Exact solution of the problem of convective heat exchange for a circular cylinder at small Prandtl numbers
type: Item
instance of: scholarly article
title: Exact solution of the problem of convective heat exchange for a circular cylinder at small Prandtl numbers
zbMATH Open document ID: 0824.76081
DOI: 10.1007/BF02330612
author: A. V. Kashevarov
published in: Fluid Dynamics
publication date: 1995-06-29T00:00:00Z
review text: The problem of the heat exchange of a circular cylinder in an incompressible flow at small Prandtl numbers \(\text{Pr}\ll 1\) is solved. The solution is expressed in terms of Mathieu functions. The isotherm patterns, the distribution of the local Nusselt number Nu along the cylinder surface for different Péclet numbers \(\text{Pe}\leq 10\), and the dependence of the average Nusselt number \(\langle\text{Nu}\rangle\) on Pe are given. A comparison is made between the Nusselt numbers Nu and the temperature profiles in the neighborhood of the windward stagnation point, obtained by solving the energy equation and the equation of the thermal boundary layer. The thermal boundary layer equation is shown to be appropriate for calculating the heat transfer at the windward stagnation point for \(\text{Pr}\ll 1\) and \(\text{Pe}\gtrsim O(1)\).
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 766922
zbMATH Keywords: incompressible flow
zbMATH Keywords: Mathieu functions
zbMATH Keywords: isotherm patterns
zbMATH Keywords: local Nusselt number
zbMATH Keywords: average Nusselt number
zbMATH Keywords: stagnation point
zbMATH Keywords: energy equation
zbMATH Keywords: thermal boundary layer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02330612
OpenAlex ID: W4254655295
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description: scientific article; zbMATH DE number 766922