IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 19 Apr 2021 11:41:12 GMT2021-04-19T11:41:12Z102081The onset of Darcy-Bénard instability in a horizontal porous channel with a free surface using a thermal nonequilibrium modelhttp://hdl.handle.net/11585/573809.1Titolo: The onset of Darcy-Bénard instability in a horizontal porous channel with a free surface using a thermal nonequilibrium model
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11585/573809.12016-01-01T00:00:00ZOn Gill’s stability problem for non-Newtonian Darcy’s flowhttp://hdl.handle.net/11585/380641Titolo: On Gill’s stability problem for non-Newtonian Darcy’s flow
Abstract: Gill’s stability problem is the analysis of the parallel buoyant flow in a vertical porous channel whose parallel walls are kept at different uniform temperatures. Gill’s classical paper [Journal of Fluid Mechanics, 35 (1969) 545–547] provides a rigorous proof that this flow is linearly stable. The aim of our study is to extend Gill’s analysis to the class of non-Newtonian viscous fluids modelled by Ostwald-de Waele power law. The main difference between Newtonian fluids and general power-law fluids is that the basic velocity profile is linear, in the Newtonian case, and nonlinear with an inflexion point at the mid-plane, in the non-Newtonian case. Despite the presence of the inflexion point, this study evidences a stable behaviour of the basic flow versus general normal mode perturbations: longitudinal, oblique and transverse rolls. Stability to longitudinal rolls is proved analytically, while the behaviour of transverse and oblique rolls is investigated numerically. The damping rates of perturbations, evaluated for oblique and transverse rolls, display increasing values as the Darcy–Rayleigh number increases. Numerical data thus suggest that linear stability holds for the whole class of power-law fluids.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3806412014-01-01T00:00:00ZAdiabatic eigenflows in a vertical porous channelhttp://hdl.handle.net/11585/380644Titolo: Adiabatic eigenflows in a vertical porous channel
Abstract: The existence of an infinite class of buoyant flows in a vertical porous channel with adiabatic and impermeable boundary walls, called adiabatic eigenflows, is discussed. A uniform heat source within the saturated medium is assumed, so that a stationary state is possible with a net vertical through-flow convecting away the excess heat. The simple isothermal flow with uniform velocity profile is a special adiabatic eigenflow if the power supplied by the heat source is zero. The linear stability analysis of the adiabatic eigenflows is carried out analytically. It is shown that these basic flows are unstable. The only exception, when the power supplied by the heat source is zero, is the uniform isothermal flow, which is stable. The existence of adiabatic eigenflows and their stability analysis is extended to the case of spanwise lateral confinement, viz. in the case of a vertical rectangular channel. A generalisation of this study to a vertical channel with an arbitrary cross-sectional shape is also presented.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3806442014-01-01T00:00:00ZInstability of parallel buoyant flow in a vertical porous layer with an internal heat sourcehttp://hdl.handle.net/11585/585835Titolo: Instability of parallel buoyant flow in a vertical porous layer with an internal heat source
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11585/5858352017-01-01T00:00:00ZDual solutions for viscous mixed convection flows in a vertical circular duct: a numerical benchmarkhttp://hdl.handle.net/11585/55997Titolo: Dual solutions for viscous mixed convection flows in a vertical circular duct: a numerical benchmark
Abstract: Forced and free convection flow in a vertical isothermal circular duct is studied by taking into accountthe internal heating due to viscous dissipation. The momentum and energy balance equations lead to a nonlinear boundary value problem that is solved numerically by means of the finite-element software Comsol Multiphysics 3.3a (Comsol, Inc.). For any prescribed value of the average velocity smaller than a maximum, two solutions exist which are completely different in thermal and mechanical characteristics (dual solutions). It is shown how the software can be used to determine the velocity and temperature fields and the main interesting physical quantities for both the solutions. The numerical results are compared with the analytical results available in the literature, thus performing a benchmark of the numerical solution.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11585/559972007-01-01T00:00:00ZUnstable mixed convection in a heated horizontal porous channelhttp://hdl.handle.net/11585/380656Titolo: Unstable mixed convection in a heated horizontal porous channel
Abstract: This paper presents a linear stability analysis of horizontal throughflow in a saturated porous channel bounded by parallel impermeable walls with heating provided from below and an insulated top. The linear stability analysis is carried out for general oblique rolls, leading to an eigenvalue problem for determining critical values for the Darcy-Rayleigh number as a function of the Péclet number, the wavenumber and the angular frequency. This problem is then solved using the Generalized Integral Transform Technique, such that the differential eigenproblem formulation analytically transformed into a matrix eigenvalue problem, which is then solved by traditional numerical algorithms. The results show that for longitudinal rolls, the only value of the angular frequency that leads to an unstable flow is zero, and that non-vanishing frequency values are obtained for oblique rolls. In addition critical values of the Darcy-Rayleigh number that lead to unstable solutions for different Péclet numbers, for different inclination angles are presented.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3806562014-01-01T00:00:00ZOnset of convection in a porous layer with continuous periodic horizontal stratification, Part II: Three-dimensional convectionhttp://hdl.handle.net/11585/380642Titolo: Onset of convection in a porous layer with continuous periodic horizontal stratification, Part II: Three-dimensional convection
