Uniform Mass Flux Research Articles

Method of determining kinetic boundary conditions in net evaporation/condensation

The aim of the present study is to develop the method of determining the kinetic boundary condition (KBC) at a vapor-liquid interface in net evaporation/condensation. We proposed a novel method for determining the KBC by combining the numerical simulations of the mean field kinetic theory and the molecular gas dynamics. The method was evaluated on steady vapor flow between two liquid slabs at different temperatures. A uniform net mass flux in the vapor phase induced by net evaporation and condensation is obtained from the numerical simulation of the mean field kinetic theory for both vapor and liquid phases. The KBC was specified by using the uniform net mass flux, and the numerical simulation of the molecular gas dynamics was conducted for the vapor phase. Comparing the macroscopic variables in the vapor phase obtained from both numerical simulations, we can validate the KBC whether the appropriate solutions are obtained. Moreover, the evaporation and condensation coefficients were estimated uniquely. The results showed that the condensation and evaporation coefficients were identical and constant in net evaporation. On the other hand, in net condensation, the condensation coefficient increased with the collision molecular mass flux. We also presented the applicable limit of the KBC which is assumed to be the isotropic Gaussian distribution at the liquid temperature. From these results, the KBCs in net evaporation and condensation, which enable the exact macroscopic variables to be determined, were proposed.

Radiation Effects on Oscillating Vertical Plate with Uniform Heat and Mass Flux

Thermal radiation effects on flow past an impulsively started infinite vertical oscillating plate with uniform heat and mass flux is studied. The fluid considered here is a gray, absorbing-emitting radiation but a nonscattering medium. The dimensionless governing equations are solved using the Laplace-transform technique. The velocity, temperature and concentration are studied for different physical parameters such as the radiation parameter, phase angle, Schmidt number and time. The variation of the skin-friction for different values of the parameters is also shown in a table

Effects of Chemical Reaction on MHD Flow Past an Impulsively Started Infinite Vertical Plate with Uniform Heat and Mass Flux

Finite difference solutions of the unsteady MHD flow past an impulsively started infinite vertical plate with uniform heat and mass flux are presented here, taking into account the homogeneous chemical reaction of first order. The dimensionless governing equations are solved by an efficient, more accurate, unconditionally stable and fast converging implicit scheme. The effects of velocity, temperature and concentration for different parameters such as chemical reaction parameter, Schmidt number, Prandtl number, thermal Grashof number, mass Grashof number and time are studied. It is observed that due to the presence of a first order chemical reaction, the velocity increases during the generative reaction and decreases in the destructive reaction. It is observed that the velocity decreases in the presence of the magnetic field, as compared to its absence.

Numerical solution of unsteady radiative flow past an oscillating semi-infinite vertical plate with uniform mass flux

Numerical solution of unsteady radiative flow past an oscillating semi-infinite vertical plate with uniform mass flux

Microdroplet evaporation in closed digital microfluidic biochips

In this paper, microdroplet evaporation in the closed digital microfluidic systems is studied for hydrophobic and hydrophilic surfaces. The contact angle and contact radius are measured by an enhanced automated polynomial fitting approach. It is observed that the contact angle for both hydrophobic and hydrophilic surfaces remains constant during the evaporation process. However, a higher evaporation rate is observed for hydrophilic droplets compared to the hydrophobic droplets. Since no contact line pinning is observed, first, an analytical model based on the uniform vapor mass flux along the liquid–vapor interface is proposed. Interestingly, it is observed that in the hydrophobic case, the analytical model gives a higher evaporation rate, whereas for the hydrophilic case, the analytical model gives a lower evaporation rate. The discrepancy between the results of the analytical modeling and the experimental values is hypothesized to be due the constant flux assumption. To verify the hypothesis, a finite volume-based numerical model is developed to find the local flux along the liquid–vapor interface. The numerical modeling results confirm that for hydrophilic droplets, the evaporation flux increases very close to the three-phase contact line. In the case of the hydrophobic droplets, on the other hand, the flux decreases close to the contact line due to vapor saturation; as a result the uniform flux assumption overestimates the mass loss.

