Laminar Free Convection on a Vertical Plate With Prescribed Nonuniform Wall Heat Flux or Prescribed Nonuniform Wall Temperature

Abstract

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-trsmfer 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-taperature variation is prescribed, graphs are presented from which the over-all rate of heat transfer from any lengbh of the plate may be obtained.Another set of graphs is presented for obtatiing 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 K&rm&n-Pohlhausen method.The solution of the resulting equatims 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 Wluence of the nonuniform thermal conditions.The first five terms of the series have been calculated. INTRODU31TIONLsminar free convection on a vertical plate has been a subject of study since 1881.Most of the analytical work has been done for the situation where the wall tempem.ture is uniform over the entire surface.An exact solution of the convection on a vertical boundary-layer differential equations for free flat plate with untiorm wall tanpratuxe is -...