Hydrodynamic Pressure Gradient Research Articles

Experiments on the flow over a hill covered by a canopy in stably stratified conditions

It has long been suspected that thermo-topographic flows, especially gravity currents, within vegetation canopies on complex terrain are one of the main reasons behind the failure to reconcile micrometeorological and biometric estimates of canopy-atmosphere exchange at many sites. However, the physical mechanisms governing the initiation and the scaling of these flows remain poorly understood. Here we present the results of a novel wind tunnel study that looks in detail at the flow within and above an open canopy in stably stratified conditions and investigates the physical mechanisms responsible for gravity currents within canopies. The wind tunnel simulations demonstrate that gravity currents are established through a complex balance of competing forces on the flow within the canopy. Three forcing terms act on the flow in the canopy as it passes over the hill. First is the hydrodynamic pressure gradient associated with the boundary layer flow aloft; second, a hydrostatic pressure gradient associated with the displacement of temperature and density surfaces by the hill, and finally a thermal wind term, where a streamwise pressure gradient is caused by changes in the depth of the temperature perturbations to the flow. The net balance of these forces is opposed by the canopy drag. Gravity currents, however, do not appear unless the turbulence, which supports the transport of momentum into the canopy, is also reduced. This suppression occurs preferentially deep within the canopy due to a Richardson number cut-off effect, which is directly linked to the different transport mechanisms of heat and momentum across the boundary layers on the canopy elements. The gravity current first appears at the ground surface, despite cooling profiles that are concentrated in the upper canopy. Once initiated, a gravity current can propagate substantial distances away from the triggering topography, driven by the thermal wind term. If shown to be robust these results have widespread implications for the micrometeorology, atmospheric boundary layer and numerical weather prediction communities.

On the cone-to-jet transition region and its significance in electrospray propulsion

A novel method for identifying the cone-to-jet transition region is proposed to characterize the electrospray dynamics, and thus the Taylor cone, a fundamental principle of ion extraction from the tip of the Taylor cone in an electric field to produce μN thrust for nanosatellites' application. A numerical model is developed and validated against the droplet's diameter with a proper characterization of the cone-to-jet transition region based on the hydrodynamic pressure gradient at the cone-jet axis. The results show that the cone-to-jet transition region is reduced when the electric potential increases and the flow rate decreases. Moreover, the current density is found to be higher for the lower flow rate and large electric potential. Interestingly, the current density at the jet axis increases significantly at the flow rate of 1 cc/hr. This implies that below a certain droplet diameter, the current density carried by the jet interface is completely migrated into the jet, and the substantial change in the current density occurs within the cone-to-jet transition region. When comparing the current density along the jet axis, the small flow rate and large electric potential carry the maximum current density at the jet interface. The identification of cone-to-jet transition region is central in modeling the ion beam trajectory via initial current density profile required for particle-in-cell calculation for assuring the performance of a field emission electric propulsion thruster.

Circular bubbles in a Hele-Shaw channel: a Hele-Shaw Newton's cradle

We consider the propagation of inviscid bubbles in a Hele-Shaw cell under a uniform background flow. We focus on the distinguished limit in which the hydrodynamic pressure gradient due to the external flow balances viscous drag effects due to thin liquid films between the bubbles and the cell walls (Bretherton, J. Fluid Mech., vol. 10, issue 2, 1961, pp. 166–188), with the ratio between these two effects measured by a single dimensionless parameter that we label $\delta$ . In this regime, we find that each bubble remains approximately circular, and its propagation velocity is determined by a net force balance. The analytical solution for the problem of an isolated bubble in an infinite Hele-Shaw cell is found to agree well with experimental data in the literature. In particular, we find that the bubble may move faster or slower than the background fluid speed, depending on whether $\delta >1$ or $\delta <1$ , or precisely with the background flow if $\delta =1$ . When the model is generalised to include the effects of multiple bubbles and boundaries in the Hele-Shaw cell, we still find that the sign of $\delta -1$ causes striking changes in the qualitative behaviour. For a train of three or more bubbles moving along a Hele-Shaw channel, we observe longitudinal waves that propagate forwards or backwards along the bubble train, depending on whether $\delta >1$ or $\delta <1$ , resembling a Hele-Shaw Newton's cradle.

Model of inverse bleb growth explains giant vacuole dynamics during cell mechanoadaptation.