Radiative flow past a parabolic started isothermal vertical plate with uniform mass flux

Radiative flow past a parabolic started isothermal vertical plate with uniform mass flux

Thermophysical properties and heat transfer performance of Al2O3/R-134a nanorefrigerants

The past decade has seen the rapid development of nanofluids science in many aspects. In recent years, refrigerant-based nanofluids have been introduced as nanorefrigerants due to their significant effects over heat transfer performance. This study investigates the thermophysical properties, pressure drop and heat transfer performance of Al2O3 nanoparticles suspended in 1, 1, 1, 2-tetrafluoroethane (R-134a). Suitable models from existing studies have been used to determine the thermal conductivity and viscosity of the nanorefrigerants for the nanoparticle concentrations of 1 to 5 vol.%. The pressure drop, pumping power and heat transfer coefficients of nanorefrigerant in a horizontal smooth tube have also been investigated with the same particle concentration at constant velocity of 5m/s and uniform mass flux of 100kg/m2s. In this study, the thermal conductivity of Al2O3/R-134a nanorefrigerant increased with the augmentation of particle concentration and temperature however, decreased with particle size intensification. In addition, the results of viscosity, pressure drop, and heat transfer coefficients of the nanorefrigerant show a significant increment with the increase of volume fractions. Therefore, optimal particle volume fraction is important to be considered in producing nanorefrigerants that can enhance the performance of refrigeration systems.

Double Diffusive Magneto-Convection Fluid Flow in a Strong Cross Magnetic Field With Uniform Surface Heat and Mass Flux

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. Asymptotic solutions are obtained for small (≪1) and large (≫1) values of local Hartmann parameter, ξ, through regular perturbation method and matched asymptotic expansion technique, respectively. However, for all values of ξ the boundary layer equations are transformed to a suitable form by using the free variable formulation (FVF) as well as the stream function formulation (SFF). The equations obtained through FVF are integrated via direct finite difference method together with Gaussian elimination technique while the others obtained through SFF are integrated numerically via Thomas algorithm. Discussion is carried out for fluids having small Pr ≪1. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10.0.

EFFECTS OF THERMAL RADIATION AND MASS DIFFUSION ON FREE CONVECTION FLOW NEAR A VERTICAL PLATE WITH NEWTONIAN HEATING

The effects of thermal radiation and mass transfer on unsteady natural convection flow of an optically dense viscous incompressible fluid near a vertical plate with Newtonian heating have been investigated. Both physically important boundary conditions of uniform wall concentration (UWC) and uniform mass flux (UMF) are considered. Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The governing dimensionless boundary layer equations are solved analytically using the Laplace transform technique. The effects of mass to thermal buoyancy ratio parameter (N), Prandtl number (Pr), Schmidt number (Sc), and the radiation parameter (R) as well as time (t) on the velocity field and skin friction are determined. It is found that velocity increases for aiding flows and it decreases for opposing flows in the cases of both UWC and UMF. The skin friction is reduced with increasing species concentration in the presence of aiding flows for both UWC and UMF. Also, the velocity is greater in the case of UWC than the case of UMF at an early time, whereas the velocity is slightly greater in the case of UMF than that of UWC at a later time in the vicinity of the plate.

Boundary-Layer Flow of a Nanofluid past a Stretching Sheet under Uniform Heat and Mass Flux

Abstract The steady boundary layer flow resulting from the stretching of a flat surface with a velocity proportional to the distance from a fixed point in a nanofluid under uniform heat and mass flux has been investigated numerically and using the nanofluid model proposed by Buongiorno (“Convective Transport in Nanofluids, ASME J. Heat Transfer, Vol. 128, 2006, pp. 240–250). The effects of Brownian motion and thermophoresis are incorporated in the model in order to obtain similarity solutions of the governing equations in terms of different parameters. The variation of the reduced Nusselt and reduced Sherwood numbers with the Prandtl number (Pr) and the Lewis number (Le) for various values of the Brownian motion parameter (Nb) and the thermophoresis parameter (Nt) is presented in tabular and graphical forms. It was found that the reduced Nusselt number is a decreasing function of each parameter (Pr, Le, Nb, and Nt), whereas the reduced Sherwood number is an increasing function of Nb and a decreasing function of Nt for each Le and Pr number.

Improved Integral Form of the Compressible Flowfield in Thin Channels with Injection

This work seeks to obtain an improved integral formulation for the rotational, inviscid, compressible motion in a solid rocket motor. Assuming a slender porous chamber, the method in this study reduces the problem to a single integral equation that can be solved numerically. Alternatively, closed-form analytical approximations are shown to exist for particular values of the specific heats ratio. These are obtained using anAbel transformation of the pressure equation. For the case of uniform surface mass flux, a recursion is derived for the pressure as a function of space and specific heats ratios. Here, the dependence of sidewall injection on chamber pressure is modeled according to SaintRobert’s power law. After overcoming some deficiencies encountered in previous work, results are presented and compared with two closed-form analytical solutions developed under oneand two-dimensional isentropic flow conditions for either uniformly distributed mass flux or wall injection velocity. Furthermore, agreement with an existing one-dimensional solution is established for the case of uniform mass flux. For constant sidewall injection velocity, the formulation is shown to compare favorably with a two-dimensional solution obtained by Maicke and Majdalani (“On the Rotational Compressible Taylor Flow in Injection-Driven Porous Chambers,” Journal of Fluid Mechanics, Vol. 603, 2008, pp. 391–411). A collection of experimental data acquired by Traineau et al. (Cold-Flow Simulation of a Two-Dimensional Nozzleless Solid-RocketMotor,”AIAAPaper 1986-1447, July 1986) is also used in the validation process, including a computational fluid dynamics verification carried out using the Reynolds stress model.

