Showing papers by "Suhas V. Patankar published in 1993"
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TL;DR: In this article, a discussion on the ray effect and false scattering occurring in discrete ordinates solution of the radiative transfer equation is presented, and four sample problems are used to explain these two effects.
Abstract: A discussion on the ray effect and false scattering occurring in discrete ordinates solution of the radiative transfer equation is presented in this article. Ray effect arises from the approximation of a continuously varying angular nature of radiation by a specified set of discrete angular directions. It is independent of the spatial discretization practice. False scattering, on the other hand, is a consequence of the spatial discretization practice and is independent of the angular discretization practice. In multidimensional computations, when a beam is not aligned with the grid line, false scattering smears the radiative intensity field. It reduces the appearance of unwanted bumps, but does not eliminate ray effect. An inappropriate view of false scattering is also presented. Four sample problems are used to explain these two effects.
286 citations
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TL;DR: In this article, an analysis of the laminar natural convection in two internally finned horizontal annuli is made using a control-volume-based finite difference method, where the governing equations were solved numerically by a control volume based finite difference (CVBD) method.
Abstract: An analysis is made of the laminar natural convection in two internally finned horizontal annuli. The governing equations were solved numerically by a control-volume-based finite difference method. Information about the flow patterns and temperature distributions is presented through velocity vectors, streamlines, and isotherm plots. The effects of Rayl1eigh number and fin height on the Nusselt numbers are presented for two selected fin orientations. Variations of the local Nusselt numbers along the inner cylinder are also presented. In the cases studied, orientations of the internal fins are found to have insignificant effects on the average Nusselt number.
49 citations
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TL;DR: In this article, the authors present an analysis of mixed convection in an idealized cold-wall horizontal chemical vapor deposition (CVD) reactor with a tapered susceptor, based on the full three-dimensional elliptic form of the conservation equations.
Abstract: We present an analysis of mixed convection in an idealized cold-wall horizontal chemical vapor deposition (CVD) reactor with a tapered susceptor. The analysis is based on the full three-dimensional elliptic form of the conservation equations. The predictions of fluid flow and heat transfer are made by solving the conservation equations for a single species and the details of chemistry and species transport are not included. Thus, the results are valid for CVD applications in which the reactants are present in very small concentrations in the inert carrier gas
20 citations
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TL;DR: In this article, a control volume finite element scheme was proposed for numerical modeling of fluid flow problems. But it is not suitable for control volume discretization, as it requires an equal order interpolation for velocity and pressure.
17 citations
01 May 1993
4 citations
01 May 1993
4 citations
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01 Jan 1993TL;DR: In this paper, three popular spatial differencing schemes for the discrete ordinates method are examined for two-dimensional Cartesian coordinates system: a positive, the step, and the diamond schemes.
Abstract: Three popular spatial differencing schemes for the discrete ordinates method are examined for two-dimensional Cartesian coordinates system. These are a positive, the step, and the diamond schemes. Contrary to the common belief that negative intensities will not occur when fine spatial discretization is used with the diamond scheme, under certain conditions, the diamond scheme will produce negative intensities irrespective of the number of control volums employed. The positive scheme can produce physically unrealistic trends. The diamond and positive schemes are also capable of producing physically unrealistic overshoots. In absorbing-emitting or absorbing-emitting-scattering media, grid refinement can result in negative intensities when the diamond or positive scheme is used.
3 citations
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01 Jul 1993TL;DR: In this paper, a control-angle, control-volume-based discrete ordinates method (CA -CV DOM) is presented, which converges to the grid independent solutions quickly and compared favorably against other published results for six test problems.
Abstract: A control-angle, control-volume-based discrete ordinates method (CA - CV DOM) is presented in this paper. A detailed formulation of the discretization equation is presented in two-dimensional Cartesian coordinate system. The procedure can be extended to curvilinear coordinate system with minor modifications. The step and modified-exponential schemes are used in this study. Present results converged to the grid independent solutions quickly and compared favorably against other published results for six test problems.
1 citations