Cells can withstand hostile environmental conditions manifest as large mechanical forces such as pressure gradients and/or shear stresses by dynamically changing their shape. Such conditions are realized in the Schlemm's canal of the eye where endothelial cells that cover the inner vessel wall are subjected to the hydrodynamic pressure gradients exerted by the aqueous humor outflow. These cells form fluid-filled dynamic outpouchings of their basal membrane called giant vacuoles. The inverses of giant vacuoles are reminiscent of cellular blebs, extracellular cytoplasmic protrusions triggered by local temporary disruption of the contractile actomyosin cortex. Inverse blebbing has also been first observed experimentally during sprouting angiogenesis, but its underlying physical mechanisms are poorly understood. Here, we hypothesize that giant vacuole formation can be described as inverse blebbing and formulate a biophysical model of this process. Our model elucidates how cell membrane mechanical properties affect the morphology and dynamics of giant vacuoles and predicts coarsening akin to Ostwald ripening between multiple invaginating vacuoles. Our results are in qualitative agreement with observations from the formation of giant vacuoles during perfusion experiments. Our model not only elucidates the biophysical mechanisms driving inverse blebbing and giant vacuole dynamics, but also identifies universal features of the cellular response to pressure loads that are relevant to many experimental contexts.

The Non-Unicity of the Film Thickness in the Hydrodynamic Lubrication: Novel Approach Generating Equivalent Micro-Grooves and Roughness

Since the 1960s, all studies have assumed that a film thickness “<i>h</i>” provides a unique pressure field “<i>p</i>” by resolving the Reynolds equation. However, it is relevant to investigate the film thickness unicity under a given hydrodynamic pressure within the inverse theory. This paper presents a new approach to deduce from an initial film thickness a widespread number of thicknesses providing the same hydrodynamic pressure under a specific condition of gradient pressure. For this purpose, three steps were presented: 1) computing the hydrodynamic pressure from an initial film thickness by resolving the Reynolds equation with Gümbel’s cavitation model, 2) using a new algorithm to generate a second film thickness, 3) comparing and validating the hydrodynamic pressure produced by both thicknesses with the modified Reynolds equation. Throughout three surface finishes: the macro-shaped, micro-textured, and rough surfaces, it has been demonstrated that under a specific hydrodynamic pressure gradient, several film thicknesses could generate the same pressure field with a slight difference by considering cavitation. Besides, this paper confirms also that with different ratios of the averaged film thickness to the root mean square (RMS) similar hydrodynamic pressure could be generated, thereby the deficiency of this ratio to define the lubrication regime as commonly known from Patir and Cheng theory.

Aggregation of a dense suspension of particles in a microwell using surface acoustic wave microcentrifugation

We investigate the aggregation of a dense suspension of particles (volume fraction, $$\varphi \sim 0.1$$ ) in a PDMS microwell by employing surface acoustic wave (SAW) microcentrifugation. In spite of acoustic attenuation at the LiNbO3–PDMS interface, a significant portion of the energy (> 80%) is available for driving fluid actuation, and, in particular, microcentrifugation in the microwell via acoustic streaming. Rapid particle aggregation can then be affected in the microcentrifugation flow, arising as a consequence of the interplay between the hydrodynamic pressure gradient force $$F_{\text{p}}$$ responsible for the migration of particles to the center of the microwell and shear-induced diffusion force $$F_{\text{SID}}$$ that opposes their aggregation. Herein, we experimentally investigated the combined effect of the particle size $$a$$ and sample concentration $$c$$ on these microcentrifugation flows. The experimental results show that particles of smaller size and lower sample concentration (such that $$F_{\text{p}} > F_{\text{SID}}$$ ) are concentrated efficiently into an equilibrium spot, whose diameter scales with the initial particle volume fraction as $$d_{\text{cs}} \sim \varphi^{0.3}$$ . In contrast, we found that as the local particle volume fraction at the center of the microwell approaches $$\varphi \sim 0.1$$ such that $$F_{\text{SID}} \ge F_{\text{p}}$$ , the particle aggregation fails. Additionally, we also investigate the effects of the well diameter, and the height, lateral positioning of microwell and the liquid volume on the microcentrifugation.

Breakup of a leaky dielectric drop in a uniform electric field.

