The combined influence of normal transpiration and tangential movement of a porous surface on the unsteady separated stagnation-point flow and heat transfer of a viscous fluid is studied. This study is based on five physical parameters, namely (i) flow strength parameter a, (ii) suction/injection parameter d, (iii) plate velocity parameter λ , (iv) unsteadiness parameter β , and (v) Prandtl number Pr. This analysis shows an interesting relation β = 2a which allows us to derive some closed-form analytic solutions depending upon the unlikely values of d. For suction d > 0, two attached flow solutions (AFS) without point of inflection are found in the range ( − a d 2 / 4 − 3 < λ < − 3 ) , whereas for λ > −3 only one solution of the same type is found for any given value of d. Besides them, the numerical computations reveal two types of AFS—one without and the other with a point of inflection in the range (−1.24658 ≤ λ ≤ −1.07) when d = β = 0. The present analysis confirms the nonexistence of the second attached flow solution after a certain value of suction d depending upon the choice of the values of λ in this range. A reverse flow solution (RFS) along with the above two solutions is found for a negative value of β which continues even for large rate of suction d. The asymptotic solutions of this flow problem have also been derived for large values of d which provide with the exact results after a certain value of d depending upon the values of the other parameters.

The interfacial instability of Rayleigh–Taylor type at the cylindrical boundary involving the liquid phase and vapor phase of a fluid has been considered when the vapor is warmer than the liquid. We use viscous potential flow theory to include the viscosity at the interface. To examine the stability of the arrangement, the normal-mode analysis is performed together with the effect of heat as well as mass transfer and free swirl. The physical system consists of an annular fluid layer restricted in a cylinder with vapor phase in the core. This work investigates the effect of a variety of variables on the instability of the interface. It is found that when the heat transfer constant increases, the range of stability increases. Also, the range of stability increases faster in the presence of swirling.

This work utilizes the direct simulation Monte Carlo (DSMC) calculations and examines the influence of rarefication on the mixing length and effective diffusion coefficient in a two-species mixing problem. There have been efforts in past rarefied mixing flow studies to bridge between the mixing evolution rate and Knudsen number. A careful review of those efforts shows that the past derived relations did not determine the weights of Reynolds (or Peclet) number in the rarefaction influences. Although they indicated that an increase in Knudsen would decrease the mixing length, such reductions were primarily due to the Reynolds (or Peclet) reduction. Therefore, those studies could not explicitly appraise the contribution of rarefaction in the total mass diffusion magnitude. This work focuses specifically on the role of rarefaction in the total diffusive mass transfer magnitude in rarefied gas mixing problems. It excludes the contributions of momentum and heat to the mass diffusion via imposing suitable velocity, pressure, and temperature fields in the mixer domain. The results show that there will be some decreases in the diffusive mass fluxes and some increases in the mixing length as Knudsen increases. Using the Fick’s law, the effective diffusion coefficient is then calculated in the mixer zone. The results show that this coefficient may vary considerably throughout the mixer zone due to the local rarefaction level variation. The results of all investigated cases indicate that the trends of their effective diffusion coefficient variations approach to a limiting value as the rarefaction level decreases.

The bulk modulus of hydraulic fluid is dependent on the quantity of entrained gas in the fluid. In this paper, an effective fluid bulk modulus model that captures dynamic gas absorption during pressure transients is derived from the overall mass transfer theory. Optical measurement of a microgas bubble volume is used to determine the interfacial mass transport. Compared to traditional models, the proposed model is able to capture the 10% gap in the pressure profile between the first and second cycles, when simulating multiple compression cycles of an oil sample with 0.65% entrained gas by volume at 8 MPa.

Lattice Boltzmann equation with Bhatnagar–Gross–Krook (BGK) model is applied to simulate unsteady laminar flow around a confined square obstacle, in order to study the vortex shedding and their interaction in the flow on the mass transfer in the parietal zone of a channel. The model was tested by comparing to an experimental study via standard particle image velocimetry (PIV). A post-processing was used to well extract instantaneous vortices contained in the flow downstream obstacles. A sensor with zero concentration on the surface is placed on the channel wall to study the effect of wake instabilities on the parietal mass transfer.

