96 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
Mixed convection with viscous dissipation and pressure work in a lid-driven square enclosure
No full textBuoyant laminar flow in a square lid-driven enclosure is analysed. The vertical sides are kept isothermal at different temperatures, while the horizontal sides are insulated. Assisting mixed convection flow due to uniform motion of the top side is considered. The governing balance equations are solved numerically by employing a Galerkin finite element method. The effects of viscous dissipation and pressure work are taken into account. In order to investigate the influence of these effects, the Nusselt number is evaluated with respect to the heat fluxes at both vertical sides, for different values of the Rayleigh number and of the Péclet number based on the lid velocity. Two sample fluids are considered: a gas and a highly viscous liquid. In the framework of the Oberbeck–Boussinesq approximation, a comparison is made between three different energy balance models: (A) enthalpy formulation (pressure work and viscous dissipation are included); (B) internal-energy formulation (viscous dissipation is included); (C) both pressure work and viscous dissipation are neglected. It is shown that, in the absence of a lid motion, the three models yield substantially the same predictions. On the other hand, when the forced flow induced by the lid motion becomes sufficiently large, the three models yield discrepant results, thus implying that pressure work and viscous dissipation are not negligible. Moreover, it is shown that, in this case, model (A) yields unphysical results, while model (B) leads to reasonable predictions
Extended Oberbeck-Boussinesq approximation study of convective instabilities in a porous layer with horizontal flow and bottom heating
No full textA study of the onset of convective instabilities in a porous layer with a horizontal basic flow is performed by including the effects of viscous dissipation and pressure work in the energy balance. Firstly, the so-called extended Oberbeck–Boussinesq approximation, i.e. the model based on the enthalpy formulation of the energy balance, is adopted. Then, the results for the marginal stability condition are compared with those obtained by the so-called Chandrasekhar approximation, i.e. the model based on the internal-energy formulation of the energy balance. It is shown that a marked discrepancy occurs between the two approaches, that becomes specially evident for high values of the Gebhart number. According to the extended Oberbeck–Boussinesq approximation, the effects of the viscous dissipation and of the pressure work result in a stabilization of the basic flow. On the contrary, the Chandrasekhar approximation predicts a destabilization of the basic flow induced by the viscous dissipation. The destabilization can be so intense that the onset of convective rolls may occur even in the absence of a boundary temperature difference, i.e. with a vanishing Darcy–Rayleigh number
Instability of Hadley-Prats flow with viscous heating in a horizontal porous layer
No full textThe onset of convective rolls instability in a horizontal porous layer subject to a basic temperature gradient inclined with respect to gravity is investigated. The basic velocity has a linear profile with a non-vanishing mass flow rate, i.e., it is the superposition of a Hadley-type flow and a uniform flow. The influence of the viscous heating contribution on the critical conditions for the onset of the instability is assessed. There are four governing parameters: a horizontal Rayleigh number and a vertical Rayleigh number defining the intensity of the inclined temperature gradient, a Péclet number associated with the basic horizontal flow rate, and a Gebhart number associated with the viscous dissipation effect. The critical wave number and the critical vertical Rayleigh number are evaluated for assigned values of the horizontal Rayleigh number, of the Péclet number, and of the Gebhart number. The linear stability analysis is performed with reference either to transverse or to longitudinal roll disturbances. It is shown that generally the longitudinal rolls represent the preferred mode of instability
The Horton-Rogers-Lapwood problem revisited: the effect of pressure work
No full textThe problem of the onset of convective roll instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures, well known as the Horton–Rogers–Lapwood problem, is revisited including the effect of pressure work and viscous dissipation in the local energy balance. A linear stability analysis of rolls disturbances is performed. The analysis shows that, while the contribution of viscous dissipation is ineffective, the
contribution of the pressure work may be important. The condition of marginal stability is investigated by adopting two solution procedures: method of weighted residuals and explicit Runge–Kutta method. The pressure work term in the energy balance yields an increase of the value of the Darcy–Rayleigh number at marginal stability. In other words, the effect of pressure work is a stabilizing one. Furthermore, while the critical value of the Darcy–Rayleigh number may be considerably affected by the pressure work contribution, the critical value of the wave number is affected only in rather extreme cases, i.e. for very high values of the Gebhart number. A nonlinear stability analysis is also performed pointing out that the joint effects of viscous dissipation and pressure work result in a reduction of the excess Nusselt number due to convection, when the Darcy–Rayleigh number is replaced by the superadiabatic Darcy–Rayleigh number
