TAILIEUCHUNG - Heat Transfer Handbook part 57

Heat Transfer Handbook part 57. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | 552 NATURAL CONVECTION Figure a Typical vertical rectangular enclosure b calculated isotherms for Pr at Ra 2 x 104. From Elder 1966. At small values of Ra Ra 1000 there is little increase in the heat transfer over that due to conduction alone for which the Nusselt number Nu hd k 1. However as Ra increases several flow regimes have been found to occur resulting in a significant increase in the Nusselt number. In laminar flow these regimes include the conduction transition and boundary layer regimes. The conduction regime is characterized by a linear temperature variation in the central region of the enclosure. In the boundary layer regime thin boundary layers appear along the vertical walls with horizontal temperature uniformity between the two layers. In the transition regime the two boundary regions are thicker and the isothermal interior region does not appear. The characteristics are seen clearly in Figs. and . As Ra increases further secondary flows appear as characterized by additional cells in the flow and transition to turbulence occurs at still higher Ra. Detailed studies of the different flow regimes and the corresponding heat transfer have been carried out along with threedimensional transport for wide ranges of the governing parameters as reviewed by Gebhart et al. 1988 . An interesting solution was obtained by Batchelor 1954 for large aspect ratios H d ro. The flow can then be assumed to be fully developed with the velocity and temperature as functions only of the horizontal coordinate y. This problem can be solved analytically to yield the velocity U and temperature 0 distributions as U Ra Y 1 12 v - Y 1 - 2Y and 0 1 - Y b c Figure Measured temperature distributions in air in a vertical rectangular enclosure a conduction regime b transition regime c boundary layer regime. From Eckert and Carlson 1961. 553 554 NATURAL CONVECTION Ra X 104 Ra X 105 Ra X 105 Ra X 106 1 yld Figure Measured velocity .

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