Article

# Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation

Journal of Heat Transfer-transactions of The Asme - J HEAT TRANSFER 01/2006; 128(2). DOI: 10.1115/1.2137761

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**ABSTRACT:**In this article, linear and nonlinear thermal instability in a rotating anisotropic porous layer with heat source has been investigated. The extended Darcy model, which includes the time derivative and Coriolis term has been employed in the momentum equation. The linear theory has been performed by using normal mode technique, while nonlinear analysis is based on minimal representation of the truncated Fourier series having only two terms. The criteria for both stationary and oscillatory convection is derived analytically. The rotation inhibits the onset of convection in both stationary and oscillatory modes. Effects of parameters on critical Rayleigh number has also been investigated. A weak nonlinear analysis based on the truncated representation of Fourier series method has been used to find the Nusselt number. The transient behavior of the Nusselt number has also been investigated by solving the finite amplitude equations using a numerical method. Steady and unsteady streamlines, and isotherms have been drawn to determine the nature of flow pattern. The results obtained during the analysis have been presented graphically. KeywordsThermal instability–Heat source–Internal Rayleigh number–Nusselt number–Streamlines–IsothermsTransport in Porous Media 01/2011; 90(2):687-705. · 1.55 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The free convection boundary-layer flow near a stagnation point in a porous medium is considered when there is local heat generation at a rate proportional to (T − T ∞)p , (p ≥ 1), where T is the fluid temperature and T ∞ the ambient temperature. Two cases are treated, when the surface is thermally insulated and when heat is supplied at a constant (dimensionless) rate h s from the boundary. If h s = 0 the solution approaches a nontrivial steady state for time t large in which the local heating has a significant effect when p ≤ 2. For p > 2 the effects of the local heating become increasingly less important and the solution dies away, with the surface temperature being of O(t −1) for t large. When h s > 0 and there is heat input from the surface, the solution for p ≤ 2 again approaches a nontrivial steady state for t large and all h s . For p > 2 there is a critical value h s,crit (dependent on the exponent p) of h s such that the solution still approaches a nontrivial steady state if h s < h s,crit. For h s > h s,crit a singularity develops in the solution at a finite time, the nature of which is analysed.Journal of Engineering Mathematics 01/2013; 79(1). · 1.08 Impact Factor - International Journal of Non-Linear Mechanics 09/2013; · 1.35 Impact Factor

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