Gravity-driven laminar film flow of power-law fluids along vertical walls

A theoretical analysis is presented which brings steady laminar film flow of power-law fluids within the framework of classical boundary layer theory. The upper part of the film, which consists of a developing viscous boundary layer and an external inviscid freestream, is treated separately from the viscous dominated part of the flow, thereby taking advantage of the distinguishing features of each flow region. It is demonstrated that the film boundary layer developing along a vertical wall can be described by a generalized Falkner-Skan type equation originally developed for wedge flow. An exact similarity solution for the velocity field in the film boundary layer is thus made available.Downstream of the boundary layer flow regime the fluid flow is completely dominated by the action of viscous shear, and fairly accurate solutions are obtained by the Von Karman integral method approach. A new form of the velocity profile is assumed, which reduces to the exact analytic solution for the fully-developed film. By matching the downstream integral method solution to the upstream generalized Falkner-Skan similarity solution, accurate estimates for the hydrodynamic entrance length are obtained. It is also shown that the flow development in the upstream region predicted by the approximate integral method closely corresponds to the exact similarity solution for that flow regime. An analytical solution of the resulting integral equation for the Newtonian case is compared with previously published results.     

On the flow of a viscous fluid driven along a channel by suction at porous walls

This paper is a theoretical treatment of the flow of a viscous incompressible fluid driven along a channel by steady uniform suction through porous parallel rigid walls. Many authors have found such flows when they are symmetric, steady and two-dimensional, by assuming a similarity form of solution due to Berman in order to reduce the Navier-Stokes equations to a nonlinear ordinary differential equation. We generalise their work by considering asymmetric flows, unsteady flows and three-dimensional perturbations. By use of numerical calculations, matched asymptotic expansions for large values of the Reynolds number, and the theory of dynamical systems, we find many more exact solutions of the Navier-Stokes equations, examine their stability, and interpret them. In particular, we show that most previously found steady solutions are unstable to antisymmetric two-dimensional disturbances. This leads to a pitchfork bifurcation, stable asymmetric steady solutions, a Hopf bifurcation, stable time-periodic solutions, stable quasi-periodic solutions, phase locking and chaos in succession as the Reynolds number increases.     

Convective magnetohydrodynamic flow in a vertical channel

An analysis is presented for the combined forced and free convective magnetohydrodynamic flow in a vertical, finite rectangular channel that is subjected simultaneously to a pressure gradient and a temperature gradient. Exact solutions are found for electrically nonconducting channel walls and perfectly conducting walls. In particular, the case of heating from below is examined and discussed.     

Transient free convective flow in a vertical channel with constant temperature and constant heat flux on walls

This note presents transient motion of a viscous and incompressible fluid in a vertical channel due to free convective currents occuring as a result of application of constant heat flux at one wall and constant temperature on other wall. The method of Laplace transform is used to solve the problem. The transient behaviour of flow on velocity and temperature fields are shown on the graphs.     

Investigation of nanofluid flow in a vertical channel considering polynomial boundary conditions by Akbari-Ganji's method

In this research, a vertical channel containing a laminar and fully developed nanofluid flow is investigated. The channel surface's boundary conditions for temperature and volume fraction functions are considered qth-order polynomials. The equations related to this problem have been extracted and then solved by the AGM and validated through the Runge-Kutta numerical method and another similar study. In the study, the effect of parameters, including Grashof number, Brownian motion parameter, etc., on the motion, velocity, temperature, and volume fraction of nanofluids have been analyzed. The results demonstrate that increasing the Gr number by 100% will increase the velocity profile function by 78% and decrease the temperature and fraction profiles by 20.87% and 120.75%. Moreover, rising the Brownian motion parameter in five different sizes (0.1, 0.2, 0.3, 0.4, and 0.5) causes lesser velocity, about 24.3% at first and 4.35% at the last level, and a maximum 52.86% increase for temperature and a 24.32% rise for Ψ occurs when N_b rises from 0.1 to 0.2. For all N_t values, at least 55.44%, 18.69%, for F(η), and Ω(η), and 20.23% rise for Ψ(η) function is observed. Furthermore, enlarging the N_r parameter from 0.25 to 0.1 leads F(η) to rise by 199.7%, fluid dimensionless temperature, and dimensional volume fraction to decrease by 18% and 92.3%. In the end, a greater value of q means a more powerful energy source, amplifying all velocity, temperature, and volume fraction functions. The main novelty of this research is the combined convection qth-order polynomials boundary condition applied to the channel walls. Moreover, The AMG semi-analytical method is used as a novel method to solve the governing equations.     

