Viscous potential flow analysis of Kelvin-Helmholtz instability with mass transfer and vaporization

Viscous potential flow analysis of Kelvin-Helmholtz instability with heat and mass transfer has been studied. A dispersion relation has been obtained. Stability criterion is given by a critical value of relative velocity. It has been found that heat and mass transfer has destabilizing effect on relative velocity when lower fluid viscosity is low while it has stabilizing effect when lower fluid viscosity is high. Various graphs have been plotted for relative velocity and growth rate. In statically unstable situation viscosity has stabilizing effect while in statically stable situation it has destabilizing effect.     

Casson fluid flow: Free convective heat and mass transfer over an unsteady permeable stretching surface considering viscous dissipation

The present study investigates a Casson fluid flow in the presence of free convection of combined heat and mass transfer toward an unsteady permeable stretching sheet with thermal radiation, viscous dissipation and chemical reaction. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations and then solved by an efficient Runge–Kutta–Fehlberg method. The dimensionless velocity is decreased by increasing values of the chemical reaction and magnetic parameter while fluid temperature is significantly reduced by increasing values of the Prandtl number. The heat transfer rate is reduced with increasing values of thermal radiation and magnetic parameters.     

Axisymmetric expanding universe with viscous fluid and heat flow

A conformally flat axisymmetric non-static metric is shown to satisfy the Einstein equations corresponding to a viscous fluid and non-zero heat flow.     

Spreading of a viscous liquid film over the corrugated surface and the heat and mass transfer calculations

There are a lot of industrial applications of structured packing. Distillation columns are one of the examples where the liquid flows over the corrugated surface as a thin film to provide a good mass-transfer surface between the liquid and vapor phase. The purpose of the present paper is to study the hydrodynamics and the heat-mass transfer of the liquid film spreading down the corrugated surfaces when the corrugation amplitude is comparable with Nusselt’s film thickness (the amplitude corresponds to a small texture of the structured packing). As a result, a nonlinear type diffusion equation is obtained to describe the evolution of the film thickness profile. The nonlinear diffusion coefficient is obtained for three cases: a smooth inclined plate, a corrugated plate with large ribs, and an inclined corrugated plate with small ribs. The equations are solved numerically. As a result, it has been obtained that the small texture significantly increases the rate of the film thickness evolution in comparison with a smooth plate. To obtain the nonlinear diffusion coefficient in the case of a small texture, the hydrodynamics of the film flow over an inclined corrugated surface are studied. The viscosity, inertia, and surface tension forces are taken into account. The calculations were carried out on the basis of the Navier-Stokes equations. The influence of the microcorrugations on both the heat transfer from the wall and the mass transfer through the free surface was investigated.     

Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al₂O₃/Cu nanoparticles suspended in H₂O past a stretched/shrinked sheet. With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles, the physical flow process is illustrated. The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity trans...     

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.     

Hydromagnetic transverse instability of two highly viscous fluid-particle flows with finite ion Larmor radius corrections

A linear analysis of the combined effect of viscosity, finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability of two superposed incompressible fluids in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be transverse to the direction of streaming. A general dispersion relation for such a configuration has been obtained using appropriate boundary conditions. The stability analysis is discussed analytically, and the obtained results are numerically confirmed. Some special cases are recovered and corrected. The limiting cases of absence of suspended particles (or fluid velocities) and finite Larmor radius, absence of suspended particles are discussed in detail. In both cases, all other physical parameters are found to have stabilizing as well as destabilizing effects on the considered system. In the former case, the kinematic viscosity is found to has a stabilizing effect, while in the later case, the finite Larmor radius is found to has a stabilizing influence for a vortex sheet. It is shown also that both finite Larmor radius and kinematic viscosity stabilizations for interchange perturbations are similar to the stabilization effect due to a magnetic field for non-interchange perturbations. Received 13 January 2003 Published online 24 April 2003 RID="a" ID="a"Also at: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt. e-mail: m.elsayed@uaeu.ac.ae     

Stability analysis of unsteady MHD stagnation point flow and heat transfer over a shrinking sheet in the presence of viscous dissipation

The unsteady MHD stagnation-point flow and heat transfer over a shrinking sheet was carried out. This study also was conducted in the existence of suction and viscous dissipation. In order to convert the governing partial differential equations to an ordinary differential equation, an appropriate similarity transformation was applied in this study. Then, the resulting equations are worked out by Bvp4c solver in Matlab. The impacts of the parameters involved in this study towards skin friction, Nusselt number, velocity and temperature profile are showed graphically and thoroughly discussed. Remarkably, there were dual solutions present in this study which made us continue deeper in performing the stability analysis. As expected, our study proves that the solution is stable only in the first one while not in the second solution.     

