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  • 1
    ISSN: 1573-1634
    Keywords: porous medium ; convection ; boundary layer ; transient ; heat flux.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract An analysis is made of the transient free convection from a vertical flat plate which is embedded in a fluid-saturated porous medium. It is assumed that for time $$\overline \tau 〈 0$$ a steady state temperature or velocity has been obtained in the boundary-layer which occurs due to a uniform flux dissipation rate $$q_1^{\prime \prime } $$ . Then at time $$\overline \tau = 0$$ the heat flux on the plate is suddenly changed to $$q_2^{\prime \prime } $$ and maintained at this value for $$\overline \tau 〉 0$$ . An analytical solution has been obtained for the temperature/velocity field for small times in which the transport effects are confined within an inner layer adjacent to the plate. These effects cause a new steady boundary layer. A numerical solution of the full boundary-layer equations is then obtained for the whole transient from $$\overline \tau = 0$$ to the steady state, firstly by means of a step-by-step method and then by a matching technique. The transition between the two distinct solution methods is always observed to occur very near to the turning point of the plate surface temperature, a time at which the fluid temperature is close to its steady state profile. The solution obtained using the step-by-step method shows excellent agreement with the small time analytical solution. Results are presented to illustrate the occurrence of transients from both small and large increases and decreases in the levels of existing energy inputs.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-1634
    Keywords: free convection ; boundary-layer ; horizontal surface ; transient ; heat flux
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This paper presents an analytical and numerical study of transient free convection from a horizontal surface that is embedded in a fluid-saturated porous medium. It is assumed that for time $$\bar \tau 〈 0$$ steady state velocity and temperature fields are obtained in the boundary-layer which occurs due to a uniform flux dissipation rate q 1′′ on the surface. Then, at $$\bar \tau = 0$$ the heat flux on the surface is suddenly changed to q 2′′ and maintained at this value for $$\bar \tau 〉 0$$ . Firstly, solutions which are valid for small and large $$\bar \tau $$ are obtained. The full boundary-layer equations are then integrated step-by-step for the transient regime from the initial unsteady state ( $$\bar \tau = 0$$ ) until such times at which this forward marching approach is no longer well posed. Beyond this time no valid solutions could be obtained which matched the final solution from the forward integration to the steady state profiles at large times $$\bar \tau \to \infty $$ .
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 889-903 
    ISSN: 0271-2091
    Keywords: SIMPLE-like algorithm ; Average pressure correction ; Paper filter ; Turbulent flow ; Sampler ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The control volume, finite difference method and the k-∊ tubulence model are employed in a numerical simulation of the turbulent fluid flow both outside and inside a blunt cylindrical sampler which houses a paper filter in its chamber. The presence of a paper filter, which has a very large resistance, results in a large pressure drop across the filter and this causes difficulties in making the SIMPLE or the SIMPLEC scheme converge. In order to improve the rate of convergence of the SIMPLE-like algorithm when the resistance of the filter is very large, an average pressure correction formula is proposed. Based on global mass conservation, a line average pressure correction for the paper filter is derived using a modified Darcy law for a porous medium. A combination of this formula and the SIMPLE-like algorithm can rapidly build up the pressure drop across the filter and hence dramatically improve the rate of convergence of the iterative scheme. Comparisons of the convergence histories and the numerical results for the fluid flow when using SIMPLE and SIMPLEC with the average pressure correction method show that the average pressure correction method for dealing with the paper filter significantly accelerates the rate of convergence of the iterative scheme.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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