The effect of heat and mass transfer on the Kelvin–Helmholtz instability between liquid and vapor phases of a fluid has been studied using three different theories: a purely irrotational theory based on the dissipation method, a hybrid irrotational-rotational theory, and an inviscid potential flow theory. These new results are compared with previous results from viscous irrotational theory. The stability criterion is given in terms of the critical value of relative velocity. The system is shown to be unstable when the relative velocity is greater than the critical value of relative velocity; otherwise, it is stable. It is observed that heat and mass transfer has a destabilizing effect on the stability of the system while vapor fraction has a stabilizing effect.

In this paper, we investigate the effect of irrotational, viscous pressure on capillary instability of the interface between two viscous, incompressible, and thermally conducting fluids in a fully saturated porous medium when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface and when there is mass and heat transfer across the interface. The analysis extends our earlier work in which the capillary instability of two viscous and thermally conducting fluids in a fully saturated porous medium was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. We use the Darcy's model, and a quadratic dispersion relation is obtained. It is observed that heat and mass transfer has a stabilizing effect on the stability of the system and this effect enhances in the presence of irrotational viscous pressure.

In this paper, the flow and mass transfer of a two-dimensional unsteady stagnation-point flow over a moving wall, considering the coupled blowing effect from mass transfer, is studied. Similarity equations are derived and solved in a closed form. The flow solution is an exact solution to the two-dimensional unsteady Navier–Stokes equations. An analytical solution of the boundary layer mass transfer equation is obtained together with the momentum solution. The examples demonstrate the significant impacts of the blowing effects on the flow and mass transfer characteristics. A higher blowing parameter results in a lower wall stress and thicker boundary layers with less mass transfer flux at the wall. The higher wall moving parameters produce higher mass transfer flux and blowing velocity. The Schmidt parameters generate a local maximum for the mass transfer flux and blowing velocity under given wall moving and blowing parameters.

In this paper, the electrohydrodynamic three-dimensional Kelvin–Helmholtz instability of a cylindrical interface with heat and mass transfer between liquid and vapor phases is studied. The liquid and the vapor are saturated, two coaxial cylindrical porous layers, and the suction/injection velocities for the fluids at the permeable boundaries are also taken into account. The dispersion relation is derived and the stability analysis is discussed for various parameters. It is found that the streaming velocity has a destabilizing effect, while the axial electric field has a stabilizing one. The suction for both the liquid and the steam has a destabilizing effect in contrast with the injection at both boundaries. The flow through porous structure is more stable than the pure flow. The case of the axisymmetric (for zero value of the azimuthal wave number m) and asymmetric (for nonzero value of the azimuthal wave number m) disturbances at large wavelength (at the wave number k→0) are always stable. Meanwhile, it is the same dispersion relation for the plane geometry at large wave number. Finally, our results are corroborated by comparing them with the previous published results.

We study the nonlinear Rayleigh–Taylor instability of the interface between two viscous fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The fluids are considered to be viscous and incompressible with different kinematic viscosities. The method of multiple expansions has been used for the investigation. In the nonlinear theory, it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. The various stability criteria are discussed both analytically and numerically and stability diagrams are obtained. It has been observed that the heat and mass transfer has stabilizing effect on the stability of the system in the nonlinear analysis.

Parallel plate disks (PPD) are often used for analyzing the effect of small amplitude oscillations with different frequencies. These devices allow the imposing of a well-known flow kinematics. Mass transfer problems and, particularly, convection-diffusion problems relating wall shear rate to mass transfer can thus be studied. Mass transfer signals can be determined from a sandwich electrodiffusion (ED) sensor frequency response. The experimental database constructed was used to check the inverse method. Indeed, the inverse method (Rehimi et al., 2006, “Inverse Method for Electrochemical Diagnostics of Flows,” Int. J. Heat Mass Transfer, 49, pp. 1242–1254) applied on a sandwich ED sensor was analyzed by comparing its instantaneous numerical wall shear rates to the known local and instantaneous experimental wall shear rate. Oscillatory flows amplitudes, frequencies effects, and flow direction effect have been studied in order to test the robustness of the inverse method to such effects. The little difference between experimental and numerical results is probably caused by the sensitivity of the sandwich sensor to such flow directions or to the neglecting of the insulating gap effect on the inverse method.