Combined forced and free convective flow in a vertical porous channel: the effects of viscous dissipation and pressure work
No full textBuoyant flow is analysed for a vertical fluid saturated porous layer bounded by an isothermal plane and an isoflux plane in the case of a fully developed flow with a parallel velocity field. The effects of viscous dissipation and pressure work are taken into account in the framework of the Oberbeck–Boussinesq approximation scheme and of the Darcy flow model. Momentum and energy balances are combined in a dimensionless nonlinear ordinary differential equation solved numerically by a Runge–Kutta method. Both cases of upward pressure force (upward driven flows) and of downward pressure force (downward driven flows) are examined. The thermal behaviour for upward driven flows and downward driven flows is quite different. For upward driven flows, the combined effects of viscous dissipation and pressure work may produce a net cooling of the fluid even in the case of a positive heat input from the isoflux wall. For downward driven flows, viscous dissipation and pressure work yield a net heating of the fluid. A general reflection on the roles played by the effects of viscous dissipation and pressure work with respect to the Oberbeck–Boussinesq approximation is proposed
Effect of pressure work and viscous dissipation in the analysis of the Rayleigh-Bénard problem
No full textThe classical Rayleigh–Bénard problem in an infinitely wide horizontal fluid layer with isothermal boundaries heated from below is revisited. The effects of pressure work and viscous dissipation are taken into account in the energy balance. A linear analysis is performed in order to obtain the conditions of marginal stability and the critical values of the wave number a and of the Rayleigh number Ra for the onset of convective rolls. Mechanical boundary conditions are considered such that the boundaries are both rigid, or both stress-free, or the upper stress-free and the lower rigid. It is shown that the critical value of Ra may be significantly affected by the contribution of pressure work, mainly through the functional dependence on the Gebhart number and on a thermodynamic Rayleigh number. While the pressure work term affects the critical conditions determined through the linear analysis, the viscous dissipation term plays no role in this analysis being a higher order effect. A nonlinear analysis is performed showing that the superadiabatic Rayleigh number replaces Ra in the functional dependence of the excess Nusselt number. Finally, a reasoning is proposed to show how the results obtained may be used as a test on the most appropriate formulation of the Oberbeck–Boussinesq model
Convection-dissipation instability in the horizontal plane Couette flow of a highly viscous fluid
No full textThe linear stability of the plane Couette flow against thermoconvective rolls is studied. The case of a flow without a boundary-imposed temperature gradient is investigated. The non-uniform, possibly unstable, basic temperature distribution is caused by the effect of the internal viscous heating. Asymmetric thermal boundary conditions are considered: the bottom boundary is adiabatic, while the top boundary is isothermal. The focus is on a fluid with a large, mathematically infinite, Prandtl number, although the two-dimensional transverse roll instability is discussed also for a finite Prandtl number. The transition to the instability is described through the governing parameter Ge*Pe^2, where Ge is the Gebhart number and Pe is the Péclet number. The response of the basic Couette flow to arbitrarily oriented oblique rolls is tested, so that a complete set of disturbance modes is taken into account. It is shown that the Couette flow is more unstable to longitudinal rolls than to any other oblique roll mode
Ada Nield Chew: England’s forgotten suffragist
No full textAn open access essay on Ada Nield Chew, author, activist, suffragist, examining her work and her legacy, published in this popular online Magazine, an extension of the BBC History Magazine
Unstably stratified Darcy flow with impressed horizontal temperature gradient, viscous dissipation and asymmetric thermal boundary conditions
No full textThe free convection flow in a horizontal porous layer with an adiabatic bottom boundary and a top boundary with a stationary and non-uniform temperature distribution is investigated. The top boundary temperature distribution is assumed to have a constant gradient and the effect of viscous dissipation is taken into account. A basic parallel buoyant flow develops in the horizontal direction where the top boundary temperature changes. The governing parameters are the Gebhart number and the horizontal Rayleigh number associated with the gradient of the prescribed boundary temperature distribution. In fact, the system experiences a more and more intense effect of the frictional heating as the Gebhart number increases. A linear stability analysis of the basic buoyant flow is carried out. Oblique roll disturbances in any arbitrary horizontal direction are studied and the critical values of the horizontal Rayleigh number are evaluated numerically. It is shown that, for realistic values of the Gebhart number, the longitudinal rolls are the most unstable. Moreover, it is proved that the viscous dissipation yields a destabilising effect
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