Electrohydrodynamic (EHD) breakup phenomena for a leaky dielectric drop suspended in another immiscible viscous dielectric and subjected to a uniform electric field are examined using the leaky dielectric theory and the explicit forcing lattice Boltzmann method, by taking into account full nonlinear inertia effects. The breakup modes are first computed for varied conductivity of the drop fluid, as the viscosity ratio λ (=μ_{in}/μ_{out}) is momentarily set to unity, that is, for the slightly conducting (R=σ_{in}/σ_{out}<10), moderately conducting (10≤R≤20), and highly conducting (R>20) cases. For slightly conducting drops (R=5) only one breakup mode via two symmetrical necks persists for permittivity ratios 0.05<Q=ɛ_{in}/ɛ_{out}<3.0 and electric capillary number Ca_{E}>Ca_{E,critical} (ratio of electric and surface tension forces), despite significant length-scale variation of mother and daughter drops. At higher Q (for increased drop permittivity) two necks move closer to the bulbous midpart of the extended droplet, which helps enlarge two daughter drops. However, in the case of moderately conducting drops (10≤R≤20) the number of necks increased to four for increased Ca_{E}. Accordingly two pairs of symmetrical daughter drops are created because of recurrent fluctuations of the electrical shear stress and centerline momentum flux. For highly conducting cases of R>20, depending on Ca_{E}, three distinctly elongated droplet states are formed prior to breakup, which results in the onset of three different breakup modes, namely, via formations of lobed ends (Ca_{E}≤0.264), pointed ends (Ca_{E}≤0.68), and nonpointed ends (Ca_{E}>0.83). While being consistent with past measurements, here we precisely characterize the associated breakup mechanisms and physics in terms of the interactive electric pressure, electric shear stress, and hydrodynamic pressure plus velocity gradients. Since the EHD drop breakup is a dynamic process, on an elongated slender drop the activated locally distinct driving forces, i.e., electric pressure at the end regions and tangential electric stress in the midsection, effectively lead to neck formations by virtue of the created high centerline velocity gradient. Accordingly, resulting variations of local extension rate and net mass flux toward drop ends or into intermediate bulbous regions facilitate the multiple-mode drop breakup via the inertia effect, whereas the developed negative curvature around a neck encourages capillary breakup. We also explicitly reveal the effect of the viscosity contrast λ, which particularly influences the breakup characteristics over a broader range of conductivity ratios.

Self-centering characteristics of a petal-shaped capsule robot

Based on the multiple wedge effects, a petal-shaped capsule robot (PCR) is proposed, and the self-centering phenomenon of the PCR is discovered. For investigating the self-centering characteristics, an innovative concept of the instantaneous fluid membrane (FM) thickness, along with the dynamic FM thickness, is proposed; thus a dynamic FM thickness model and a hydrodynamic pressure (HP) model are derived when the PCR axis deviates from the pipe axis under the effect of gravity. A kinematics equation during suspending process in the vertical direction and a swimming kinematics equation in axial direction are derived respectively. Four capsule robots with different eccentricities of the tiles were manufactured and tested, the theoretical and experimental results show that the HP gradient is a fundamental reason for the self-centering phenomenon. The PCR with the self-centering ability can directly avoid the contact with the bottom of the gastrointestinal (GI) tract, achieving the excellent obstacle surmounting ability in the GI complex environment with the less twisted impact on the GI tract, which has a promising application prospect in the GI diagnosis.

Lateral line layout correlates with the differential hydrodynamic pressure on swimming fish.

The lateral line of fish includes the canal subsystem that detects hydrodynamic pressure gradients and is thought to be important in swimming behaviors such as rheotaxis and prey tracking. Here, we explore the hypothesis that this sensory system is concentrated at locations where changes in pressure are greatest during motion through water. Using high-fidelity models of rainbow trout, we mimic the flows encountered during swimming while measuring pressure with fine spatial and temporal resolution. The variations in pressure for perturbations in body orientation and for disturbances to the incoming stream are seen to correlate with the sensory network. These findings support a view of the lateral line as a "hydrodynamic antenna" that is configured to retrieve flow signals and also suggest a physical explanation for the nearly universal sensory layout across diverse species.