Electrization and liquid glow in a coaxial channel with dielectric walls

Dielectric-liquid flows in narrow channels with walls composed of different dielectrics are investigated experimentally. It is revealed that at a certain flow velocity, as a result of electrization, on the interface between the dielectrics the liquid begins to glow. The glow is discrete in the form of frequent pulses and is accompanied by electromagnetic noise on the radio-frequency range. It is shown that with decrease in the channel thickness the glow appears at smaller flow velocities. The glow is accompanied by heating of the liquid in the wall region to temperatures that may reach several tens of degrees. The electrization potential reaches more than 100 kV. The mechanisms of electrization and liquid glow are discussed.     

Investigation of pulsed discharges in a dielectric channel with ablating walls

The current-voltage characteristics of a pulsed discharge in a hollow cylindrical channel formed by dielectric walls are investigated. The erosion of the channel walls is measured, together with the mean velocity of the plasma flowing into a vacuum through an opening in one of the electrodes, and related to the channel geometry. Conclusions are drawn regarding the temperature of the plasma in the channel and the mechanism of heat transfer to the walls.Notation d channel diameter - l channel length - C capacitance of capacitor bank - U capacitor voltage; - M consumption of dielectric per discharge - m specific consumption - W discharge energy - r₀ resistance of discharge gap at instant of maximum current - R variable resistance of discharge channel - I_m maximum discharge current - W₁ chemical bond rupture energy of dielectric of mass M - W₂ ionization energy of dielectric of mass M - W₃ kinetic energy of dielectric of mass M - W₄ electrode heating energy per discharge - W₅ thermal energy of dielectric of mass M - T mean temperature of channel plasma - S energy of light flux on dielectric layer - h depth of dielectric layer heated to temperature T - density of dielectric - c specific heat of dielectric - m₀ mass of dielectric layer heated to temperature T - T temperature of heated layer - k₁, k₂ constants - u residual stress     

Heat transfer enhancement through liquid film evaporation into countercurrent moist air flow in a vertical plate channel

A numerical analysis has been carried out to study the heat removal process from hot channel plate through liquid film evaporation into a countercurrent air flow. The influences of the wall heat flux, the inlet Reynolds number of liquid film and the inlet Reynolds number of moist air on the transfer characteristics are investigated detailedly. The Results show that the interface latent heat transfer associated with the film vaporization causes a temperature drop of the heated plate in the entry region of air flow, which is more significant for a system with higherq _w , lowerRe _l,in or largerRe _{c, in} . The overall temperature rise of the heated wall is rather small, as compared with the case without interface latent heat transfer. In addition, the difference in results obtained by the one-dimensional and two-dimensional methods is substantial.Die numerische Untersuchung bezieht sich auf den Wärmetransportprozeß von heißen, plattenförmigen Kanalwänden durch Flüssigfilmverdampfung in gegenströmende Luft. Die Einflüsse des Wärmeflusses, der Reynolds-Zahlen, des Flüssigkeitfilms und der Feuchtluft (jeweils am Eintritt) auf das Wärmeübertragungsverhalten werden eingehend untersucht. Die Ergebnisse zeigen, daß die bei der Filmverdampfung eingespeicherte latente Wärme eine Temperaturabnahme der Heizplatte am Eintritt der Luft bewirkt, die mit den Wärmefluß und steigender Reynolds-Zahl für Feuchtluft zunimmt. Die gesamte Temperaturerhöhung der beheizten Wand ist sehr gering im Vergleich mit dem Fall ohne Latentwärmeaustausch. Darüber hinaus resultieren erhebliche Unterschiede in den Ergebnissen, je nachdem, ob eindimensionale oder zweidimensionale Methoden angewandt werden.The financial support of this study by the engineering division of the National Science Council, Taiwan, R.O.C., through the contract NSC 82-0401-E-150-049 is greatly appreciated.     

