On analytical solution of stationary two dimensional boundary problem of natural convection

AbstractApproximate analytical solution of two dimensional problem for sta-tionary Navier-Stokes, continuity and Fourier-Kirchho equations describ-ing free convective heat transfer from isothermal surface of half in nitevertical plate is presented. The problem formulation is based on the typ-ical for natural convection assumptions: the uid noncompressibility andBoussinesq approximation. We also assume that orthogonal to the platecomponent of velocity is small. Apart from the basic equations it includesboundary conditions: the constant temperature and zero velocity on theplate. At the starting point of the ow we x average temperature andvertical component of velocity, as well as basic conservation laws in in-tegral form. The solution of the boundary problem is represented as aTaylor Series in horizontal variable with coecients depending on verticalvariable. 1 Introduction The results of theoretical and experimental study of free convective ows fromheating objects are widely published and they are very useful to determineconvective heat losses from apparatus, devices, pipes in industrial or energeticinstallations, electronic equipment, architectonic objects and so on by engineersand designers.The problem of convective ow development traditionally is based either onboundary layer theory or on self-similarity theory [1], [2], [3]. Both methodsof natural convection heat transfer description use simpli cations that allow totransform the basic fundamental equations of Navier-Stokes, mass and Fourier-Kirchho equations. As a main point of the methods is an ordinary di erential1