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.     

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.     

Turbulent natural convection flow in a vertical channel with anti-symmetric heating

This paper presents the fluid flow characteristics of natural convection flow in an anti-symmetrically heated parallel-plate vertical channel using the Particle Image Velocimetry (PIV) system. The channel walls were subjected to uniform temperature conditions, with one wall heated above ambient and the opposing wall maintained below ambient temperature. Velocity measurements were conducted at three different sections on the horizontal plane to validate two-dimensionality of the flow and at three different heights in the vertical plane to establish vertical mean velocity profiles. The results indicate that the flow recirculation in the channel exhibits a similar character to that of a closed cavity and the induced flow rate is much lower than the one for a channel with both walls heated. A correlation for the dimensionless flow rate is developed.     

Dynamics of disk-like particles in turbulent vertical channel flow

The dynamical behavior of inertial disk-like particles in turbulent vertical channel flow is investigated by an Eulerian–Lagrangian point-particle approach. Gravity effects on distribution, translation, rotation and orientation statistics of non-spherical particles modeled as oblate spheroids have been studied both in an upward and a downward flow and compared with results obtained in the absence of gravity. Altogether 12 different particle classes have been studied, with inertia and shape parameterized by means of Stokes number St and aspect ratio λ ≤ 1. The St = 5 disk-like particles distribute more evenly across the channel in upward than in downward flow. The gravity effect on the particle concentration diminishes with large inertia and the spheroid shape has only a modest influence. Although the gravity significantly affects the streamwise and wall-normal mean slip velocities with increasing inertia, the particle shape rarely has any impact on the translational motion, except for the mean wall-normal velocity. The fluctuations of the velocity of disk-like particles are mainly ascribed to inertia, whereas the gravity and shape only have marginal effects. The presence of gravity is moreover found to have a negligible effect on the particles’ orientation and rotation, in spite of the striking effect of λ on the orientation and rotation seen in the near-wall region. The tendency of the disks to align their symmetry axis orthogonal to the fluid vorticity in the channel center is stronger for particles with modest inertia. In the near-wall region, however, oblate spheroids preferentially align with the fluid vorticity for St >> 1. The observed behavior is believed to be caused by the influence of the gravity force on the turbophoresis; i.e. that inertial particles move towards low-turbulence regions.     

Transient natural convection flow of a particulate suspension through a vertical channel

Continuum equations governing transient, laminar, fully-developed natural convection flow of a particulate suspension through an infinitely long vertical channel are developed. The equations account for particulate viscous effects which are absent from the original dusty-gas model. The walls of the channel are maintained at constant but different temperatures. No-slip boundary conditions are employed for the particle phase at the channel walls. The general transient problem is solved analytically using trigonometric Fourier series and the Laplace transform method. A parametric study of some physical parameters involved in the problem is performed to illustrate the influence of these parameters on the flow and thermal aspects of the problem.     

Entropy generation in flow field subjected to a porous block in a vertical channel

Entropy generation in the flow field subjected to a porous block situated in a vertical channel is examined. The effects of channel inlet port height (vertical height between channel inlet port and the block center), porosity, and block aspect ratio on the entropy generation rate due to fluid friction and heat transfer in the fluid are examined. The governing equations of flow, heat transfer, and entropy are solved numerically using a control volume approach. Air is used as the flowing fluid in the channel. A uniform heat flux is considered in the block and natural convection is accommodated in the analysis. It is found that entropy generation rate due to fluid friction increases with increasing inlet port height, while this increase becomes gradual for entropy generation rate due to heat transfer for the inlet port height exceeding 0.03 m. The porosity lowers entropy generation rate due to fluid friction and heat transfer. The effect of block aspect ratio on entropy generation rate is notable; in which case, entropy generation rate increases for the block aspect ratio of 1:2.     