Determining the molecular mass transfer boundary in a plane vertical channel with mass impermeable walls

The molecular mass transfer boundary in an isothermal ternary gas system is numerically determined for a plane vertical diffusive channel with mass-impermeable walls. The critical Rayleigh number of diffusion-convection transition is determined for a slot channel. Theoretical studies performed within the framework of the linear stability theory are shown to be in agreement with the experimental data.     

Free-convection boundary-layer flow of a non-Newtonian fluid along a vertical wavy surface

A theoretical analysis of laminar free-convection flow over a vertical isothermal wavy surface in a non-Nevvtonian power-law fluid is considered. The governing equations are first cast into a nondimensional form by using suitable boundary-layer variables that substract out the effect of the wavy surface from the boundary conditions. The boundary-layer equations are then solved numerically by a very efficient implicit finite-difference method known as the Keller-Box method. A sinusoidal surface is used to elucidate the effects of the power-law index, amplitude wavelength, and Prandtl number on the velocity and temperature fields, as well as on the local Nusselt number. It is shown that the local Nusselt number varies periodically along the wavy surface. The wave-length of the local Nusselt number variation is half that of the wavy surface, irrespective of whether the fluid is a Newtonian fluid or a non-Newtonian fluid. Comparisons with earlier works are also made, and the agreement is found to be very good.     

Stability of wave regimes in film flow along a vertical surface

The stability of nonlinear traveling waves with respect to all possible two-dimensional infinitesimal perturbations is numerically investigated. The stability zones are determined for two families. It is shown that regimes of the second family, which in the limit go over into positive solitons, are the more stable. Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 126–131, September–October, 1988.     

Laminar flow of a reacting gaseous mixture through a vertical duct with catalytic walls

Numerical analysis has been performed for predicting the onset and establishment of a steady state flow of a reactive hydrogen/air/vapour mixture through a two-dimensional vertical duct of finite length with its side walls coated by catalytic material. The flow is initiated by the exothermic reaction of hydrogen with air oxygen on the catalytic wall, that causes the hot gases to flow upwards through the vertical duct and by continuity sucks fresh mixture through the lower end of the duct. The flow is always laminar and the two-dimensional governing transport differential equations are solved by means of the numerical finite volume method, using a collocated variable arrangement. Comparisons between calculated and experimental data are presented, showing good agreement between them. The method is employed for various initial mixture compositions and duct geometries.     

Heat removal from oscillating flow in a vertical annular channel

In this study, heat removal from a surface, which is located into the reciprocating flow in a vertical annular liquid column, is investigated experimentally. The experiments are carried out for four different oscillation frequencies and three heat fluxes while the amplitude remains constant for all cases. Instantaneous and time-averaged surface and bulk temperature variations are presented. The cycle-averaged values are considered in the calculation of heat transfer using the experimental measurements. Heat removal from the cold surface due to the oscillating liquid column is determined in terms of Nusselt number. Based on the experimental data, an empirical equation is obtained for the cycle averaged Nusselt number as a function of kinetic Reynolds number.     

Laminar flow through a channel with uniformly porous walls of different permeability

Summary The steady laminar flow of a viscous incompressible fluid through a two-dimensional channel, having fluid sucked or injected with different velocities through its uniformly porous parallel walls is considered. A solution for small suction Reynolds number has been given by the authors in a previous paper. The purpose of this paper is to present a solution valid for large Reynolds numbers for the cases of (i) suction at both walls, and (ii) suction at one wall and injection at the other. A technique of matching outer and inner expansions is used to obtain an asymptotic solution for both of these cases. Further a perturbation solution for the case of suction at one wall and injection at the other is obtained by choosing the difference between two wall velocities as the perturbation parameter. Both asymptotic and perturbation solutions are confirmed by exact numerical solutions. As expected, the resulting solutions show the presence of the usual suction boundary layers in both types of flow considered in this paper.