Waves in liquids with vapour bubbles

1988 ◽  
Vol 186 ◽  
pp. 85-117 ◽  
Author(s):  
R. I. Nigmatulin ◽  
N. S. Khabeev ◽  
Zuong Ngok Hai
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Volume Fraction ◽  
Initial Conditions ◽  
Wave Structure ◽  
Original System ◽  
Shock Adiabat ◽  
Vapour Phase ◽  
Physical Parameters ◽  
Dissipative Effects

An investigation of wave processes in liquids with vapour bubbles with interphase heat and mass transfer is presented. A single-velocity two-pressure model is used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution around the bubbles. An analysis of the microscopic fields of physical parameters is aimed at closing the system of equations for averaged characteristics. The original system of differential equations of the model is modified to a form suitable for numerical integration. An elliptic equation is obtained to determine the field of the mixture average pressure at an arbitrary time through the known fields of the remaining quantities. The existence of the steady structure of shock waves, either monotonic or oscillatory, is proved. The effect of the initial conditions, shock strength, volume fraction, and dispersity of the vapour phase and of the thermophysical properties of the phases on shock-wave structure and relaxation time is studied. The influence of nonlinear, dispersion and dissipative effects on the wave evolution is also investigated. The shock adiabat for reflected waves is analysed. The results obtained have proved that the interphase heat and mass transfer determined by the thermal diffusivity of the liquid greatly influences the wave structure. The possible enhancement of disturbances in the region of their initiation is shown. The model has been tested for suitability and the results of calculations have been compared with experimental data.

Shock Waves in Liquids With Bubbles Containing Evaporating Drops

2000 ◽  
Author(s):  
Nail S. Khabeev ◽  
Arnold F. Bertelsen ◽  
Oleg R. Ganiev
Keyword(s):  
Shock Waves ◽  
Static Pressure ◽  
Volume Fraction ◽  
Initial Conditions ◽  
Wave Structure ◽  
Physical Parameters ◽  
Volume Changes ◽  
Wave Processes ◽  
Steady Shock ◽  
Evaporating Drops

Abstract An investigation of wave processes in liquids with bubbles containing evaporating drops is presented. A model is used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution inside and around the bubbles. An analysis of the microsopic fields of physical parameters is aimed at closing the system of equations for averaged characteristics. The evolution of non-steady shock waves in liquids with bubbles containing evaporating drops is studied by numerical methods. The effect of the initial conditions, shock strength, volume fraction, dispersity of the vapor phase, initial static pressure and of the thermophysical properties of the phases on shock-wave structure and evolution is studied. The possible enhancement of disturbances in the region of their initiation is shown. The phenomenon of the nonlinear anomalous enhancement of waves reflected from a wall is established.

Unsteady MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

2017 ◽  
Vol 6 (10) ◽  
pp. 116
Author(s):  
J. Buggaramulu ◽  
M. Venkatakrishna ◽  
Y. Harikrishna
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Physical Parameters ◽  
Governing Equations ◽  
Vertical Porous Plate ◽  
Flow Past ◽  
Transfer Flow

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

scholarly journals On the Influence of Soret and Dufour Effects on MHD Free Convective Heat and Mass Transfer Flow over a Vertical Channel with Constant Suction and Viscous Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Ime Jimmy Uwanta ◽  
Halima Usman
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Convective Heat ◽  
Vertical Channel ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Soret And Dufour Effects ◽  
Constant Suction ◽  
Dufour Number

The present paper investigates the combined effects of Soret and Dufour on free convective heat and mass transfer on the unsteady one-dimensional boundary layer flow over a vertical channel in the presence of viscous dissipation and constant suction. The governing partial differential equations are solved numerically using the implicit Crank-Nicolson method. The velocity, temperature, and concentration distributions are discussed numerically and presented through graphs. Numerical values of the skin-friction coefficient, Nusselt number, and Sherwood number at the plate are discussed numerically for various values of physical parameters and are presented through tables. It has been observed that the velocity and temperature increase with the increase in the viscous dissipation parameter and Dufour number, while an increase in Soret number causes a reduction in temperature and a rise in the velocity and concentration.

Radiative Non-Coaxial Rotation of Magnetohydrodynamic Newtonian Carbon Nanofluid Flow in Porous Medium with Heat and Mass Transfer Effects

2020 ◽  
Vol 9 (4) ◽  
pp. 321-335
Author(s):  
Wan Nura’in Nabilah Noranuar ◽  
Ahmad Qushairi Mohamad ◽  
Sharidan Shafie ◽  
Ilyas Khan ◽  
Lim Yeou Jiann
Keyword(s):  
Carbon Nanotubes ◽  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Nuclear Reactor ◽  
Volume Fraction ◽  
Heating System ◽  
Transform Method ◽  
Rotation System ◽  
Walled Carbon Nanotubes

