397 research outputs found
Response to Comment on “Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and PressureWork” by A. Barletta and D. A. Nield, Transport in Porous Media, DOI 10.1007/s11242-008-9320-y, 2009
No full textThis short note is a response to the comment (TIPM936) on our recently published paper cited in the title. All the points raised by the author of the comment are discussed. It is shown that one of the remarks, concerning eigenflow solutions in the limiting case of forced convection, has not a sound physical basis. In fact, it refers to a circumstance, a fluid with a thermal expansion coefficient greater than that of a perfect gas, of marginal or no interest in the framework of convection in porous media
Comment on the comment by V.A.F. Costa, IJTS 49 (9) (2010) 1874-1875, on the paper by I. A. Badruddin, Z. A. Zainal, Z. A. Khan, Z. Mallick "Effect of viscous dissipation and radiation on natural convection in a porous medium embedded within vertical annulus", IJTS 46 (3) (2007) 221-227
No full textA comment on a recent paper about the combined effects of radiation and viscous dissipation on the convection in an annular porous enclosure has raised the problem of the role played by the viscous dissipation and the pressure work contributions in buoyant flows. The aim of this further comment is to show that the criticism expressed by Costa on the model of the viscous dissipation effect employed in the paper by Badruddin and co-workers is unjustified
Thermal instability in a plane channel with internal heating and horizontal Poiseuille throughflow
No full textThe effect of a basic Poiseuille throughflow on the thermal instability of a horizontal fluid layer bounded by two plane parallel walls is studied. An unstable thermal stratification is studied, entirely due to a uniform internal heat generation in the fluid, whereas the thermal boundary conditions do not impress any temperature difference across the fluid layer. Two cases are investigated: a symmetric case where both boundaries are perfectly conducting; a non-symmetric case where the lower boundary is adiabatic and the upper boundary is perfectly conducting. A linear stability analysis is carried out and the eigenvalue problem is solved numerically for arbitrary oblique rolls, and by a symbolic weighted residual method in the special case of longitudinal rolls. The main result is that the basic Poiseuille flow does not influence the thermoconvective instability at the onset of the least stable modes, i.e. the longitudinal rolls. Thus, the critical conditions are just the same as for a fluid at rest in the basic state. Although the focus is on the thermoconvective instability, it is proved that, even in the presence of the internal heat generation, Squire’s theorem holds for the hydrodynamic instability of the plane Poiseuille flow
Linear instability of the horizontal throughflow in a plane porous layer saturated by a power-law fluid
No full textThe onset of the convective instability in the horizontal throughflow of a power-law fluid saturating a horizontal porous layer heated from below is studied. A linear stability analysis of the basic flow is carried out and the disturbance equations are solved analytically. The problem examined here is an extension of the classical Prats problem for Newtonian fluids. It is shown that the marginal stability condition, as well as the critical values of the wave number and of the Darcy–Rayleigh number, is affected by the value of the Péclet number associated with the basic flow, except for the special case of a Newtonian fluid. The limit of a vanishingly small Péclet number is considered leading to the special case of the Horton–Rogers–Lapwood (HRL) problem for a power-law fluid, i.e., the Prats problem with a vanishing basic throughflow. It is shown that the generalized HRL problem is always linearly stable for pseudoplastic fluids and always linearly unstable for dilatant fluids
Thermosolutal convective instability and viscous dissipation effect in a fluid-saturated porous medium
No full textThe combined effects of the double-diffusion and of the viscous dissipation on the convective instability in a fluid-saturated porous medium with a basic horizontal throughflow are investigated. A horizontal porous layer with an impermeable adiabatic lower wall and an impermeable isothermal upper wall is considered. The parallel boundary walls are assumed to have uniform, but unequal, concentrations of the solute. A linear stability analysis is carried out both numerically and by a first-order perturbation method. General disturbances having the form of oblique rolls are considered, reducing either to longitudinal rolls or to transverse rolls in the special cases of roll axes parallel or orthogonal to the basic flow direction, respectively. It is shown that the combined effects of viscous dissipation and mass diffusion may lead to the instability of the basic horizontal flow. Either the longitudinal rolls or the transverse rolls may be the preferred modes of instability depending on the value of the viscous dissipation parameter Xi. The longitudinal rolls are the most unstable when Xi < 61.86657
Double-diffusive convection instability and viscous dissipation in a fluid saturated porous layer with horizontal forced flow
No full textA horizontal porous layer with an impermeable adiabatic bottom wall and an impermeable isothermal top wall is studied. An impressed concentration gradient across the layer is assumed. A linear stability analysis is carried out both numerically and by a first-order perturbation method. It is shown that the combined effects of viscous dissipation and mass diffusion may lead to the instability of a basic horizontal uniform flow through the layer
