Spontaneous Breakdown of the Definiteness in Some Convective Heat Transfer Problems

In this study, it is shown that above a critical value of a governing parameter, the solutions of some convective heat transfer problems can undergo a bifurcation into a continuum of a non-denumerable infinity of solutions. Thus, the corresponding Nusselt number becomes indeterminate. The origin of this anomalous bifurcation resides in the stability change of the asymptotic state θ(∞) from that of an unstable to that of a stable equilibrium point of the system. As a consequence, the boundary condition θ(∞)=0 becomes automatically satisfied and thus ineffective in determining the integration constants. Accordingly, the well-posed problem changes spontaneously into an ill-posed one. This remarkable phenomenon will be discussed in detail in the case of an unsteady forced and mixed convection heat transfer problem encountered in an article published recently in Transport in Porous Media. Subsequently, the mentioned loss of definiteness will be explained intuitively with the aid of a simple point-mechanical analog

Cases of mutual compensation of the magnetic and buoyancy forces in mixed convection past a moving vertical surface

It is shown in this Note that under certain conditions, in the hydromagnetic mixed convection flow over a stretching vertical surface, between the magnetic and the buoyancy forces a mutual compensation effect can occur, such that the mixed convection problem reduces to a simple forced convection proble

Comment on "Flow of a Weakly Conducting Fluid in a Channel Filled with a Porous Medium” by A. Pantokratoras and T. Fang, Transport in Porous Media , DOI 10.1007/s11242-009-9470-6

In a recent article by Pantokratoras and Fang (Transport in Porous Media, doi:10.1007/s11242-009-9470-6, 2009), the title problem for the fully developed flow regime was considered, and exact solutions for two types of boundary conditions were reported. However, for a certain parameter combination, some terms of these exact solutions become singular. As a consequence, the solutions cannot be evaluated by a direct substitution of the respective parameter values. The aim of the present note is to (i) show how the singularities can be removed, (ii) give the corresponding nonsingular solutions in an explicit form, and (iii) discuss the physical meaning of the singular case

Comment on the homogeneous nanofluid models applied to convective heat transfer problems

In several recent papers, the heat transfer characteristics of nanofluids have been investigated by simply replacing the transport coefficients of the base fluid by the effective transport coefficients of the nanofluids. The present note emphasizes, however, that the governing equations of these homogeneous nanofluid models (in which the velocity-slip effects of the nanoparticles are neglected) can be reduced with the aid of elementary scaling transformations to the respective equations of the regular fluids. Thus, the corresponding nanofluid results can be recovered from the solutions of already solved regular problems by simple arithmetic operations, without any additional research effort. This feature is illustrated here by the specific examples of the classical Blasius and Sakiadis forced convection heat transfer problem

The Vadasz-Olek Model Regarded as a System of Coupled Oscillators

The Vadasz-Olek model of chaotic convection in a porous layer is revisited in this article. The first-order differential equations of this Lorenz-type model are transformed in the governing equations of a damped nonlinear oscillator, modulated by a linear degenerated overdamped oscillator (relaxator) which in turn is coupled to former one by a nonlinear cross force. The benefit of this mechanical analogy is an intuitive picture of the regular and chaotic dynamics described by the Vadasz-Olek model. Thus, there turns out that the "eyes” of the chaotic attractor correspond to the minima of the potential energy of the modulated nonlinear oscillator having a double-well shape. Several new aspects of the subcritical and supercritical dynamic regimes are discussed in some detai

"Note on "Flows induced by a plate moving normal to stagnation-point flow” by P. D. Weidman and M. A. Sprague (Acta Mech. 219, 219-229, 2011)”

In a recent paper of Weidman and Sprague (Acta Mech., 2011), the unsteady flows generated by an impermeable infinite flat plate advancing with constant velocity V toward, or receding from an orthogonal (plane or axisymmetric) stagnation-point flow, have been investigated by an exact similarity reduction of the Navier-Stokes equations. It has been shown that in the co-moving reference frame of the plate, the induced flow appears as a steady flow, with an additional term R f′′ in the governing equation of the similar stream function f (η). The Reynolds number R involved in this additional term is proportional to the plate velocity V. The present paper shows, however, that with the aid of a simple transformation, the additional term R f′′ can be removed from the governing equation, its effect being transferred in the boundary condition for f (η). As a consequence, the unsteady flow problems of Weidman and Sprague reduce to the classical steady stagnation-point flow problems for permeable surfaces with a uniform lateral suction or injection of the fluid, so that the transpiration parameter f (0) coincides with R for the plane and with R/2 for the axisymmetric flow, respectively. The main benefit of this approach is that all the results of the latter well-investigated problems can simply be transcribed for the problems formulated by Weidman and Sprague (Acta Mech, 2011

Gravity-flow dominated sedimentation on the Buda paleoslope (Hungary): Record of Late Eocene continental escape of the Bakony unit

The Upper Eocene sequence of the Buda Hills consists of fluvial and shallow marine conglomerates, sandstones, bioclastic shallow-water limestone, marlstone and pelagic Globigerina marl. The succession illustrates rapid, overall subsidence of the area, from terrestrial environments to bathyal depths. Sedimentation occurred on slopes situated on the flanks of synsedimentary basement antiforms. Vertical growth of antiforms caused progressive tilting of beds, layerparallel extension by boudinage and faulting, and induced redeposition by mass flow. Antiforms are localised in the dextral Budaörs shear zone and in the Buda imbricate stack, which accommodated the dextral displacement. The latter is underlain by blind reverse faults probably merging into a detachment tault at shallow depths. These structures were formed by WNW-ESE oriented compression and NNE-SSW directed tension. The morphological expression of the imbricate stack is the SE-facing Buda slope. The Bakony unit, while "escaping" from the Alps, was bordered by a northern sinistral and a southern dextral shear zone. Synsedimentary tectonics in the Buda Hills demonstrates the style of deformation inside the escaping block, close to the southern border zone. Tectonically controlled sedimentation suggests that escape tectonics was active as early as Late Eocene time