Finite time analyticity for the two and three dimensional Kelvin-Helmholtz instability

The well-posed property for the finite time vortex sheet problem with analytic initial data was first conjectured by Birkhoff in two dimensions and is shown here to hold both in two and three dimensions. Incompressible, inviscid and irrotational flow with a velocity jump across an interface is assumed. In two dimensions, global existence of a weak solution to the Euler equation with such initial conditions is established. In three dimensions, a Lagrangian representation of the vortex sheet analogous to the Birkhoff equation in two dimensions is presented.This work was performed while C.B. was visiting the Dept. de Mathématiques, Nice     

Boundary layer flow and heat transfer of a nanofluid over a permeable unsteady stretching sheet with viscous dissipation

A numerical study of the boundary layer flow past unsteady stretching surface in nanofluid under the effects of suction and viscous dissipation is investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented, which depends on the unsteadiness parameter A, Eckert number Ec, ζ suction or injection parameter, Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt. The governing partial differential equations were converted to nonlinear ordinary differential equations by using a suitable similarity transformation, which are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration scheme. The accuracy of the numerical method is tested by performing various comparisons with the previously published work, and the results are found to be in excellent agreement. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal and nanoparticle volume fraction boundary layers. The thermal boundary layer thickens with a rise in the local temperature as the Brownianmotion, thermophoresis, and convective heating each intensify.     

L型混沌流道流动与传热特性的数值分析

采用周期性模型对L型混沌流道内流体流动与传热性能进行数值模拟,并与普通平直流道相对比,分析得到了两种流道内流体流场与温度场分布的细观信息,同时还讨论了不同Re数对混沌流道内流体传热与流动的影响。设计制作了测试流体流动性能的冷模试验装置,采用激光多普勒测速仪对L型混沌流道中流道内特殊点的速度进行测量,并将试验测量结果与数值模拟计算结果进行对比。结果标明:试验测量结果与数值模拟计算结果总体变化趋势基本一致,主流方向上速度相对误差最大为13.8%,在工程允许的误差范围之内,由此验证了数值模拟计算的可靠性。     

A new viscous sublayer influx (VSI) concept for near-wall turbulent momentum,heat and mass transfer

This paper presents a new viscous sublayer influx (VSI) concept to describe near-wall turbulent momentum, heat and mass transfer. Based on visual studies, this concept takes account of a viscous sublayer adjacent to the wall, which is not directly affected by the bursts occurring in the wall region. Fluid penetrates only due to a wallward flow into this viscous sublayer. Thus, in contrast to the known surface renewal concept, the new VSI concept is consistent with visual flow studies and, in addition, makes it possible to meet the experimentally found limiting condition Sh ∼ ³√Sc_Sc→∞ for mass transfer. In this work, two models have been developed from the new VSI concept. The simplified viscous sublayer influx model follows the known models in literature and provides analytical equations for the profiles in the wall region. This model gives an explanation for the varying experimental results on the time intervals between successive bursts and predicts them in quantity by using measured Sherwood numbers at very high Schmidt numbers. The second, more detailed viscous sublayer influx model approximates the wallward flow in the viscous sublayer with a spherical stagnation point flow. The profiles are calculated from two ordinary differential equations. Using measured Sherwood numbers at very high Schmidt numbers, this model provides normal velocity fluctuations at the wall that agree well with experimental data. Furthermore, both models provide axial velocity fluctuations near the wall and Nusselt/Sherwood numbers in the range 0.5 ≤ Pr, Sc≤ 10⁵ that both correspond with experimental data.     

Study of heat and mass transfer for hypersonic flow past a complex body of revolution

The experimental approach is outlined for study of heat fluxes on the surface of a blunt body of revolution (with kinked generatrix) in a hypersonic gas flow. The main attention is paid to the effect of coolant injection flow rate on resulting heat flux at different Reynolds numbers and attack angles. The significant role of distributed gas blowing on a body surface for the heat flux distribution has been demonstrated.     

