Bifurcation in steady laminar mixed convection flow in horizontal ducts

K. Nandakumar; Jacob H. Masliyah; Hin Sum Law

doi:10.1017/S0022112085000611

Bifurcation in steady laminar mixed convection flow in horizontal ducts

K. Nandakumar, Jacob H. Masliyah, Hin Sum Law

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Abstract

The fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition. Dual solutions with a two- and a four-vortex flow pattern have been observed in all cases. The rectangular geometry, with its aspect ratio and Grashof number as parameters, is posed as a two-parameter problem. In this parameter-space, the critical points where the transition between the two- and the four-vortex pattern occur, follow a tilted cusp. This is akin to the phenomenon in the Taylor problem which has been thoroughly investigated by Benjamin and co-workers in a general study of bifurcation phenomena for viscous flow problems. The bifurcation phenomenon in circular ducts, which is essentially a one-parameter problem, has features similar to that observed for the Dean problem, by Nandakumar and Masliyah.

Original language	English
Pages (from-to)	145-161
Number of pages	17
Journal	Journal of Fluid Mechanics
Volume	152
DOIs	https://doi.org/10.1017/S0022112085000611
State	Published - Mar 1985
Externally published	Yes

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title = "Bifurcation in steady laminar mixed convection flow in horizontal ducts",

abstract = "The fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition. Dual solutions with a two- and a four-vortex flow pattern have been observed in all cases. The rectangular geometry, with its aspect ratio and Grashof number as parameters, is posed as a two-parameter problem. In this parameter-space, the critical points where the transition between the two- and the four-vortex pattern occur, follow a tilted cusp. This is akin to the phenomenon in the Taylor problem which has been thoroughly investigated by Benjamin and co-workers in a general study of bifurcation phenomena for viscous flow problems. The bifurcation phenomenon in circular ducts, which is essentially a one-parameter problem, has features similar to that observed for the Dean problem, by Nandakumar and Masliyah.",

author = "K. Nandakumar and Masliyah, {Jacob H.} and Law, {Hin Sum}",

year = "1985",

month = mar,

doi = "10.1017/S0022112085000611",

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volume = "152",

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journal = "Journal of Fluid Mechanics",

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T1 - Bifurcation in steady laminar mixed convection flow in horizontal ducts

AU - Nandakumar, K.

AU - Masliyah, Jacob H.

AU - Law, Hin Sum

PY - 1985/3

Y1 - 1985/3

N2 - The fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition. Dual solutions with a two- and a four-vortex flow pattern have been observed in all cases. The rectangular geometry, with its aspect ratio and Grashof number as parameters, is posed as a two-parameter problem. In this parameter-space, the critical points where the transition between the two- and the four-vortex pattern occur, follow a tilted cusp. This is akin to the phenomenon in the Taylor problem which has been thoroughly investigated by Benjamin and co-workers in a general study of bifurcation phenomena for viscous flow problems. The bifurcation phenomenon in circular ducts, which is essentially a one-parameter problem, has features similar to that observed for the Dean problem, by Nandakumar and Masliyah.

AB - The fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition. Dual solutions with a two- and a four-vortex flow pattern have been observed in all cases. The rectangular geometry, with its aspect ratio and Grashof number as parameters, is posed as a two-parameter problem. In this parameter-space, the critical points where the transition between the two- and the four-vortex pattern occur, follow a tilted cusp. This is akin to the phenomenon in the Taylor problem which has been thoroughly investigated by Benjamin and co-workers in a general study of bifurcation phenomena for viscous flow problems. The bifurcation phenomenon in circular ducts, which is essentially a one-parameter problem, has features similar to that observed for the Dean problem, by Nandakumar and Masliyah.

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JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -

Bifurcation in steady laminar mixed convection flow in horizontal ducts

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