Abstract: The onset of convection in a porous layer which is heated from below is considered. In particular we seek to determine the effect of spatially periodic variations in the permeability field on the identity of the onset mode as a function of both the period P of this variation and its amplitude A. A Floquet theory is assumed in order to ensure that the analysis is as general as possible. It is found that convection is always three-dimensional and that the critical Rayleigh number always decreases as either the period or the amplitude of the permeability variation increases. Furthermore, the corresponding Floquet exponent ν is either 0 or 1, and the range of values of P over which ν=1 corresponds to the favoured mode has been obtained as a function of A.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3806422014-01-01T00:00:00ZBuoyant Couette-Bingham flow between vertical parallel plateshttp://hdl.handle.net/11585/62275Titolo: Buoyant Couette-Bingham flow between vertical parallel plates
Abstract: The present paper is closely related to a recent work of Bayazitoglu et al. [Y. Bayazitoglu, P.R. Paslay, P. Cernocky, Laminar Bingham fluid flow between vertical parallel plates, Int. J. Thermal Sci. 46 (2007) 349–357], in which the free convection of a Bingham material in a vertical parallel plane channel with a constant temperature differential across the walls has been investigated. Our interest is directed on the additional effect of an external shear, applied on the wall–fluid interface. This forcing shear is induced (in our mathematical model) by a uniform vertical motion of the hot wall of the channel in its own plane. The physically most interesting five-domain configuration of the velocity field of the resulting buoyant Couette–Bingham flow is examined in detail. For the initiation temperature of the flow, whose existence has been predicted in [Y. Bayazitoglu, P.R. Paslay, P. Cernocky, Laminar Bingham fluid flow between vertical parallel plates, Int. J. Thermal Sci. 46 (2007) 349–357], a generally valid formula is reported. Subsequently, it is shown that the core velocities with rigid body motion depend on the wall velocity sensitively. The hot and cold cores possess the same width which, however, decreases with increasing wall velocity rapidly. There always exists a critical downward pointing wall velocity for which the upward motion of the hot core is dropped.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/622752008-01-01T00:00:00ZParallel and non-parallel laminar mixed convection flow in an inclined tube: the effect of the boundary conditionshttp://hdl.handle.net/11585/62270Titolo: Parallel and non-parallel laminar mixed convection flow in an inclined tube: the effect of the boundary conditions
Abstract: The necessary condition for the onset of parallel flow in the fully developed region of an inclined duct is applied to the case of a circular tube. Parallel flow in inclined ducts is an uncommon regime, since in most cases buoyancy tends to produce the onset of secondary flow. The present study shows how proper thermal boundary conditions may preserve parallel flow regime. Mixed convection flow is studied for a special non-axisymmetric thermal boundary condition that, with a proper choice of a switch parameter, may be compatible with parallel flow. More precisely, a circumferentially variable heat flux distribution is prescribed on the tube wall, expressed as a sinusoidal function of the azimuthal coordinate with period 2pi. A pi/2 rotation in the position of the maximum heat flux, achieved by setting the switch parameter, may allow or not the existence of parallel flow. Two cases are considered corresponding to parallel and non-parallel flow. In the first case, the governing balance equations allow a simple analytical solution. On the contrary, in the second case, the local balance equations are solved numerically by employing a finite element method.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/622702008-01-01T00:00:00ZConjugate forced convection heat transfer in a plane channel: longitudinally periodic regimehttp://hdl.handle.net/11585/62265Titolo: Conjugate forced convection heat transfer in a plane channel: longitudinally periodic regime
Abstract: The present paper studies the conjugate heat transfer problem in a parallel-plane channel. Laminar and stationary forced convection is studied, with a boundary condition given by a temperature distribution on the external side of the channel wall, which undergoes a sinusoidal longitudinal change. The local energy balance equation is written with reference to the fully developed region, where the temperature distribution can be expressed as a periodic function of the longitudinal coordinate. The temperature field in the solid wall and in the fluid, as well as the local and average Nusselt number, are determined analytically and numerically. A comparison between the values obtained analytically, by employing a complex temperature method, and those evaluated numerically, by employing a Bubnov–Galerkin finite element method, reveals an excellent agreement.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/622652008-01-01T00:00:00Z