The effect of magnetic fields on the stability of a cylindrical flow with mass and heat transfer

The effect of axial and radial magnetic fields on the Kelvin-Helmholtz stability of a cylindrical interface between the vapor and liquid phases of a fluid is studied when the vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. Both axisymmetric and asymmetric disturbances are considered. The linear dispersion relations are obtained and discussed. It is found that a uniform axial magnetic field has a stabilizing effect on the interface, while the effect of a radial magnetic field depends strongly on the choice of some physical parameters of the system. It is also found that the instability criterion is independent of heat and mass transfer coefficient, but it is different fromthat in the same problem without heat and mass transfer. Finally, the heat and mass transfer has a destabilizing influence on the system.     

Blockage effects on viscous fluid flow and heat transfer past a magnetic obstacle in a duct

The effect of lateral walls on fluid flow and heat transfer is investigated when a fluid passes a magnetic obstacle. The blockage ratio β that represents the ratio between the width of external magnet M y and the spanwise width L y is employed to depict the effect. The finite volume method (FVM) based on the PISO algorithm is applied for the blockage ratios of 0.2, 0.3, and 0.4. The results show that the value of Strouhal number St increases as the blockage ratio β increases, and for small β , the variation of St is very small when the interaction parameter and Reynolds number are increasing. Moreover, the cross-stream mixing induced by the magnetic obstacle can enhance the wall-heat transfer and the maximum value of the overall heat transfer increment is about 50.5%.     

On the viscous and inviscid stability of magnetohydrodynamic shock waves

We study the viscous and inviscid stability of shock waves in barotropic and full magnetohydrodynamics. We show that there are magnetohydrodynamic shock waves that are one-dimensionally stable as viscous shock profiles while they are multidimensionally strongly unstable as planar shock discontinuities.     

Role of radial magnetic field on heat transfer in MHD Couette flow in an annulus with viscous and Joule dissipation

This paper presents an analytical investigation of steady, fully developed MHD Couette flow of viscous, incompressible, electrically conducting fluid in the presence of radial magnetic field. Exact solutions are derived for the governing energy and momentum equations by taking into account the effects of viscous and Joule dissipations under relevant boundary conditions. The solutions obtained are graphically represented and the effects of various controlling parameters such as Hartmann number and Brinkman number on the temperature profile and consequently the Nusselt numbers are discussed. The significant result from the study is that increase in Hartmann number leads to enhancement on the Nusselt number at outer surface of inner cylinder while the role of Hartmann number is just reverse on Nusselt number at inner surface of outer cylinder. In addition, the Brinkman number has an insignificant effect on the Nusselt numbers when both surfaces are kept at equal temperature.     

Three-dimensional magnetohydrodynamics axisymmetric stagnation flow and heat transfer due to an axisymmetric shrinking/stretching sheet with viscous dissipation and heat source/sink

The present work is concerned with the effects of viscous dissipation and heat source/sink on a three-dimensional magnetohydrodynamic boundary layer axisymmetric stagnation flow, and the heat transfer of an electrically conducting fluid over a sheet, which shrinks or stretches axisymmetrically in its own plane where the line of the symmetry of the stagnation flow and that of the shrinking （stretching） sheet are, in general, not aligned. The governing equations are transformed into ordinary differential equations by using suitable similarity transformations and then solved numerically by a shooting technique. This investigation explores the conditions of the non-existence, existence and uniqueness of the solutions of the similar equations numerically. It is noted that the range of the velocity ratio parameter, where the similarity solution exists, is increased with the increase of the value of the magnetic parameter. Furthermore, the study reveals that the non-alignment function affects the shrinking sheet more than the stretching sheet. In addition, the numerical results of the velocity profile, temperature profile, skin-friction coefficient, and rate of heat transfer at the sheet are discussed in detail with different parameters.     

Nonlinear electrohydrodynamic Rayleigh-Taylor instability with mass and heat transfer subject to a vertical oscillating force and a horizontal electric field

Weakly nonlinear stability of interfacial waves propagating between two electrified inviscid fluids influenced by a vertical periodic forcing and a constant horizontal electric field is studied. Based on the method of multiple-scale expansion for a small-amplitude periodic force, two parametric nonlinear Schrödinger equations with complex coefficients are derived in the resonance cases. A standard nonlinear Schrödinger equation with complex coefficients is derived in the nonresonance case. A temporal solution is carried out for the parametric nonlinear Schrödinger equation. The stability analysis is discussed both analytically and numerically.