Non-coaxial rotation system has encountered in various fields such as engineering field in designing advanced cooling and heating system, food processing and mixer machines. In the present study, the effect of the non-coaxial rotation of a vertical disk on the heat and mass transfer of Newtonian nanofluids in a porous medium is analytically discussed. The influence of the magnetic field and thermal radiation is also taken into the consideration. Two different types of nanofluids which are single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with water as the base fluid are analyzed and compared. Suitable dimensionless variables are utilized to convert the governing partial differential equations associated with the initial and boundary conditions into the dimensionless form. Then, the exact solutions of the dimensionless governing equations are calculated by using the Laplace transform method. A limiting case study of the obtained analytical solutions is constructed to compare with the previously published results to verify its validity. The distributions of the velocity, temperature, and concentration along with the Skin friction, Nusselt number, and Sherwood number due to the variation of the pertinent parameters are displayed and scrutinized through graphs and tables. In the frame of non-coaxial rotation, the nanofluid with the SWCNTs nanoparticles have illustrated a higher rate of heat transfer as compared to MWCNTs nanofluid. Moreover, the heat transmission in the nanofluid has been enhanced by increasing the volume fraction of the nanoparticle and also the intensity of the radiation. This suggests that heating or cooling in a system such as a nuclear reactor can be improved by properly selecting the type of the nanofluid and also the volume fraction of the nanoparticle.

scholarly journals Analysis of a Chemically Reactive Mhd Flow With Heat and Mass Transfer Over a Permeable Surface

2019 ◽  
Vol 24 (1) ◽  
pp. 53-66
Author(s):  
O.J. Fenuga ◽  
S.J. Aroloye ◽  
A.O. Popoola
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Permeable Surface ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Special Cases ◽  
Momentum Boundary Layer

Abstract This paper investigates a chemically reactive Magnetohydrodynamics fluid flow with heat and mass transfer over a permeable surface taking into consideration the buoyancy force, injection/suction, heat source/sink and thermal radiation. The governing momentum, energy and concentration balance equations are transformed into a set of ordinary differential equations by method of similarity transformation and solved numerically by Runge- Kutta method based on Shooting technique. The influence of various pertinent parameters on the velocity, temperature, concentration fields are discussed graphically. Comparison of this work with previously published works on special cases of the problem was carried out and the results are in excellent agreement. Results also show that the thermo physical parameters in the momentum boundary layer equations increase the skin friction coefficient but decrease the momentum boundary layer. Fluid suction/injection and Prandtl number increase the rate of heat transfer. The order of chemical reaction is quite significant and there is a faster rate of mass transfer when the reaction rate and Schmidt number are increased.

scholarly journals Influence of Couple Stresses and Thermophoresis on Free Convective Heat and Mass Transfer of Viscoelastic Fluid.

2020 ◽  
Vol 17 ◽  
pp. 50-63
Author(s):  
N. T. M. Eldabe ◽  
Ahmed Refaie Ali ◽  
Gamil Ali Shalaby
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Viscoelastic Model ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Couple Stresses ◽  
Linear Differential

A theoretical study has been developed to investigate the influence of thermophoresis and couple stresses on the steady flow of non-Newtonian fluid with free convective heat and mass transfer over a channel bounded by two permeable plates. The considered non-Newtonian fluid follows a viscoelastic model. The problem is modulated mathematically by a system of non-linear differential equations pertaining to describe the continuity, momentum, energy, and concentration. These equations involve the effects of viscous dissipation and chemical reaction. The numerical solutions of the dimensionless equations are found as a function of the physical parameters of this problem. The numerical formulas of the velocity (u), temperature Φ and concentration Θ as well as skin friction coefficient T*, Nusselt number(Nu) and Sherwood number(Sh) are computed. The physical parameter's effects of the problem on these formulas are described and illustrated graphically through some figures and tables. It is observed that any increase in the thermophoretic parameter T leads to reduce in velocity profiles as well as concentration layers. In contrast, the velocity increases with increasing the couple stresses inverse parameter.

scholarly journals Thermophoresis and suction/injection roles on free convective MHD flow of Ag–kerosene oil nanofluid

2020 ◽  
Vol 7 (3) ◽  
pp. 386-396
Author(s):  
Himanshu Upreti ◽  
Alok Kumar Pandey ◽  
Manoj Kumar
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Mass Transfer Rate ◽  
Brownian Diffusion ◽  
Particle Volume ◽  
Ohmic Dissipation ◽  
Surface Mass

Abstract In this article, the mass and heat transfer flow of Ag–kerosene oil nanofluid over a cone under the effects of suction/injection, magnetic field, thermophoresis, Brownian diffusion, and Ohmic-viscous dissipation was examined. On applying the suitable transformation, PDEs directing the flow of nanofluid were molded to dimensionless ODEs. The solution of the reduced boundary value problem was accomplished by applying Runge–Kutta–Fehlberg method via shooting scheme and the upshots were sketched and interpreted. The values of shear stress and coefficients of heat and mass transfer were attained for some selected values of governing factors. The obtained results showed that when the amount of surface mass flux shifts from injection to the suction domain, the heat and mass transfer rate grew uniformly. However, they have regularly condensed with the rise in the magnitude of the magnetic field and particle volume fraction. Several researches have been done using cone-shaped geometry under the influence of various factors affecting the fluid flow, yet, there exists no such investigation that incorporated the response of viscous-Ohmic dissipation, heat absorption/generation, suction/blowing, Brownian diffusion, and thermophoresis on the hydro-magnetic flow of silver-kerosene oil nanofluid over a cone.

