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RESEARCH PAPERS: Natural and Mixed Convection

# Neutral Instability and Optimum Convective Mode in a Fluid Layer with PCM Particles

[+] Author and Article Information
Chuanshan Dai

College of Mechanical Engineering,  Tianjin University, Tianjin 300072, People’s Republic of Chinacsdai@yahoo.com

Hideo Inaba

Department of Mechanical Engineering,  Okayama University, Okayama 700-8530, Japaninaba@mech.okayama-u.ac.jp

J. Heat Transfer 127(12), 1289-1295 (Jun 10, 2005) (7 pages) doi:10.1115/1.2060728 History: Received March 23, 2004; Revised June 10, 2005

## Abstract

Linear stability analysis is performed to determine the critical Rayleigh number for the onset of convection in a fluid layer with phase-change-material particles. Sine and Gaussian functions are used for describing the large variation of apparent specific heat in a narrow phase changing temperature range. The critical conditions are numerically obtained using the fourth order Runge-Kutta-Gill finite difference method with Newton-Raphson iteration. The critical eigenfunctions of temperature and velocity perturbations are obtained. The results show that the critical Rayleigh number decreases monotonically with the amplitude of Sine or Gaussian function. There is a minimum critical Rayleigh number while the phase angle is between $π∕2$ and $π$, which corresponds to the optimum experimental convective mode.

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## Figures

Figure 1

Schematic diagram of a PCM fluid layer heated from below and cooled from above

Figure 2

Normalized specific heat models [Eqs. 215,216]. The curves are for b=1.688 and c=20, the solid cycles are experimental data measured by DSC.

Figure 3

Various modes of bottom heating for: a complete cycle of specific heat variation with temperature: ψ=π; less than a cycle: ψ<π; and over a cycle: ψ>π

Figure 4

Grid number dependence test for numerical integration (solid points) and numerical differentiation (open points) methods

Figure 5

Critical Rayleigh number versus the amplitude b of normalized specific heat at various boundary conditions, subscript “s” for a sine variation, and “g” a Gaussian variation

Figure 6

Critical Rayleigh number (a) and wave number (b) versus phase angle ψ at constant amplitude b for Gaussian variations and for the case R∕R

Figure 7

Variation of the normalized vertical velocity (a) and (c), and temperature disturbance (b) and (d) with the normalized depth of the layer z for the case of R∕R and the Gaussian variation of specific heat with temperature, the solid curve is for a fluid with constant specific heat, ψ=π is denoted with ◻; ψ=π∕2 with 엯; and ▵ denotes the phase angle ψop at which has the minimum critical Rayleigh number

Figure 8

Graph matching between the measured specific heat Cp by DSC and the coefficient of thermal expansion β by adjusting the vertical coordinate linearly

Figure 9

Heat transfer coefficient h against the lower heating plate temperature Th while the top cooling plate temperature Tc is fixed at 40°C. The vertical dashed lines are for the predicted temperatures at which a maximum heat transfer coefficient can be obtained. The data are from Inaba (12). The mass concentrations of the various PCM slurries are 30% (◻), the amplitude b is approximately 1.688; 20%(▴), 10% (엯), and 5% (∎).

## Errata

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