E. Magyari

Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface

The similarity solutions describing the steady plane (flow and thermal) boundary layers on an exponentially stretching continuous surface with an exponential temperature distribution are examined both analytically and numerically. The mass- and heat-transfer characteristics of these boundary layers are described and compared with the results of earlier authors, obtained under the more familiar power-law boundary conditions.

Direct observation of the carbonation process on the surface of calcium hydroxide crystals in hardened cement paste using an Atomic Force Microscope

The surface carbonation process of calcium hydroxide crystals in samples of hardened Portland cement paste has been investigated at the nanometer scale with the aid of an Atomic Force Microscope (AFM). The AFM, encapsulated in a glove-box, was operated in contact mode at ambient temperature. Successive real-time measurements were performed in (i) a pure non-reacting N2 atmosphere, (ii) a N2 + H2O, (iii) a N2 + CO2 and finally (iv) in a N2 + CO2 + H2O atmosphere, respectively. In the N2 + H2O atmosphere, until 30–40% relative humidity, a minor change as surface smoothing with an occurring instability was detected. In the N2 + CO2 atmosphere, no change was detected, except for some very small grains becoming after two days even a little bit smaller. However, in the N2 + CO2 + H2O atmosphere, i.e., in a simultaneous CO2 + H2O environment, with a stepwise increase of the relative humidity until 26%–30%, on the surface of the calcium hydroxide crystals several small scattered spots were found. These spots were weakly linked to the surface and could be pushed away with the scanning tip. Under constant conditions (temperature, humidity- and CO2-content), the small spots start to grow, and after a long-term exposition of the crystals to the ambient humid air, develop a specific spherular structure. The latter is interpreted to be calcium carbonate, a result of the surface carbonation process of the initial calcium hydroxide crystals.

AFM investigation of cement paste in humid air at different relative humidities

The surface structure of cement paste has been investigated in humid air by contact mode atomic force microscopy (AFM). The samples have been prepared by the novel mica-replication-method (MRM). For relative humidities between 3% and 20%, a structure change from coarse to fine grains has been recognized. Above this range no further significant changes were found.

The ‘Missing’ Self-Similar Free Convection Boundary-Layer Flow Over a Vertical Permeable Surface in a Porous Medium

The free convection boundary-layer flow of a Darcy–Boussinesq fluid from a vertical permeable plate with an inverse-linear temperature distribution is considered. The outstanding characteristics of this self-similar flow which, according to the usual reduction procedure of pseudo-similarity to full similarity, should not exist at all, are analyzed in detail. Thus it is shown that this flow only exists if a lateral suction with a sufficiently large suction parameter γ ≥ γmin = 1.079131 is applied. For the threshold value γmin the solution is unique but above it multiple solutions are encountered for every given value of γ.

Heat transfer characteristics of a boundary-layer flow driven by a power-law shear over a semi-infinite flat plate

Abstract The hydrodynamic and thermal boundary layer similarity flows driven past a semi-infinite impermeable flat plate by a power-law shear with asymptotic velocity profile U ∞ ( y )= βy −1/2 ( y →∞, β >0) is considered ( y denotes the coordinate normal to the plate). Assuming that the buoyancy and viscous dissipation effects may be neglected, the special cases of an isothermal and of an adiabatic flat plate are examined both analytically and numerically.

The Development of the Asymptotic Viscous Dissipation Profile in a Vertical Free Convective Boundary Layer Flow in a Porous Medium

The effect of viscous dissipation on the development of the boundary layer flow from a cold vertical surface embedded in a Darcian porous medium is investigated. It is found that the flow evolves gradually from the classical Cheng–Minkowycz form to the recently discovered asymptotic dissipation profile which is a parallel flow.

The Opposing Effect of Viscous Dissipation Allows for a Parallel Free Convection Boundary-Layer Flow Along a Cold Vertical Flat Plate

External free convection boundary-layer flows are usually treated by neglecting the effect of viscous dissipation. This assumption always results in a non-parallel flow, besides a strong parallel component also a weak transversal component of the (steady) velocity field occurs. The present paper shows, however, that the weak opposing effect of the buoyancy forces due to heat release by viscous dissipation, can give rise along a cold vertical plate adjacent to a fluid saturated porous medium to a strictly parallel steady free convection flow. This boundary-layer flow is described by an algebraically decaying exact analytical solution of the basic balance equations.

The {\cal PT} -symmetric Rosen?Morse II potential: effects of the asymptotically non-vanishing imaginary potential component

Bound and scattering solutions of the -symmetric Rosen–Morse II potential are investigated. The energy eigenvalues and the corresponding wavefunctions are written in a closed analytic form, and it is shown that this potential always supports at least one bound state. It is found that with increasing non-Hermiticity the real bound-state energy spectrum does not turn into complex conjugate pairs, i.e. the spontaneous breakdown of symmetry does not occur, rather the energy eigenvalues remain real and shift to positive values. Closed expression is found for the pseudo-norm of the bound states, and its sign is found to follow the (−1)n rule. Similarly to the known scattering examples, the reflection coefficients exhibit a handedness effect, while the transmission coefficient picks up a complex phase factor when the direction of the incoming wave is reversed. It is argued that the unusual findings might be caused by the asymptotically non-vanishing, though finite imaginary potential component. Comparison with the real Rosen–Morse II potential is also made.

The storage capacity of a harmonically heated slab revisited

Abstract The physical origin of the well-known maximum occurring in the dynamic heat storage capacity of a harmonically excited stab is analysed in terms of the fundamental solutions of Fouriers equation. It is shown that, in addition to this maximum, an infinite sequence of exponentially decaying lateral minima and maxima occur which are generated by a coherent superposition of two thermal waves propagating in opposite directions within the slab. By passing from the parabolic to the hyperbolic description of heat conduction, this effect becomes much more pronounced.

Buoyancy Sustained by Viscous Dissipation

The quasi-parallel regime of a Darcy–Boussinesq boundary-layer flow over a permeable vertical flat plate adjacent to a fluid saturated porous medium is considered. ‘Quasi-parallel’ means here a plane flow with a constant transversal velocity v=−v0 directed perpendicularly towards the vertical surface, where a lateral suction with the same velocity −v0 is applied. The plate is held at a constant temperature Tw which coincides with the ambient temperature T∞ of the fluid. The heat released by viscous dissipation induces a density gradient in the fluid. Thus, although Tw=T∞, a thermal convection occurs. The steady regime of this ‘self-sustaining buoyant flow’ has been examined in detail. Wall jet-like profiles with a continuous but finite spectrum of the momentum flow have been found. These self-sustaining buoyant jets show a universal behavior, that is, there exist certain length, velocity and temperature scales such that the flow characteristics become independent of the (constant) material properties of the fluid and the porous medium as well.