Laminar Free Convection on a Vertical Plate with Prescribed Nonuniform Wall Heat Flux or Prescribed Nonuniform Wall Temperature
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS CLEVELAND OH CLEVELAND
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An analysis is made for laminar free with nonuniform thermal conditions at the are considered for the wall heat flux and convection on a vertical plate surface. Prescribed variations for the wall temperature. For the situation where the wall-heat-flux variation is prescribed, graphs are presented from which the resulting wall-temperature variation may be obtained. Local heat-transfer coefficients may be readily determined using the information given on the graphs. Results for the important special case of uniform wall heat flux are also given. For the situation where the wall-temperature variation is prescribed, graphs are presented from which the over-all rate of heat transfer from any length of the plate may be obtained. Another set of graphs is presented for obtaining local heat-transfer coefficients. KU. the aforementioned results are given for fluids having Prandtl numbers h the range 0.01 to 1000. The flow is taken to be of the boundary-layer type, and the problem is formulated by the Karman-Pohlhausen method. The solution of the resulting equations is achieved by series expansion. The first term of the series corresponds to the result for uniform thermal conditions on the wall. The succeeding terms give the influence of the nonuniform thermal conditions. The first five terms of the series have been calculated.