PTV experiments of subcooled boiling flow through a vertical rectangular channel

Time resolved Particle Tracking Velocimetry (PTV) experiments were carried out to investigate turbulent, subcooled boiling flow of refrigerant HFE-301 through a vertical rectangular channel with one heated wall. Measurements were performed with liquid Reynolds numbers (based on the hydraulic diameter) of Re = 3309, 9929 and 16,549 over a wall heat flux range of 0.0–64.0 kW/m². Turbulence statistics are inferred from PTV full-field velocity measurements. Quantities such as: instantaneous 2D velocity fields, time-averaged axial and normal velocities, axial and normal turbulence intensities, and Reynolds stresses are obtained. The present results agree well with previous studies and provides new information due to the full-field nature of the technique. This work is an attempt to provide turbulent subcooled boiling flow data for validation and improvement of two-phase flow computational models.     

Effect of inlet subcooling on two-phase flow oscillations in a vertical boiling channel

In this work, results of experimental research to investigate the effects of heat transfer augmentation and inlet subcooling on two-phase flow instabilities are presented. For this purpose, a simple set-up was designed and built. The effect of inlet subcooling was investigated using different heat transfer surfaces and inlet temperatures at constant heat input of 415 W. Freon-11 has been used as the test fluid, and the experiments were carried out for six heater tubes having different heat transfer surfaces. Inlet temperatures were in the range of –9.8°C to 38°C. The results indicate that, in the range of present experiments, the system becomes more stable, that it's instability boundary moves into lower mass flow rates, with increase in the inlet subcooling. However, the amplitudes and the periods of the oscillations increase with increase in the inlet subcooling. For some of the tested surfaces there was a particular inlet subcooling, above and below which the system's stability decreased.

---

Der Einfluß der Eintrittsunterkühlung auf die Oszillationen einer Zwei-Phasen-Strömung in einem senkrechten Siede-Kanal

Zusammenfassung In dieser Arbeit werden die Ergebnisse einer experimentellen Untersuchung des Einflusses von Verbesserungen der Wärmeübertragung und der Eintrittsunterkühlung auf Instabilitäten der Zweiphasenströmung dargestellt. Zu diesem Zweck wurde ein einfacher Aufbau konstruiert und aufgebaut. Der Einfluß der Eintrittsunterkühlung wurde unter Benutzung verschiedener Wärmeübertragungsoberflächen und Eintrittstemperaturen bei einer konstanten Wärmezufuhr von 415 W untersucht. Als Testfluid wurde Freon-11 benutzt. Die Experimente wurden für sechs Heizrohre mit verschiedenen Wärmeübertragungsoberflächen durchgeführt. Die Eintrittstemperaturen lagen in diesem Bereich von –9.8°C bis 38°C. Die Ergebnisse zeigen, daß in dem Bereich der vorliegenden Untersuchungen das System mit einem Ansteigen der Eintrittsunterkühlung stabiler wird und daß dessen Instabilitätsgrenze sich zu niedrigeren Massenstromdichten bewegt. Die Amplituden und Perioden der Schwingungen steigen mit Zunahme der Eintrittsunterkühlung an. Für einige der getesteten Oberflächen existierte eine bestimmte Eintrittsunterkühlung, über bzw. unter welcher die Stabilität des Systems abnahm.

     

Void fraction and pressure fluctuations of bubbly flow in a vertical annular channel

In this investigation some hydrodynamic characteristics of two phase, two component, air water bubbly flow in a vertical annulus were studied. In particular, the void fraction profiles, and the pressure fluctuations were measured by the electrical resistivity probe and a capacitive type differential transducer respectively. These measurements were assessed under various system parameters, viz the air and water flux, the perforation ratio (Area of holes/channel cross sectional area) and the dimensionless axial distance. In addition, the pressure drop calculated from the void fraction measurements was in very good agreement with the corresponding one measured by the pressure transducers.List of symbols D _eq equivalent diameter of the annular channel (m) - j flux (discharge/channel cross sectional area) (m/s) - m mass flow rate (kg/s) - P pressure (Pa) - AP static pressure difference along the test section (Pa) - P pressure fluctuations (Pa) - P ^* dimensionless pressure (P _m/P _S.P. ) - P dimensionless pressure fluctuations (P _max /P _T.P. ) - r radius (m) - z axial distance (m) Greek symbols void fraction - dimensionless axial distance (Z/Dimeq) - perforation ratio (area of holes/channel cross sectional area) - density (kg/m3) - time (s) - dimensionless radial distance (r–r _i )/(r _o-r _i ) Suffix g gas - i inner - L liquid - m mean - Max Maximum - O outer - S.P. single-phase - T.P. two-phase     

