A Numerical Method For Studying Impulsively
Generated Convection From Heated Tubes
Author(s)
S. J. D. D’Alessio
Abstract
This study presents a numerical method for solving the two-dimensional unsteady
problem of laminar free convection from a heated tube in an otherwise quiescent
fluid. The governing Navier–Stokes and energy equations are formulated in terms
of the streamfunction and vorticity. The numerical scheme is designed to handle a
large range of Grashof numbers and to capture the physical behaviour inherent in
the initial flow. To numerically solve the governing equations a spectral finitedifference
method is proposed. The temperature and vorticity are advanced in
time using an implicit scheme of Crank-Nicholson type. The streamfunction,
on the other hand, is expanded in a truncated Fourier series. To determine the
surface vorticity exact integral conditions are derived and incorporated into the
numerical method. The numerical results have been verified against derived
analytical solutions which are valid for small times and large Grashof numbers.
The numerical and analytical results are found to be in good agreement.
Keywords: unsteady, laminar, viscous, incompressible, Boussinesq, spectral finitedifference
scheme.
1 Introduction
Free convection from a horizontal two-dimensional body is a fundamental thermal-
fluid problem. It has received numerous numerical, experimental and theoretical
studies over the years. This paper deals with the unsteady behaviour of laminar,
two-dimensional flow caused by free convection from a heated elliptic cylinder
emitting a constant surface heat flux into the surrounding fluid which is initially at
rest. This problem is of interest for both theoretical and practical reasons since it
has important applications in engineering such as heat transfer from heated tubes,
hot wire anemometry, thermal pollution and even in the design of heat exchangers.
Keywords
unsteady, laminar, viscous, incompressible, Boussinesq, spectral finitedifference
scheme.
Related Book
Other papers in this volume
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