Natural convection from narrow horizontal plates at moderate Rayleigh numbers

Abstract The present work deals with the natural convection flow and heat transfer from a horizontal plate cooled from above. Experiments are carried out for rectangular plates having aspect ratios between φ=0.036 and 0.43 and Rayleigh numbers in the range 290⩽Raw⩽3.3×105. These values of Raw and φ have been selected below those commonly considered in previous research in view of a future application to the design of printed circuit boards. The plates are made of two different metals, copper and steel. The choice of a metal is relevant to the present problem because the plates are heated by means of an electric current. Important variations of the surface temperature are observed along the transverse direction for the steel plates. The surface of the copper plates is almost isothermal because of the high thermal conductivity of the metal. Calculations for a semi-infinite plate are carried out to predict the transverse profiles of the surface temperature and heat flux and to visualize the structure of the flow. Three-dimensional calculations are also used at a qualitative level to observe the changes in the flow structure due to the finite length of the plate. Present results are compared with both previous experimental work and analyses that are based on boundary layer theory. It is shown that analyses for an infinite boundary layer are not completely applicable to the present problem because of its different physics. The most relevant feature of the natural convection flow, which is not predicted by boundary layer analyses, is a thermal plume rising near the center of the plate. Present heat transfer results differ from previous experimental work because of the lower Rayleigh numbers and aspect ratios investigated here. The Nusselt number is found to depend on Rawn, with the exponent n=0.17 being lower than most of the values reported in the literature. This comparatively low value is related to the transverse conduction of heat through the air, which becomes increasingly significant as Raw approaches zero. It is shown that such a low-Raw effect can be accounted for in a physically consistent manner by adding a constant term to the heat transfer correlation. On the other hand, it is found that the Nusselt number does not significantly depend on the aspect ratio in the range of φ investigated contrary to what has been previously reported for wider plates.

[1]  F. J. Sanchez,et al.  ESTIMA: A Thermal Simulation Software For The Optimal Design OfPrinted Circuit Board In The Automotive Industry , 2000 .

[2]  R. J. Goldstein,et al.  Natural convection mass transfer adjacent to horizontal plates , 1973 .

[3]  L. Burmeister.  Convective heat transfer , 1983 .

[4]  M. Al-Arabi,et al.  Natural convection heat transfer from isothermal horizontal plates of different shapes , 1976 .

[5]  Yogesh Jaluria,et al.  Natural Convection: Heat and Mass Transfer , 1980 .

[6]  W. Yousef,et al.  Free Convection Heat Transfer From Upward-Facing Isothermal Horizontal Surfaces , 1982 .

[7]  B. Gebhart,et al.  ON THE STABILITY OF NATURAL CONVECTION BOUNDARY LAYER FLOW OVER HORIZONTAL AND SLIGHTLY INCLINED SURFACES , 1973 .

[8]  Stuart W. Churchill,et al.  Correlating equations for laminar and turbulent free convection from a horizontal cylinder , 1975 .

[9]  T. Yuge,et al.  Experiments on Heat Transfer From Spheres Including Combined Natural and Forced Convection , 1960 .

[10]  Zeev Rotem,et al.  Natural convection above unconfined horizontal surfaces , 1969, Journal of Fluid Mechanics.

[11]  B. Chambers,et al.  A Numerical Study of Local and Average Natural Convection Nusselt Numbers for Simultaneous Convection Above and Below a Uniformly Heated Horizontal Thin Plate , 1997 .

[12]  Frank P. Incropera,et al.  Convection heat transfer in electronic equipment cooling , 1988 .

[13]  K. Hassan,et al.  Natural convection from isothermal flat surfaces , 1970 .

[14]  Ephraim M Sparrow,et al.  Local and average natural convection Nusselt numbers for a uniformly heated, shrouded or unshrouded horizontal plate , 1986 .

[15]  J. Lloyd,et al.  Natural Convection Adjacent to Horizontal Surface of Various Planforms , 1974 .

[16]  S. Churchill,et al.  Correlating equations for laminar and turbulent free convection from a vertical plate , 1975 .

[17]  俊夫 阿部,et al.  加熱された水平上向き面上の自然対流 : 第2報,流れ場の乱れと熱伝達率 , 1977 .

[18]  V. Morgan.  The Overall Convective Heat Transfer from Smooth Circular Cylinders , 1975 .

[19]  J. Humphrey,et al.  Non-isothermal laminar flow and heat transfer between disks corotating in a fixed enclosure , 1999 .

[20]  Dino J. Farina,et al.  A system for making temperature measurements using thermochromic liquid crystals , 1994 .

[21]  M. Fishenden,et al.  An Introduction To Heat Transfer , 1950 .

[22]  Hideaki Imura,et al.  Natural-convection heat transfer from a plate with arbitrary inclination , 1972 .

[23]  Fumiyoshi Kimura,et al.  Heat transfer and fluid flow of natural convection adjacent to upward-facing horizontal plates , 1995 .

[24]  J. Humphrey,et al.  Unsteady laminar flow between a pair of disks corotating in a fixed cylindrical enclosure , 1995 .

[25]  Witold M. Lewandowski,et al.  Free convection heat transfer and fluid flow above horizontal rectangular plates , 2000 .