Efficiently employing two-phase flows for cooling objectives requires comprehensive knowledge of their behavior in different conditions. Models, capable of predicting heat transfer and fluid flow trends in this area, are of great value. Numerical/analytical models in the literature are one-dimensional models involving with many simplifying assumptions. These assumptions in most cases include neglecting some mechanisms of mass transfer in two-phase flows. This study is devoted to developing an analytical two-dimensional model for simulation of fluid flow and mass transfer in two-phase flows considering the all mass transfer mechanisms (entrainment, evaporation, deposition and condensation). The correlation employed for modeling entrainment in this study, is a semiempirical correlation derived based on physical concept of entrainment phenomenon. Emphasis is put on the annular flow pattern of liquid vapor two-phase flow since this regime is the last encountered two-phase regime and has a higher heat transfer coefficient among other two-phase flow patterns. Attempts are made to employ the least possible simplification assumptions and empirical correlations in the modeling procedure. The model is then verified with experimental models of Shanawany et al., Stevanovic et al. and analytical model of Qu and Mudawar. It will be shown, considering pressure variations in both radial and axial directions along with applying our semiempirical entrainment correlation has improved the present analytical model accuracy in comparison with the accuracy of available analytical models.

Characteristics of turbulent mass transfer around a rotating circular cylinder have been investigated by Direct Numerical Simulation. The concentration field was computed for three different cases of Schmidt number, Sc = 1, 10 and 100 at Re R * = 336. Our results confirm that the thickness of the Nernst diffusion layer decreases as Sc increases. Wall-limiting behavior within the diffusion layer was examined and compared with that of channel flow. Concentration fluctuation time scale was found to scale with r +2 , while the time scale ratio nearly equals the Schmidt number throughout the diffusion layer. Scalar modeling closure constants based on gradient diffusion models were found to vary considerably within the diffusion layer. Results of an octant analysis show the significant role played by the ejection and sweep events just as is found for flat plate, channel, and pipe flow boundary layers. Turbulence budgets revealed a strong Sc dependence of turbulent scalar transport.

This communication reports the heat and mass transfer analysis in the stagnation-point flow toward a stretching sheet. An incompressible micropolar fluid takes into account the diffusion-thermo- (Dufour) and thermal-diffusion (Soret) effects. The arising nonlinear differential system is solved by homotopy analysis method. Convergence of the obtained homotopy solutions is clearly justified. Special emphasis has been given to various physical parameters through graphs and tables. It is noticed that fields are influenced appreciably with the variation of embedding parameters. A comparison of the present results with the existing numerical solution is discussed in a limiting sense.

The cavitating flows around a highly skewed model marine propeller in both uniform flow and wake flow have been simulated by applying a mass transfer cavitation model based on Rayleigh–Plesset equation and k - ω shear stress transport (SST) turbulence model. From comparison of numerical results with the experiment, it is seen that the thrust and torque coefficients of the propeller are predicted satisfactory. It is also clarified from unsteady simulation of cavitating flow around the propeller in wake flow that the whole process of cavitating-flow evolution can be reasonably reproduced including sheet cavitation and tip vortex cavitation observed in the experiments. Furthermore, to study the effect of pressure fluctuation on the surrounding, pressure fluctuations induced by the cavitation as well as the propeller rotation are predicted at three reference positions above the propeller for comparison with the experimental data: The amplitudes of the dominant components corresponding to the first, second, and third blade passing frequencies were satisfactorily predicted. It is noted that the maximum difference of pressure fluctuation between the calculation and experiment reached 20%, which might be acceptable by usual engineering applications.

Mass transfer rates were measured in a large scale system, which is consisted of an 8.4 m tall by 0.76 m diameter column, containing one of the three fluids: water with an antifoam agent, water without an antifoam agent, and AZ101 simulant, which simulated a non-Newtonian nuclear waste. The testing contributed to the evaluation of large scale mass transfer of hydrogen in nuclear waste tanks. Due to its radioactivity, the waste was chemically simulated and due to flammability concerns, oxygen was used in lieu of hydrogen. Different liquids were used to better understand the mass transfer processes, where each of the fluids was saturated with oxygen, and the oxygen was then removed from the solution as air bubbled up or sparged through the solution from the bottom of the column. Air sparging was supplied by a single tube, which was co-axial to the column; the decrease in oxygen concentration was recorded, and oxygen measurements were then used to determine the mass transfer coefficients to describe the rate of oxygen transfer from solution. Superficial, average, sparging velocities of 2 mm/s, 5mm/s, and 10 mm/s were applied to each of the liquids at three different column fill levels, and mass transfer coefficient test results are presented here for combinations of superficial velocities and fluid levels.