Linearized analysis of magnetohydrodynamic entrance flow in a vertical channel with combined thermal convection

A linearized analysis is presented for the magnetohydrodynamic entrance flow with combined forced and free convection in a vertical, constant wall temperature parallel-plate channel. Numerical results are obtained for slug velocity profile at the entrance and for various Hartmann and Grashof Numbers. The results agree well with the finite difference numerical solutions obtained elsewhere. They demonstrate that the velocity development and pressure gradient in the channel entrance region are greatly influenced by the Hartmann Number and the Grashof Number. Increasing Hartmann Number decreases velocity entrance length while increasing Grashof Number increases it. Thermal development is also found to be dependent on the above mentioned parameters, but to a relatively minor extent.Nomenclature A _m constant defined by equation (23) - B ₀ applied magnetic field - C _n constant defined by equation (13) - E ₀ constant electric field - e nondimensional electric field parameter, E ₀/U _mB₀ - Gr Grashof Number, gL ³(T _w–T ₀)/ ² - L half-width of the channel - M Hartmann Number, B ₀ L(/)^1/2 - Nu Nusselt Number, (/y) _y=1/( _w– _m) - P pressure - Pr Prandtl Number, / - p nondimensional pressure parameter, (P–P ₀+ ₀ gX)/P ₀ U _m ² - Re Reynolds Number, U _m L/ - T temperature - T ₀ inlet temperature - T _w wall temperature - U velocity, X direction - U _m average velocity, (1/L) ₀ ^L UdY - u nondimensional form of U, U/U _m - u ₀(y) nondimensional inlet velocity - V velocity, Y direction - v nondimensional form of V, VL/ - X coordinate, axial direction - x nondimensional form of X, vX/L ² U _m - Y coordinate perpendicular to the channel - y nondimensional form of Y, Y/L - thermal diffusivity - _m eigenvalue defined by equation (25) - thermal expansion coefficient - _m eigenvalue defined by equation (24) - stretching factor, weighting function - nondimensional form of T, (T–T ₀)/(T _w–T ₀) - _m mean nondimensional temperature, ₀ ¹ udy - kinematic viscosity - magnetic permeability - mass density - electrical conductivity     

Experimental investigation of water laminar mixed-convection flow with sub-millimeter bubbles in a vertical channel

This paper describes flow and heat transfer characteristics of laminar mixed-convection flows of water with sub-millimeter bubbles in a vertical channel. We use thermocouples and a particle tracking velocimetry technique for the temperature and velocity measurements. The working fluid used is tap water, and hydrogen bubbles generated by electrolysis of the water are used as the sub-millimeter bubbles. The Reynolds number of the main flow ranges from 100 to 200. The ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection (the heat transfer coefficient ratio) ranges from 1.24 to 1.38. The heat transfer coefficient ratio decreases with the increase in the Reynolds number. We conclude from velocity measurements that this decrease is mainly caused by a decrease in the advection effect due to sub-millimeter bubbles.     

Longwave instability of a binary mixture flow in a vertical channel in the presence of vibration

The longwave instability of a hybrid (thermogravitational and thermovibrational) flow of a binary incompressible liquid mixture occurring in a plane vertical channel, whose boundaries are maintained at constant but different temperatures, is studied. The investigation is carried out with account for the Soret thermal-diffusion effect on the ranges of normal and anomalous values of the mixture separation coefficient. It is shown that, owing to the properties of the system, the subharmonic response to an external action is absent. The ranges on which secondary flows arise are analytically determined using the asymptotic expansion method, both under weightlessness conditions and in the presence of the gravity effect. The parameter ranges on which longwave disturbances present the greatest danger for the main flow stability are determined.     

Effect of heat transfer augmentation on two-phase flow instabilities in a vertical boiling channel

The effect of different heater surface configurations on two-phase flow instabilities has been investigated in a single channel, forced convection, open loop, up-flow system. Freon-11 is used as the test fluid, and six different heater tubes with various inside surface configurations have been tested at five different heat inputs. In addition to temperature and pressure recordings, high speed motion pictures of the two-phase flow were taken for some of the experiments to study the two-phase flow behavior at different operating points. Experimental results are shown on system pressure drop versus mass flow rate curves, and stability boundaries are also indicated on these curves. Comparison of different heater tubes is made by the use of the stability boundary maps and the plots of inlet throttling necessary to stabilize the system versus mass flow rate. Tubes with internal springs were found to be more stable than the other tubes.     