Network Simulation of Laminar Convective Heat and Mass Transfer over a Vertical Slender Cylinder with Uniform Surface Heat and Mass Flux

The steady, laminar axisymmetric convective heat and mass transfer in boundary layer flow over a vertical thin cylindrical configuration in the presence of significant surface heat and mass flux is studied theoretically and numerically. The governing boundary-layer equations for momentum, energy and species conservation are transformed from a set of partial differential equations in a (x,r) coordinate system to a ([,K) system using a group of similarity transformations. The resulting equations are solved using the Network Simulation Method (NSM) for the buoyancy-assisted pure free convection and also the pure forced convection cases, wherein the effects of Schmidt number, Prandtl number and surface mass parameter on velocity, temperature and concentration distributions in the regime are presented graphically and discussed. For the buoyancy-assisted pure free convection case, nondimensional velocity (wf/wK) is found to increase with a rise in surface mass transfer (S) but decrease with increasing Prandtl number (Pr), particularly in the vicinity of the cylinder surface (small radial coordinate, K). Dimensionless temperature (T) decreases however with increasing S values from the cylinder surface into the free stream; with increasing Prandtl number, temperature is strongly reduced, with the most significant decrease at the cylinder surface. Dimensionless concentration (I) is decreased continuously throughout the boundary layer regime with an increase in S; conversely I is enhanced for all radial coordinate values with an increase in Prandtl number. For the pure forced convection case, velocity increases both with dimensionless axial coordinate ([) and dimensionless radial coordinate (K) but decays smoothly with increasing Prandtl number and increasing Schmidt number, from the cylinder surface to the edge of the boundary layer domain. The model finds applications in industrial metallurgical processes, thermal energy systems, polymer processing, etc.

Magnetic effect on free convection in a non-darcy porous medium saturated with doubly stratified power-law fluid

Natural convection heat and mass transfer along a vertical plate embedded in a doubly stratified power-law fluid saturated non-Darcy porous medium with uniform heat and mass flux is presented. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically. The effects of magnetic parameter, stratification parameter and power-law index on the velocity, temperature and concentration are illustrated graphically.

Radiation and Mass Transfer Effects on Transient Free Convection Flow of a Dissipative Fluid past Semi-Infinite Vertical Plate with Uniform Heat and Mass Flux

Effect of radiation and mass transfer on the transient free convection flow of a dissipative past semi-infinite vertical plate with uniform heat and mass flux is analyzed, by taking into account the effect of viscous dissipation. This type of problems finds application in many technological and engineering fields such as plasma studies, petroleum industries, MHD energy generators, cooling of nuclear reactors, the boundary layer control in aerodynamics, crystal growth and furnace engineering. The Rosseland approximation is used to describe the radiative heat transfer in the limit of the optically thick fluid. The non-linear, coupled equations are solved using an implicit finite difference scheme of Crank-Nicolson type. Transient temperature, concentration and velocity profiles, local and average skinfriction coefficient, Nusselt number and Sherwood number are presented graphically and discussed. It is observed that, when the radiation parameter increases the velocity and temperature decrease accompanied by simultaneous reduction in both momentum and thermal boundary layers.

Thermal radiation on linearly accelerated vertical plate with variable temperature and uniform mass flux

Radiative heat transfer effects on unsteady flow of viscous incompressible fluid past a uniformly accelerated infinite vertical plate with variable temperature and uniform mass flux has been studied. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. An exact solution to the dimensionless governing equations has been obtained by the Laplace transform method, when the plate is linearly accelerated with a velocity u = (u 3 0 / ν) t'in its own plane. The plate temperature is raised linearly with time and the concentration level near the plate is also raised at a uniform rate. The velocity, temperature and concentration fields are studied for different physical parameters like thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, radiation parameter and time. It is observed that the velocity increases with increasing values of thermal Grashof number or mass Grashof number. But the trend is just reversed with respect to the thermal radiation parameter.

