995 work: the duct flow [7,8], Eqs. (7)-(10).…”

Section: Synergymentioning

confidence: 99%

“…Important is that in these reviews one could see Fig. 1: the heatlines in duct flow and boundary layer flow, which I had published with my doctoral student Alexandru Morega in 1993 [7,8]. New heatlines are being published regularly, as shown in the extensive bibliography compiled in the most current publications, for example, Refs.…”

mentioning

confidence: 99%

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Heatlines (1983) versus synergy (1998)

Bejan

2015

International Journal of Heat and Mass Transfer

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a b s t r a c tA picture is worth a thousand words. This article is about a picture known as ''heatlines'' since 1983, and ''synergy'' since 1998. Both concepts, heatlines and synergy, are about visualizing the physics of convection, which is the combination (superposition) of heat conduction lines and enthalpy flow lines over a material in motion. Heatlines and synergy are reviewed here comparatively. This comparison reveals that synergy is a remake of heatlines, and that synergy has no physical connection with heat transfer enhancement. At bottom, it has become a lot easier to take an existing idea change some key words and drawings and publish the old idea as new.

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Section: Heatlinesmentioning

confidence: 94%

“…(3)- (6). Instead, they used the simpler version, from my 1993-1995 work: the duct flow [7,8], Eqs. (7)-(10).…”

Section: Synergymentioning

confidence: 99%

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Heatlines (1983) versus synergy (1998)

Bejan

2015

International Journal of Heat and Mass Transfer

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“…When the temperature profile is fully developed one can write 0 x θ ∂ = ∂ (Bejan [10]). The thermal boundary conditions of Equation (5) …”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Thermal Radiation, Joule Heating, and Viscous Dissipation Effects on MHD Forced Convection Flow with Uniform Surface Temperature

Jamalabadi¹,

Park²

2014

OJFD

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In this paper, we studied the effects of thermal radiation, Joule heating and viscous dissipation on forced convection flow in a magnetohydrodynamics (namely MHD) pump in rectangular channel with uniform surface temperature. Numerical results were obtained by solving the nonlinear governing momentum and energy equations with steady state fully developed assumptions by finite difference method. The Lorentz force in momentum and Joule heating, and viscous dissipation in energy equation with the Rossel and approximation are assumed to increase the knowledge of the details of the temperature and flow field in order to design a MHD pump. The purpose of this study is the parametric study of a Newtonian fluid in a MHD pump. The values of maximum velocity, fully developed Nusselt number for different values of magnetic density flux, Brinkman number, viscous heating and radiation number are obtained. However, the maximum temperature stays almost constant with magnetic field, as current increases, the velocity and the temperature increase too. Besides, the increase of thermal radiation number causes the increase in effective thermal conductivity and decrease in thermal boundary layer and the Nusselt number at wall.

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“…Then, the massline concept was proposed for convective mass transfer problems [2]. Morega and Bejan [3] and Nield and Bejan [4] visualized heatlines in forced convection laminar boundary layers and in porous media, respectively. A review study was reported by Costa [5] to summarize the application of heatline visualization technique in different heat and mass transfer problems.…”

Section: Introductionmentioning

confidence: 99%

Visualization of diffusion and convection heat transport in a square cavity with natural convection

Mobedi

Özkol

Sundén

2010

International Journal of Heat and Mass Transfer

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a b s t r a c tIn this study, the total heatfunction equation which includes diffusion and convection transport is divided into the corresponding heatfunction equations. The superposition rule is used to obtain the mathematical definitions of diffusion and convection heatfunctions and corresponding boundary conditions. It is observed that the separate visualization of diffusion and convection heatlines provides significant information on understanding of the mechanism of heat transfer in a convective flow. The direction of the diffusion and convection heat transport as well as the strength of convection compared to the conduction in entire or in a portion of a domain can be visualized. The diffusion heatlines demonstrate a potential flow like behavior while convective heat flow rotates due to the source term of the convection heatfunction equation, similar to the rotation of fluid flow generated by fluid flow vorticity. The similarity between the streamfunction and the total heatfunction yields a concept of heat flow vorticity, X t . The obtained results show that the maximum absolute value of the convection heatfunction may be an appropriate parameter for determination of the convection strength. The diffusion and convection heatfunction equations for natural convection in a differentially heated square cavity for four different length of the heated surface on the right vertical wall as s p = L/4, L/2, 3L/4 and L and a fixed length of the cooled surface on the right vertical wall as L/4 are obtained and corresponding heatlines are drawn. The values of the conduction heatfunction are positive while the sign of convection heatfunction values is negative for the studied cases. Based on the distribution of total heatlines, two regions are detected in the cavity, an active region with the positive values of heatlines signifying dominant conduction heat transfer and a passive region with the negative heatfunction values in where convection heat flow is dominant and heat only rotates in a closed contour pattern. The variations of average Nusselt number, average of heat flow vorticity, maximum absolute values of convection heatfunction and streamfunction at different Rayleigh numbers and lengths of the heated surface are presented.

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Heatline visualization of forced convection laminar boundary layers

Cited by 77 publications

References 11 publications

Heatlines (1983) versus synergy (1998)

Heatlines (1983) versus synergy (1998)

Thermal Radiation, Joule Heating, and Viscous Dissipation Effects on MHD Forced Convection Flow with Uniform Surface Temperature

Visualization of diffusion and convection heat transport in a square cavity with natural convection

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