Theory and measurement of plasmonic terahertz detector response to large signals

Electron gas in the conduction channel of a Field Effect Transistor (FET) can support collective plasma oscillations tunable by the gate voltage. In the Dyakonov-Shur terahertz (THz) detector, nonlinearities in the plasma wave propagation in the gated channel of a FET lead to a constant source-to-drain voltage providing the detector output. We present the detector theory in the frame of the hydrodynamic model using the electron plasma Navier-Stokes and thermal transport equations, thus fully accounting for the hydrodynamic non-linearity, the viscosity, and pressure gradients in the detector response. Both resonant and broadband operations of the high electron mobility transistor (HEMT) based plasmonic detectors are described by this model. The relation between the electron channel density and gate voltage was modeled by the unified charge control model applicable both above and below the threshold voltage. The theoretical results are compared with the response measured in the short channel InGaAs HEMT and the analytical approximation. The THz source was operating at 1.63 THz, and the response was measured at varying signal intensities. The response of the detector operated in the open drain mode was measured above and below the threshold, and the theoretical and experimental results are shown to be in good agreement.

Pressure Evolution and Production Performance of Waterflooding inn-Heptane-Saturated Fired Berea Cores

SummaryThis work presents experimental results and interpretation of injection pressure and recovery performance of waterflooding in strongly water-wet fired Berea cores saturated with n-heptane. The experiments were conducted at constant injection rate at room conditions, and the effects of injection rate and initial water saturation on the oil-recovery performance and dynamic-injection pressure were investigated. Elements of surprise were observed in the injection-pressure data. The pressure profiles showed four distinct regimes, each governed by capillary or viscous forces. At low capillary numbers (Ca=uμ/σ&amp;lt;10–6), capillarity governed two pressure regimes, corresponding to the core inlet and outlet. In the early part of waterflooding, pressure stayed constant for a considerable time before hydrodynamic pressure gradient could overcome the capillary pressure gradient. After viscous forces dominated, a linear increase in injection pressure over time was observed up to breakthrough time. A sudden pressure rise was observed close to breakthrough because of capillary retention at the core outlet. The pressure became constant after the breakthrough when the water- and oil-saturation distributions were stabilized. Changing the injection rate by an order of magnitude in the range from 2.2 to 22.2 pore volumes (PV)/D (equivalent to Ca = 10–7 to 10–6) did not appreciably change the oil-recovery performance; similar breakthrough time and final oil recovery were observed. The effect of initial water saturation was also investigated. When lowering the initial water saturation beyond that established in oil flooding, production performance and injection pressure were similar to those of a core without the initial water saturation. The injection pressure at breakthrough was found to decrease with increase of the initial water saturation. Waterflooding was modeled by including the capillary pressure and excellent agreement was obtained with experimental results of production and injection pressure. We find that in the absence of in-situ saturation measurements, the injection pressure is a better variable for tuning the model parameters compared with the production history alone.

Potential hydrodynamic origin of frictional transients in sliding mesothelial tissues

AbstractSteady-state and transient variations in frictional force observed in tribological experiments of mesothelial tissues sliding in lubricant were analyzed with a mathematical model to test the hypothesis that such phenomena are manifestations of elastohydrodynamic lubrication and, importantly, do not require physical contact between the sliding surfaces. The model incorporates three phenomena characteristic of elastohydrodynamic lubrication: thinning of the liquid layer between sliding surfaces under a normal load (“squeeze-out”), thickening of the liquid layer due to hydrodynamic pumping, and smoothing of the elastic surfaces caused by hydrodynamic pressure gradients. Observations in soft mesothelial tissues sliding in lubricant showed variations in steady state friction with velocity, load, and lubricant viscosity. In non-steady sliding, the decay rate of frictional transients at the start of rotation varied with velocity, the amplitudes of these transients varied with the preceding periods without rotation, and frictional force varied during sinusoidal sliding. Model simulations were qualitatively similar to experimental results, supporting these mechanisms. Higher lubricant viscosity increased lubricating layer thickness and lowered friction at low speeds and increased friction at high speeds, supporting hydrodynamic pumping. We conclude that the frictional variations seen with sliding mesothelial tissues are consistent with elastohydrodynamic lubrication without contact between the sliding surfaces.

