Utilizing the Integral Technique for Obtaining a New Dimensionless Group for Prandtl Number Dependence for Natural Convection Heat Transfer From an Isothermal Vertical Flat Plate

Abstract

Research is presented in this paper where the integral technique is utilized to find a primary dimensionless group for natural convection heat transfer from an isothermal vertical flat plate. The discovery of this group from fundamental principles demonstrates the value of the chronologically mature integral technique even in this advanced era where numerical techniques are much more prevalent. The integral solution in the current research compares very favorably with experimental data for a wide range of Prandtl numbers, and also with several numerical models in the archival literature as well as empirical correlations. The good agreement, coupled with the closed-form nature of the solutions, should once again affirm the usefulness of the integral technique as a research as well as an educational tool. The result of the research in this paper is the discovery of a fundamental parameter for Prandtl number dependence in the case of natural convection from an isothermal flat plate. With this fundamental parameter, the Prandtl number dependence is effectively linearized over the entire range of data available, and a simple empirical correlation derived, whose general form may be used for other geometries.