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REVIEW ARTICLES

Bejan’s Heatlines and Masslines for Convection Visualization and Analysis

[+] Author and Article Information
V. A. Costa

Departamento de Engenharia Mecânica da Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugalv̱costa@mec.ua.pt

Appl. Mech. Rev 59(3), 126-145 (May 01, 2006) (20 pages) doi:10.1115/1.2177684 History:

Heatlines were proposed in 1983 by Kimura and Bejan (1983) as adequate tools for visualization and analysis of convection heat transfer. The masslines, their equivalent to apply to convection mass transfer, were proposed in 1987 by Trevisan and Bejan. These visualization and analysis tools proved to be useful, and their application in the fields of convective heat and/or mass transfer is still increasing. When the heat function and/or the mass function are made dimensionless in an adequate way, their values are closely related with the Nusselt and/or Sherwood numbers. The basics of the method were established in the 1980(s), and some novelties were subsequently added in order to increase the applicability range and facility of use of such visualization tools. Main steps included their use in unsteady problems, their use in polar cylindrical and spherical coordinate systems, development of similarity expressions for the heat function in laminar convective boundary layers, application of the method to turbulent flow problems, unification of the streamline, heatline, and massline methods (involving isotropic or anisotropic media), and the extension and unification of the method to apply to reacting flows. The method is now well established, and the efforts made towards unification resulted in very useful tools for visualization and analysis, which can be easily included in software packages for numerical heat transfer and fluid flow. This review describes the origins and evolution of the heatlines and masslines as visualization and analysis tools, from their first steps to the present.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Perpendicularity between the isotherms and the heat flux lines in heat conduction

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Figure 3

Physical model and geometry for the work of Kimura and Bejan (3) (reprinted with permission from (3))

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Figure 4

Heatlines in the work of Kimura and Bejan (3), for Pr=7 and (a) Ra=140 and (b) Ra=1.4×105 (reprinted with permission from (3))

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Figure 5

Masslines for the double-diffusive natural convection problem in a square enclosure subjected to constant wall heat and mass fluxes for Ra=3.5×105, Le=1, Pr=7 and (a) N=−4 and (b) N=−0.9 (reprinted with permission from (5))

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Figure 6

Streamlines (right) and heatlines (left) (isotherms are the dashed lines) for the thermogravitational convection in concentric and eccentric annuli, for different values of the Rayleigh number (reprinted with permission from (19))

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Figure 7

Heatlines in a solid sphere subjected to cooling (reprinted with permission from (22))

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Figure 8

Boundary layer in forced convection near a flat plate for a fluid with Pr<1 (top) and for a fluid with Pr>1 (bottom)

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Figure 17

Lines of constant ϕ and lines of constant Φ, normal to each other at any point, near the interface s between media 1 and 2 of different diffusion coefficients (reprinted with permission from (31))

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Figure 18

Physical model and geometry for the analyzed problems involving anisotropic media. The left and right parts of the domain are under different conditions, and they have different properties (reprinted with permission from (32)).

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Figure 19

Streamlines (top), isotherms (center), and heatlines (bottom), for natural convection in a rectangular porous enclosure (left-half of the domain) and pure conduction on the right-half of the domain, for different properties and anisotropic characteristics of the involved media (reprinted with permission from (32))

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Figure 20

Enthalpy lines (solid lines) and streamlines (dashed lines) for a planar hot jet of air issuing into an ambient at lower velocity, under normal gravity conditions (left) and absent gravity conditions (right) (reprinted with permission from (34))

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Figure 21

Mixture fraction lines for nonpremixed planar methane-air jet flames superposed on heat release rate contours, under normal gravity (left), and absent gravity (right). Solid lines for the H element, and dotted lines for the C element. The heat release contours enable the finding of the position of the flame (reprinted with permission from (34)).

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Figure 1

Elementary segment ds=dx2+dy2 crossed by the mass flux Jm

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Figure 9

Heatlines obtained from the similarity solution of the heatfunction for the forced convection near a flat plate, for Pr=7 (a) near a hot isothermal wall and (b) near a cold isothermal wall (reprinted with permission from (23))

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Figure 10

Heatlines obtained from the similarity solution of the heat function for the forced convection near a flat plate, for Pr=0.02 (a) near a hot isothermal wall and (b) near a cold isothermal wall (reprinted with permission from (23)

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Figure 11

Heatlines obtained from the analytical solution of the heat function for the forced convection in a fluid-saturated porous medium inside a channel. (Top) Near a hot isothermal wall and (bottom) near a cold isothermal wall (reprinted with permission from (24)).

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Figure 12

Heatlines obtained from the analytical solution of the heat function for the forced convection of a pure fluid in slug flow inside a channel. (Top) Near a hot wall and (bottom) near a cold wall (reprinted with permission from (24)).

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Figure 13

Boundary layer in natural convection near a vertical flat plate

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Figure 14

Heatlines obtained from the similarity solution of the heat function for the natural convection near a vertical isothermal hot flat plate (left) and vertical isothermal cold flat plate (right) (reprinted with permission from (25))

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Figure 15

Heatlines obtained from the similarity solution of the heat function for the natural convection near a vertical hot flat plate under constant wall heat flux (reprinted with permission from (25))

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Figure 16

Streamlines (top), heatlines (center), and masslines (bottom) for the double-diffusive natural convection in a square enclosure with heat and mass diffusive walls, and opposed buoyancy effects (reprinted with permission from (30))

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