Thromboembolism and Congenital Malformations

To propose a pathophysiologic mechanism to unify a variety of disparate sporadic congenital malformations. Inductive and deductive analyses to correlate malformation laterality with asymmetries in thoracic anatomy, critical analysis of malformations with female predominance, and concepts of hydrodynamic pressure gradients in vascular growth were applied to the ensuing development of guiding tissue scaffolds for cellular proliferation, differentiation, and apoptosis. Duane syndrome may develop following a focal vascular insult to the sixth nerve trunk with axonal degeneration, allowing for substitutive innervation from third nerve axons to the lateral rectus muscle. Causative fibrin clots may originate from the venous system and paradoxically migrate through physiological right-to left shunts, or they may arise directly from the heart. Hence, the unilateral, left-sided, and female predominance of Duane syndrome results from the asymmetry in the thoracic anatomy and from thrombosis risk factors. Embolic occlusions may also alter local hemodynamic pressure gradients, leading to the compensatory enlargement and persistence of the fetal vasculature and may dysregulate tissue growth. Within the eye, this results in forms of Peters anomaly, unilateral congenital cataracts, and the morning glory disc anomaly, all in the vascular territory of the carotid arteries that also share a propensity for left-sided involvement in girls. Most aberrant misinnervation phenomena (eg, jaw-winking syndrome, crocodile tear syndrome, Brown syndrome, and congenital fibrosis syndrome) and, by extrapolation, the hypoplasia or dysgenesis of noncephalic anatomical structures (including limbs) may be similarly explained. Such malformations will occur more frequently under thrombogenic conditions, such as those induced by thalidomide. Fibrin emboli and focal hypoperfusion may explain the development of many sporadic congenital malformations.

Hydrodynamic Pressure Gradient Correlation of Some Iraqi Oil Wells

Hydrodynamic Pressure Gradient Correlation of Some Iraqi Oil Wells

Night-time airflow in a forest canopy near a mountain crest

Night-time airflow within a deep and dense canopy near the top of a mountain ridge is investigated based on measurements at Bily Kriz, Czech Republic. The site is characterized by a young Norway spruce forest on a 13° slope and the occurrence of almost exclusively upslope or downslope flows. The forest canopy reaches the ground surface. A decoupled two-layer structure of canopy flow typically develops at night. While the above-canopy flow is most frequently an upslope-directed larger-scale flow over the ridge, the lower-canopy flow is downslope (katabatic). However, the lower-canopy flow can be forced upslope when the wind speed above the canopy exceeds a well-defined limit. Less frequently, on the lee slope to the larger-scale flow, both the above-canopy and the lower-canopy flow are usually downslope, although a flow reversal in the lower canopy is also observed, accompanied with a large shear stress (friction velocity) above the canopy. The occurrence of opposing flows is not limited to sunset/sunrise transition periods. In a simplified modelling approach to the dynamics of the nocturnal lower-canopy flow decoupled from above, local equilibrium is assumed of solely two opposing driving forces – one induced by the negative buoyancy (due to radiative cooling of the canopy) and the other by the hydrodynamic pressure gradient (resulting from the larger-scale flow over the ridge) – and the canopy drag as a retarding force. The diagnostic model gives realistic values of the major driving terms for Bily Kriz, and the downslope or upslope direction and speed of the lower-canopy flow that agree well with the measurements. The model contributes to better interpretation of the experimental results, which are in accordance with recent publications on the flow patterns on forested hills. Knowledge of the lower-canopy flow behaviour and of the degree of its decoupling from the flow aloft is necessary for assessing the contribution of advection to the CO 2 budget at sloping forest sites, and for analysis of the flux footprint.

Relevance of hindrance factors and hydrodynamic pressure gradient in the modelization of the transport of neutral solutes across nanofiltration membranes

Abstract Here we show how the usual model for the transport of neutral solutes through porous membranes, lead to equations that can be compared with the thermodynamic equations of transport. This is done in detail and paying special attention to the assumptions made that frequently have been not taken into account. This model can be used to get information on the pore size from functional data on retention and permeability. Two parameters are needed to fit experimental results of retention versus volume flow. We show the total equivalence of using the Staverman reflection coefficient and the solute permeability coefficient as parameters or the pore radius and the ratio of porosity and pore length. It is also equivalent to measure, adequate and separately, the reflection and the permeability coefficients and to evaluate from them the pore radius and the ratio of porosity versus pore length or vice versa. Moreover, the effect of the amplification of viscosity in small pores and the information contained in the pure water permeability are included in the model to reduce the number of required parameters to one, as for example the pore radius. We show that when the pore reflection coefficient is considered some bounds for the values of the pore hindrance factors must be accomplished for big and small molecules as compared to the pore size. Criteria to allow an election among the many expressions proposed for such hindrance factors in literature are proposed based on these requirements. An adequate consideration of pore wall friction and applied pressure gradient is shown to be very important as far as when these factors are inappropriately neglected, very significant errors appear in the prediction of performances of nanofiltration membranes, mainly for intermediate retentions.

