Free convection from a point source of heat, and heat transfer from spheres at small Grashof numbers
type: Item
instance of: scholarly article
title: Free convection from a point source of heat, and heat transfer from spheres at small Grashof numbers
zbMATH Open document ID: 0973.76083
DOI: 10.1016/S0017-9310(99)00052-6
author: Vadim N. Kurdyumov
author: A. Liñán
published in: International Journal of Heat and Mass Transfer
publication date: 2000-04-27T00:00:00Z
review text: This paper presents an investigation of steady free convection flows due to a point heat source and heated spheres placed in viscous incompressible fluid. The paper starts with the non-dimensionalized formulation of the problem for the point source, and gives numerical solutions for a wide range of Prandtl number. An asymptotic solution is also presented for the temperature, stream function and vorticity near the point source, i.e. for small values of radial coordinate. Other asymptotic solution is obtained for large values of radial coordinate for different Prandtl numbers. The analytical solutions for temperature and flow fields close to the point source include constants which are evaluated numerically, and then are used to describe the flow field around heated spheres for small Grashof numbers, and to perform a correction of Nusselt number, according to the free convection regime, from its pure heat conduction value. This is done by using the matching conditions between the inner heat-conduction-dominated solution and the outer solution for the point heat source. The asymptotic solutions for large and small Grashof numbers allow to derive a correlation equation for Nusselt and Grashof numbers, valid for all values of Grashof number as long as the boundary layer flow is laminar.
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 76M45
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 1436730
zbMATH Keywords: Prandtl number
zbMATH Keywords: Grashof number
zbMATH Keywords: free convection
zbMATH Keywords: point heat source
zbMATH Keywords: heated spheres
zbMATH Keywords: viscous incompressible fluid
zbMATH Keywords: asymptotic solution
zbMATH Keywords: temperature
zbMATH Keywords: stream function
zbMATH Keywords: vorticity
reviewed by: Ioan Pop
MaRDI profile type: Publication
full work available at URL: s0017-9310(99)00052-6
OpenAlex ID: W2041062962
Wikidata QID: Q127782939
description: scientific article; zbMATH DE number 1436730