SESSION 11

COMPUTATIONAL HEAT TRANSFER


INTEGRAL TRANSFORMS IN TRANSIENT CONVECTION:
- BENCHMARKS AND ENGINEERING SIMULATIONS

Renato M. Cotta
Laboratório de Transmissão e Tecnologia do Calor - LTTC
Mechanical Engineering Dept. - Universidade Federal do Rio de Janeiro
EE/COPPE/UFRJ
Cidade Universitária - Cx. Postal 68503 - Rio de Janeiro, RJ - 21945.970 - Brasil

This paper reviews the solution of linear and nonlinear transient convection-diffusion problems with applications in heat and mass transfer. The Generalized Integral Transform Technique (GITT) is the basic tool behind such developments offering analytical or hybrid numerical-analytical solutions within user prescribed accuracy. A number of examples are selected from the available literature to illustrate the relative merits of this novel approach.

HYBRID-ANALYTICAL INVESTIGATION OF UNSTEADY LAMINAR FORCED CONVECTION IN PARALLEL-PLATE CHANNELS

S. Cheroto, C. A. C. Santos*, and S. Kakaš
Department of Mechanical Engineering, University of Miami
Coral Gables - Fl 33124 USA
*Department of Mechanical Technology, Universidade Federal da Paraiba
João Pessoa - Pb 58059-900 BRAZIL

An analytical study of unsteady laminar forced convection in a parallel plate channel with hydrodynamically fully developed flow is performed. A general boundary condition of the fifth kind that accounts for both external convection and wall heat capacitance effect is used. The flow is subjected to a periodic variation of inlet temperature, and the thermal response of the system to periodic perturbations is sought after the initial transient has completely disappeared. The generalized integral transform technique is used to provide hybrid analytical-numerical solution. The periodic analysis is performed by using two coupled similar problems for real and imaginary parts, and the resulting coupled equations are solved simultaneously. In addition, a filtering technique is developed to improve the solution and accelerate the convergence.

TRANSIENT NATURAL CONVECTION IN SIDE OPENING CAVITIES

A. A. Merrikh and A. A. Mohamad
Department of Mechanical Engineering
Eastern Mediterranean University
G. Magosa, T.R.N.C.
Mersin 10, Turkey

Transient, naturally buoyant flow and heat transfer in a side opening cavity is studied numerically. A second order accurate scheme in time and space is used (MacCormack scheme). The vertical wall of the cavity is kept at constant temperature where the horizontal walls are assumed adiabatic. The right lateral side of the cavity is open to ambient. The ambient is assumed to have a temperature less than the vertical wall temperature. Prandtl number and the aspect ratio are both fixed to unity and results are analyzed for Rayleigh numbers in the range 1*103 to 1*107. It is found that flow in the cavity interacts with the ambient after a certain period of time. This period of time decreases as Rayleigh number increases. Also, it is found that flow exhibits regular fluctuations for Ra=1*107.

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