Numerical Study on Flow and Heat and Mass Transfer in Pulsating Heat Pipe

2019 ◽  
Author(s):  
Jian-Hong Liu ◽  
Fu-Min Shang ◽  
Nikolay Efimov
Keyword(s):  
Numerical Simulation ◽  
Mass Transfer ◽  
Heat Pipe ◽  
Gas Phase ◽  
Heat And Mass Transfer ◽  
Mixture Model ◽  
Volume Fraction ◽  
Pulsating Heat Pipe ◽  
Two Phase ◽  
Pipe Model

Abstract Numerical simulation was performed to establishing a two-dimensional pulsating heat pipe model, to investigate the flow and heat transfer characteristics in the pulsating heat pipe by using the Mixture and Euler models, which were unsteady models of vapor-liquid two-phase, based on the control-volume numerical procedure utilizing the semi-implicit method. Through comparing and analyzing the volume fraction and velocity magnitude of gas phase to decide which model was more suitable for numerical simulation of the pulsating heat pipe in heat and mass transfer research. It was showed there had gas phase forming in stable circulation flow in the heating section, the adiabatic section using the Mixture and Euler models respectively, and they were all in a fluctuating state at 10s, besides, the pulsating heat pipe had been starting up at 1s and stabilizing at 5s, it was all found that small bubbles in the heat pipe coalescing into large bubbles and gradually forming into liquid plugs and gas columns from the contours of volume fraction of the gas phase; through comparing the contours of gas phase velocity, it could be seen that there had further stably oscillating flow and relatively stabler gas-liquid two-phase running speed in the pulsating heat pipe used the Mixture model, the result was consistent with the conclusion of the paper[11] extremely, from this it could conclude that the Mixture model could be better simulate the vaporization-condensation process in the pulsating heat pipe, which could provide an effective theoretical support for further understanding and studying the phase change heat and mass transfer mechanism of the pulsating heat pipe.

Hall and ion slip current’s impact on magneto-sodium alginate hybrid nanoliquid past a moving vertical plate with ramped heating, velocity slip and Darcy effects

2020 ◽  
Vol 17 (1) ◽  
pp. 65-101 ◽  
Author(s):  
A. Ali ◽  
Soma Mitra Banerjee ◽  
S. Das
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Sodium Alginate ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Transform Method ◽  
Content Type ◽  
Slip Effects ◽  
Ion Slip

PurposeThe purpose of this study is to analyze an unsteady MHD Darcy flow of nonNewtonian hybrid nanoliquid past an exponentially accelerated vertical plate under the influence of velocity slip, Hall and ion slip effects in a rotating frame of reference. The fluids in the flow domain are assumed to be viscously incompressible electrically conducting. Sodium alginate (SA) has been taken as a base Casson liquid. A strong uniform magnetic field is applied under the assumption of low magnetic Reynolds number. Effect of Hall and ion-slip currents on the flow field is examined. The ramped heating and time-varying concentration at the plate are taken into consideration. First-order homogeneous chemical reaction and heat absorption are also considered. Copper and alumina nanoparticles are dispersed in base fluid sodium alginate to be formed as hybrid nanoliquid.Design/methodology/approachThe model problem is first formulated in terms of partial differential equations (PDEs) with physical conditions. Laplace transform method (LTM) is used on the nondimensional governing equations for their closed-form solution. Based on these results, expressions for nondimensional shear stresses, rate of heat and mass transfer are also determined. Graphical presentations are chalked out to inspect the impacts of physical parameters on the pertinent physical flow characteristics. Numerical values of the shear stresses, rate of heat and mass transfer at the plate are tabulated for various physical parameters.FindingsNumerical exploration reveals that a significant increase in the secondary flow (i.e. crossflow) near the plate is guaranteed with an augmenting in Hall parameter or ion slip parameter. MHD and porosity have an opposite effect on velocity component profiles for both types of nanoliquids. Result addresses that both shear stresses are strongly enhanced by the Casson effect. Also, hybrid nanosuspension in Casson fluid (sodium alginate) exhibits a lower rate of heat transfer than usual nanoliquid.Social implicationsThis model may be pertinent in cooling processes of metallic infinite plate in bath and hybrid magnetohydrodynamic (MHD) generators, metallurgical process, manufacturing dynamics of nanopolymers, magnetic field control of material processing, synthesis of smart polymers, making of paper and polyethylene, casting of metals, etc.Originality/valueThe originality of this study is to obtain an analytical solution of the modeled problem by using the Laplace transform method (LTM). Such an exact solution of nonNewtonian fluid flow, heat and mass transfer is rare in the literature. It is also worth remarking that the influence of Hall and ion slip effects on the flow of nonNewtonian hybrid nanoliquid is still an open question.

Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Soraya Torkaman ◽  
Ghasem Barid Loghmani ◽  
Mohammad Heydari ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Operational Matrices ◽  
Nanofluid Flow ◽  
Content Type ◽  
Nonlinearly Stretching Sheet

Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

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