On Hadley flow in a porous layer with vertical heterogeneity
No full textThe onset of thermoconvective instability in a horizontal porous layer with a basic Hadley flow is studied, under the assumption of weak vertical heterogeneity. Hadley flow is a single-cell convective circulation induced by horizontal linear changes of the layer boundary temperatures. When combined with heating from below, these thermal boundary conditions yield a temperature gradient inclined to the vertical, in the basic state. The linear stability of the basic state is studied by considering small-amplitude disturbances of the velocity field and the temperature field. The linearized governing equations for the disturbances are then solved both by Galerkin’s method of weighted residuals and by a combined use of the Runge–Kutta method and the shooting method. The effect of weak heterogeneity of the permeability and the effective thermal conductivity of the porous medium is studied with respect to neutral stability conditions. It is shown that, among the normal mode disturbances, the most unstable are longitudinal rolls, that is, plane waves with a wave vector perpendicular to the imposed horizontal temperature gradient. The effect of heterogeneity becomes important only for high values of the horizontal Rayleigh number, associated with the horizontal temperature gradient, approximately greater than 60. In this regime, the effect of heterogeneity is destabilizing. It is shown that heterogeneity with respect to thermal conductivity is of major importance in the onset of instability
Variable viscosity effects on the dissipation instability in a porous layer with horizontal throughflow
No full textThe role of viscous heating in the onset of the instability in a liquid-saturated porous medium is studied. The change of the liquid viscosity with the temperature is taken into account by using a linear fluidity model. The system examined is a horizontal porous layer with an adiabatic lower boundary and an isothermal upper boundary. The combined effects of the viscous heating and of the variable viscosity yield a basic stationary and parallel throughflow in a horizontal direction. This basic solution may display singularities when the product between the Péclet number and the viscosity-temperature slope parameter exceeds the threshold value π/2. The linear stability of the basic solution is studied with respect to normal modes disturbances arbitrarily oriented to the basic flow direction. In all the physically realistic cases, the most unstable disturbances are proved to be the longitudinal rolls (the wave vector is perpendicular to the basic velocity). The instability to the longitudinal rolls occurs when the product between the Péclet number and the viscosity-temperature slope parameter exceeds its critical value. This critical value is smaller than π/2, for every nonzero value of the buoyancy parameter, viz., the Gebhart number. As a consequence, the parametric domain where the singularities of the basic solution arise is in fact included in the instability domain
Linear instability to longitudinal rolls of the Darcy-Hadley flow in a weakly heterogeneous porous medium
No full textThe aim of this contribution is to investigate the effects of a weak vertical heterogeneity of the porous medium on the stability of the Darcy-Hadley flow. We will assume that the permeability and the thermal conductivity of the porous medium undergo a weak linear change in the vertical direction. The stability analysis will be carried out by considering linear perturbations of the basic state in the form of longitudinal rolls, under the hypothesis that the weak heterogeneity does not alter the result that these modes are the most unstable. The neutral stability conditions and the critical values of the vertical Darcy-Rayleigh number will be obtained on varying the horizontal Darcy-Rayleigh number as well as the parameters of heterogeneity relative both to the permeability and to the conductivity. The solution of the linear disturbance equations will be obtained by employing Galerkin’s method of weighted residuals
On the Rayleigh-Bénard-Poiseuille problem with internal heat generation
No full textThe Rayleigh-Bénard-Poiseuille flow system with a uniform internal heat source is analyzed. A horizontal plane channel is bounded by two plane isothermal walls with unequal temperatures. The boundary heating from below and theinternal heating are parametrized by the Rayleigh number and by the internal Rayleigh number, respectively. Other governing parameters are the Prandtl number of the fluid and the Reynolds number associated with the basic Poiseuille flow. The linear stability to small-amplitude disturbances arbitrarily inclined to the basic flow direction is studied. A range of sufficiently small Reynolds numbers is investigated, where the thermoconvective instability has no interplay with the hydrodynamic (Orr-Sommerfeld) instability of the Poiseuille flow. In this range, the wavelike disturbances with a wave vector perpendicular to the Poiseuille flow direction, i.e. the longitudinal rolls, are the least stable modes. These modes are non-travelling, and they are not affected either by the Reynolds number or by the Prandtl number. On the other hand, the critical values of the wave number and of the Rayleigh number change with the internal Rayleigh number. The critical Rayleigh number can be even zero or negative, meaning heating from above, when the internal Rayleigh number is equal or greater than 37325.17
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