An approximate-analytical solution method is presented for the problem of mass transfer in a rigid tube with pulsatile flow. For the case of constant wall concentration, it is shown that the generalized integral transform (GIT) method can be used to obtain a solution in terms of a perturbation expansion, where the coefficients of each term are given by a system of coupled ordinary differential equations. Truncating the system at some large value of the parameter N , an approximate solution for the system is obtained for the first term in the perturbation expansion, and the GIT-based solution is verified by comparison to a numerical solution. The GIT approximate-analytical solution indicates that for small to moderate nondimensional frequencies for any distance from the inlet of the tube, there is a positive peak in the bulk concentration C 1 b due to pulsation, thereby, producing a higher mass transfer mixing efficiency in the tube. As we further increase the frequency, the positive peak is followed by a negative peak in the time-averaged bulk concentration and then the bulk concentration C 1 b oscillates and dampens to zero. Initially, for small frequencies the relative Sherwood number is negative indicating that the effect of pulsation tends to reduce mass transfer. There is a band of frequencies, where the relative Sherwood number is positive indicating that the effect of pulsation tends to increase mass transfer. The positive peak in bulk concentration corresponds to a matching of the phase of the pulsatile velocity and the concentration, respectively, where the unique maximum of both occur for certain time in the cycle. The oscillatory component of concentration is also determined radially in the tube where the concentration develops first near the wall of the tube, and the lobes of the concentration curves increase with increasing distance downstream until the concentration becomes fully developed. The GIT method proves to be a working approach to solve the first two perturbation terms in the governing equations involved.

We describe an approach to simulate dynamic cavitation behavior based on large eddy simulation of the governing flow, using an implicit approach for the subgrid terms together with a wall model and a single fluid, two-phase mixture description of the cavitation combined with a finite rate mass transfer model. The pressure-velocity coupling is handled using a PISO algorithm with a modified pressure equation for improved stability when the mass transfer terms are active. The computational model is first applied to a propeller flow in homogeneous inflow in both wetted and cavitating conditions and then tested in an artificial wake condition yielding a dynamic cavitation behavior. Although the predicted cavity extent shows discrepancy with the experimental data, the most important cavitation mechanisms are present in the simulation, including internal jets and leading edge desinence. Based on the ability of the model to predict these mechanisms, we believe that numerical assessment of the risk of cavitation nuisance, such as erosion or noise, is tangible in the near future.

Laminar falling film condensations over a vertical plate with an accelerating vapor flow is analyzed in this work in the presence of condensate suction or slip effects at the plate surface. The following assumptions are made: (i) laminar condensate flow having constant properties, (ii) pure vapor with a uniform saturation temperature in the vapor region, and (iii) the shear stress at the liquid/vapor interface is negligible. The appropriate fundamental governing partial differential equations for the condensate and vapor flows (continuity, momentum, and energy equations) for the above case are identified, nondimensionalized, and transformed using nonsimilarity transformation. The transformed equations were solved using numerical, iterative, and implicit finite-difference methods. It is shown that the freestream striking angle has insignificant influence on the condensation mass and heat transfer rates, except when slip condition is present and at relatively small Gr l / Re 2 values. Moreover, it is shown that increasing the values of the dimensionless suction parameter ( V S ) results to an increase in dimensionless mass of condensate ( Γ ( L ) / ( μ l Re ) ) and Nusselt number ( Nu ( L ) / Re 1 / 2 ) . Thus, it results in an increase in condensation mass and heat transfer rates. Finally, it is found that the condensation and heat transfer rates increase as Jakob number, slip parameter, and saturation temperature increase. Finally, the results of this work not only enrich the literature of condensation but also provide additional methods for saving thermal energy.

This paper describes optimality principles for the design of an engineering bifurcating-tube tree consisting of the convection and diffusion zones to attain the most effective gas transport. An optimality principle is formulated for the diffusion zone to maximize the total diffusion mass-transfer rate of gas across tube walls under a constant total-volume constraint. This optimality principle produces a new diameter distribution for the diffusion zone in contrast to the classical distribution for the convection zone. In addition. this paper gives a length distribution for an engineering tree based on an optimality principle for minimizing the total weight of the tree under constraints of a finite surface and elastic criteria for structural stability. Furthermore, the optimum branching angles are evaluated based on local optimality principles for a single bifurcating-tube branch.