Thermophoretic deposition of particles in fully developed mixed convection flow in a parallel-plate vertical channel

A theoretical analysis is made for thermophoretic transport of small particles through a fully developed laminar, mixed convection flow in a parallel vertical channel. The governing gas-particle ordinary differential equations are expressed in non-dimensional form and are solved numerically for some values of the governing parameters so as to investigate extensively their distinct influence on the flow pattern. These equations are solved also analytically in the special case when the thermophoretic effect is absent and the obtained analytical solution can be regarded as a verification of the numerical results, simultaneously. The parameter zone for the occurrence of reversed flow is presented. It is found that the effect of thermophoretic can be quite significant in appropriate situations.     

Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer

In the present paper we discuss the magnetohydrodynamic (MHD) peristaltic flow of a hyperbolic tangent fluid model in a vertical asymmetric channel under a zero Reynolds number and long wavelength approximation. Exact solution of the temperature equation in the absence of dissipation term has been computed and the analytical ex- pression for stream function and axial pressure gradient are established. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The expression for pressure rise has been computed numerically. The physical features of pertinent parameters are analyzed by plotting graphs and discussed in detail.     

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.     

MHD free-convective flow of micropolar and Newtonian fluids through porous medium in a vertical channel

We have studied the fully-developed free-convective flow of an electrically conducting fluid in a vertical channel occupied by porous medium under the influence of transverse magnetic field. The internal prefecture of the channel is divided into two regions; one region filled with micropolar fluid and the other region with a Newtonian fluid or both the regions filled by Newtonian fluids. Analytical solutions of the governing equations of fluid flow are found to be in excellent agreement with analytical prediction. Analytical results for the details of the velocity, micro-rotation velocity and temperature fields are shown through graphs for various values of physical parameters. It is noticed that Newtonian fluids prop up the linear velocity of the fluid in contrast to micropolar fluid. Also the skin friction coefficient at both the walls is derived and its numerical values are offered through tables.     

Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε.     

The effect of two-way coupling and inter-particle collisions on turbulence modulation in a vertical channel flow

Turbulence modulation due to its interaction with dispersed solid particles in a downward fully developed channel flow was studied. The Eulerian framework was used for the gas-phase, whereas the Lagrangian approach was used for the particle-phase. The steady-state equations of conservation of mass and momentum were used for the gas-phase, and the effect of turbulence on the flow-field was included via the standard k–ε model. The particle equation of motion included the drag, the Saffman lift and the gravity forces. Turbulence dispersion effect on the particles was simulated as a continuous Gaussian random field. The effects of particles on the flow were modeled by appropriate source terms in the momentum, k and ε equations. Particle–particle collisions and particle–wall collisions were accounted for in these simulations. Gas-phase velocities and turbulence kinetic energy in the presence of 2–100% mass loadings of two particle classes (50 μm glass and 70 μm copper) were evaluated, and the results were compared with the available experimental data and earlier numerical results. The simulation results showed that when the inter-particle collisions were important and was included in the computational model, the fluid turbulence was attenuated. The level of turbulence attenuation increased with particle mass loading, particle Stokes number, and the distance from the wall. When the inter-particle collisions were negligible and/or was neglected in the model, the fluid turbulence was augmented for the range of particle sizes considered.     

Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel

In this paper, the influence of heat transfer and induced magnetic field on peristaltic flow of a Johnson-Segalman fluid is studied. The purpose of the present investigation is to study the effects of induced magnetic field on the peristaltic flow of non-Newtonian fluid. The two-dimensional equations of a Johnson-Segalman fluid are simplified by assuming a long wavelength and a low Reynolds number. The obtained equations are solved for the stream function, magnetic force function, and axial pressure gradient by using a regular perturbation method. The expressions for the pressure rise, temperature, induced magnetic field, pressure gradient, and stream function are sketched and interpreted for various embedded parameters.