Mixed convection with heating effects in a vertical porous annulus with a radially varying magnetic field

Fully developed parallel flow in an annular region filled with a porous medium surrounding an electric cable is investigated. The effects of buoyancy and MHD force as well as the heat generation due to Joule heating and viscous dissipation are taken into account. The mixed convection seepage flow is analyzed according to Darcy law and to Boussinesq approximation. Buoyancy effect is modelled by setting the isoflux wall temperature as the reference temperature. As a consequence of this choice, the local momentum and energy balance equations and the boundary conditions can be written in a dimensionless form that defines an initial value problem instead of a boundary value problem. The initial value problem is solved both by an analytical series method and by numerical integration. The effect of the radially varying magnetic field on the fluid velocity and temperature distributions is analyzed. It is shown that a significantly strong magnetic force tends to inhibit the flow even for a high hydrodynamic pressure gradient.

Buoyant Poiseuille–Couette flow with viscous dissipation in a vertical channel

Steady combined forced and free convection is investigated in a vertical channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The moving wall is thermally insulated, while the wall at rest is kept at a uniform temperature. The analysis deals with the fully–developed parallel flow regime. The governing equations yield a boundary value problem, that is solved analytically by employing a power series expansion of the velocity field with respect to the transverse coordinate. It is shown that the nonlinear interplay between buoyancy and viscous dissipation may determine the existence of dual solutions of the boundary value problem corresponding to fixed values of the applied shear stress on the moving wall and of the hydrodynamic pressure gradient. It is shown that a nontrivial fully separated flow may occur such that the hydrodynamic pressure gradient is zero and the shear stress vanishes on both walls.

Hydrodynamic thickening of lubricating fluid layer beneath sliding mesothelial tissues

The delicate mesothelial surfaces of the pleural space and other serosal cavities slide relative to each, lubricated by pleural fluid. In the absence of breathing motion, differences between lung and chest wall shape could eventually cause the lungs and chest wall to come into contact. Whether sliding motion keeps lungs and chest wall separated by a continuous liquid layer is not known. To explore the effects of hydrodynamic pressures generated by mesothelial sliding, we measured the thickness of the liquid layer beneath the peritoneal surface of a 3-cm disk of rat abdominal wall under a normal stress of 2 cm H 2O sliding against a glass plate rotating at 0–1 rev/s. Thickness of the lubricating layer was determined microscopically from the appearance of fluorescent microspheres adherent to the tissue and glass. Usually, fluid thickness near the center of the tissue disk increased with the onset of glass rotation, increasing to 50–200 μm at higher rotation rates, suggesting hydrodynamic pumping. However, thickness changes often differed substantially among tissue samples and between clockwise and counter-clockwise rotation, and sometimes thickness decreased with rotation, suggesting that topographic features of the tissue are important in determining global hydrodynamic effects. We conclude that mesothelial sliding induces local hydrodynamic pressure gradients and global hydrodynamic pumping that typically increases the thickness of the lubricating fluid layer, moving fluid against the global pressure gradient. A similar phenomenon could maintain fluid continuity in the pleural space, reducing frictional force and shear stress during breathing.

Buoyant MHD flows in a vertical channel: the levitation regime

Buoyant magnetohydrodynamic (MHD) flows with Joulean and viscous heating effects are considered in a vertical parallel plate channel. The applied magnetic field is uniform and perpendicular to the plates which are subject to adiabatic and isothermal boundary conditions, respectively. The main issue of the paper is the levitation regime, i.e., the fully developed flow regime for large values of the Hartmann number M, when the hydrodynamic pressure gradient evaluated at the temperature of the adiabatic wall is vanishing. The problem is solved analytically by Taylor series method and the solution is validated numerically. It is found that the fluid velocity points everywhere and for all values of M downward. For small M’s, the velocity field extends nearly symmetrically (with respect to the mid-plane) over the whole section of the channel between the adiabatic and the isothermal walls. For large values of M, by contrast, the fluid levitates over a broad transversal range of the channel, while the motion becomes concentrated in a narrow boundary layer in the neighborhood of the isothermal wall. Accordingly, the fluid temperature is nearly uniform in the levitation range and decreases rapidly within the boundary layer in front of the isothermal wall. It also turns out that not only the volumetric heat generation by the Joule effect, but also that by viscous friction increases rapidly with increasing values of M, the latter effect being even larger than the former one for all M.