Thermal radiation on linearly accelerated vertical plate with variable temperature and uniform mass flux

Radiative heat transfer effects on unsteady flow of viscous incompressible fluid past a uniformly accelerated infinite vertical plate with variable temperature and uniform mass flux has been studied. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. An exact solution to the dimensionless governing equations has been obtained by the Laplace transform method, when the plate is linearly accelerated with a velocity u = (u 3 0 / ν) t'in its own plane. The plate temperature is raised linearly with time and the concentration level near the plate is also raised at a uniform rate. The velocity, temperature and concentration fields are studied for different physical parameters like thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, radiation parameter and time. It is observed that the velocity increases with increasing values of thermal Grashof number or mass Grashof number. But the trend is just reversed with respect to the thermal radiation parameter.

Exact solution of thermal radiation on vertical oscillating plate with variable temperature and mass flux

Thermal radiation effects on unsteady flow past an infinite vertical oscillating plate in the presence of variable temperature and uniform mass flux is considered. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised linearly with time and the mass is diffused from the plate to the fluid at an uniform rate. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, concentration and temperature are studied for different physical parameters like the phase angle, radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time. It is observed that the velocity increases with decreasing phase angle ?t.

Radiation effects on hydromagnetic free convective and mass transfer flow of a gas past a circular cylinder with uniform heat and mass flux

PurposeThe purpose of this paper is to highlight the effect of combined heat and mass transfer characteristics of magnetohydrodynamic (MHD) free convection flow of an electrically conducting Newtonian fluid on circular cylinder with uniform heat/mass flux, taking into consideration the effects of uniform transverse magnetic field and thermal radiation.Design/methodology/approachAn analysis is performed to study the momentum, combined heat and mass transfer characteristics of MHD free convection flow past a circular cylinder surface under the effect of thermal radiation with uniform heat and mass flux. By using Lie group method, the infinitesimal generators of governing equations are calculated. Using the resulting generators for the boundary value problem, the equations are transformed into an ordinary differential system. Numerical solutions of the outcoming non‐linear differential equations are found by using a combination of a Runge–Kutta algorithm and shooting technique.FindingsApplication of a magnetic field normal to the flow of an electrically conducting fluid gives rise to a resistive force that acts in the direction opposite to that of the flow. This resistive force tends to slow down the motion of the fluid along the cylinder and causes increases in its temperature and concentration and hence the respective changes in the wall shear stress, local Nusselt and Sherwood numbers as the magnetic parameter, respectively are changed with various values of angle which is measured in degrees from the front stagnation point on the surface. It is noted that these coefficients reduced as the magnetic parameter increases. Also, the effect of thermal radiation works as a heat source and so the quantity of heat added to the fluid increases, therefore the local Nusselt number reduced as the radiation parameter increases.Research limitations/implicationsAn analysis is performed to study the momentum, combined heat and mass transfer characteristics of MHD free convection flow of an electrically conducting Newtonian fluid on circular cylinder with uniform heat/mass flux with the effects of uniform transverse magnetic field and thermal radiation.Practical implicationsThis paper provides a very useful source of coefficient of heat and mass transfer values for engineers planning to transfer heat and mass by using electrically conducting gases with uniform heat/mass flux.Originality/valueThe combined heat and mass transfer of an electrically conducting gases on free convection flow in the presence of magneto and thermal radiation effects are investigated and can be used by different engineers working on industry, geothermal, geophysical, technological and engineering applications.

Influence of double stratification on MHD free convection with Soret and Dufour effects in a Darcian porous media

AbstractThe heat and mass transfer characteristics of natural convection about a vertical surface embedded in a doubly stratified saturated porous medium subjected to a magnetic field is studied, taking into account the Dufour and Soret effects. It is found that the similarity solution exists for the case of uniform surface heat and mass flux conditions when the thermal and solutal stratification of the medium are assumed to have power function form x1/3. The resulting set of ordinary coupled nonlinear differential equations is solved numerically using shooting technique. Nusselt and Sherwood numbers are tabulated for various values of the involved parameters. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

CFD Model of Apple Atmospheric Freeze Drying at Low Temperature

An Internet-controlled atmospheric freeze dryer was designed, built, and tested in the Department of Heat and Mass Transfer, Technical University of Łódź. A film sublimation-based CFD model was developed and verified using Fluent 6.1 commercial CFD software. The model enables the simulation of phase change and water vapor diffusion process within porous media. Transport of non-condensable species can be calculated with species transport inbuilt model of Fluent 6.1 and used to predict sublimation rate under given conditions. Results were compared with AFD experimental data of 10-mm Idared apple cubes. The viability of applying the film sublimation model to atmospheric freeze-drying process was demonstrated. Higher mass flux was found on the leading edge, relatively uniform mass flux within the porous zone illustrates that vapor diffusion dominates atmospheric freeze drying process at low temperature (below 0°C). CFD results for apple cubes show a predomination of diffusional resistance of porous tissue.