Mass Transfer in Laminar Flow About a Rotating Cone

Starting from the differential equation of mass transfer in laminar flow and the appropriate boundary condition, expressions are derived for the rate of mass transfer from (a) a flat plate in a longitudinal fluid stream, (b) a vertical flat plate by natural convection, (c) the forward stagnation point of a sphere in a fluid stream. Only outward mass transfer is considered; this corresponds to blowing outwards from the plate at a rate inversely proportional to the boundary-layer thickness. The Kármán-Pohlhausen-Kroujiline method is used. Where appropriate the Prandtl or Schmidt number has been taken as 0⋅71. The calculations are valid for all mass-transfer processes for which a single diffusion coefficient can be ascribed to the diffusing property, but are particularly relevant to the combustion of liquid fuels, for which the outward mass-transfer rates are so high that important deviations occur from boundary-layer profiles without mass transfer. Despite the great temperature variations present in boundary layers with combustion, mean values for the fluid properties are assumed. In the case of natural convection, it is assumed that the body forces on the fluid in the boundary layer are everywhere zero; this leads to a less serious over-estimate of the buoyancy than the usual assumptions which are valid only for small temperature differences.

Gas-liquid mass transfer in rotating perforated-disc contactors

Theoretical investigation of magnetohydrodynamics (MHD) Casson and Williamson fluid flow and heat and mass transfer in laminar flow through a stretching sheet in the presence of heat generation is carried out in this study. The convective wall temperature and convective wall mass boundary condition are taken into account in this study. A study is also provided, which looks into the impact of viscous dissipation. Except for a temperature‐dependent thermal conductivity, all properties of the proposed model are assumed to be constants in the study. The spectral collocation method based on the shifted Vieta–Lucas polynomials is used to give an approximate formula for the n‐order derivative and solve numerically the coupled momentum, energy, and mass equations. This method is used to convert the problem’s system of ordinary differential equations (ODEs) into a nonlinear system of algebraic equations. This system is built as a restricted optimization problem and optimized to obtain the series solution’s unknown coefficients. Some theorems are provided to investigate the method’s convergence. The statistics, which are given visually, were compared to the results of other researchers’ theoretical analysis.

Analytical solution to mass transfer in laminar flow in hollow fiber with heterogeneous chemical reaction

The absorption of carbon dioxide by aqueous glycerine solutions in a column containing a string of spheres and cylinders has been studied. The Reynolds number was varied between 5 and 560. Using a model based on Higbie's penetration theory, modified to fit the characteristics of this absorber, the number of surface renewals that takes place in the column has been evaluated and correlated with the operating variables that can influence it. The liquid viscosity has no influence on the surface renewal which depends mainly on the liquid rate.

The experimental data from literature on the augmentation of heat and gas transport in the laminar flow of suspensions of polystyrene spheres have been correlated on common coordinates. The correlation includes the influences of particle size, tube diameter and length, shear rate of flow, transport properties of diffusing species (heat or gas) in suspending liquids, and of the particle interactions on the augmentation of heat or gas transfer in flowing suspensions.

The unsteady 2-D forced convective mass and heat transfer flow of an incompressible, viscous and electrically conducting fluid along a porous wedge is examined in this article using numerical analysis to survey the effects of a magnetic field and thermophoresis. This is done in the existence of temperature-dependent thermal conductivity, a variable Prandtl number, and the effect of cross diffusion. The governing nonlinear PDEs have been converted into nonlinear ODEs by using a similarity transformation. The modified ODEs are solved for similar solutions using the shooting technique and the Runge–Kutta fourth-order method. The temperature, velocity, concentration, thermophoretic velocity, and thermophoretic particle deposition velocity results for various parameters are provided. The Dufour number’s effect enhances the temperature profile and rate of heat transfer. Moreover, it is noted that the rate of mass transfer is meaningfully influenced by the variation of the thermophoresis parameter and Soret number. Thus, in any physical model where the thermal conductivity of the fluid is temperature dependent, the Prandtl number within the BL have to be treated as variable rather than constant.

The problem of heat and mass transfer in a visco-elastic fluid flow over a stretching sheet in the presence of a uniform magnetic field is examined. The important physical quantities such as the skin friction coefficient, heat transfer co-efficient and the mass transfer co-efficient are determined. It is found that the heat and mass transfer distribution decreases with the increasing values of the visco-elastic parameter k<sub>1</sub>.

Purpose This paper aims to address the problem of double-diffusive magnetohydrodynamics (MHD) non-Darcy convective flow of heat and mass transfer over a stretching sheet embedded in a thermally-stratified porous medium. The controlling parameters such as chemical reaction parameter, permeability parameter, etc., are extensively discussed and illustrated in this paper. Design/methodology/approach With the help of appropriate similarity variables, the governing partial differential equations are converted into ordinary differential equations. The transformed equations are solved using the spectral homotopy analysis method (SHAM). SHAM is a numerical method, which uses Chebyshev pseudospectral and homotopy analysis method in solving science and engineering problems. Findings The effects of all controlling parameters are presented using graphical representations. The results revealed that the applied magnetic field in the transverse direction to the flow gives rise to a resistive force called Lorentz. This force tends to reduce the flow of an electrically conducting fluid in the problem of heat and mass transfer. As a result, the fluid velocity reduces in the boundary layer. Also, the suction increases the velocity, temperature, and concentration of the fluid, respectively. The present results can be used in complex problems dealing with double-diffusive MHD non-Darcy convective flow of heat and mass transfer. Originality/value The uniqueness of this paper is the examination of double-diffusive MHD non-Darcy convective flow of heat and mass transfer. It is considered over a stretching sheet embedded in a thermally-stratified porous medium. To the best of the knowledge, a problem of this type has not been considered in the past. A novel method called SHAM is used to solve this modelled problem. The novelty of this method is its accuracy and fastness in computation.

Chapter 10 - Mass Transfer

A qualitative computational study of mass transfer in upward bubble train flow through square and rectangular mini-channels

A theoretical analysis of the steady free convective and mass transfer flow is presented, when a viscous and incompressible fluid flows through a porous medium occupying a semi-infinite region of the space bounded by an infinite vertical porous plate. The fluid is subjected to a normal suction velocity, and the heat flux at the plate is constant. The free-stream velocity is assumed constant.

Wall mass transfer was measured in fully developed pulsating laminar flow in a tube using the diffusion‐controlled electrode technique. The average Reynolds number, pulsating frequency and amplitude, and length of the mass transfer surface were the independent variables studied. The results are given in the form of the amplitude ratio and phase angle of the pulsating wall transfer rate. At lower frequencies the amplitude and phase were found to be correlated by the variable ωd2 Gz−2/3 in accordance with theory. At higher frequencies an empirical correlation with the variable ωd2 Gz−1/3(L/D)1/3 was found. While this may show some deficiency in the usual theoretical model, it is also possible that other causes such as nondevelopment of the flow are responsible. Time‐averaged transfer rates were found to be only slightly different from the corresponding steady flow transfer rates in the range of variables investigated.

The design and calculation of micro mixers is done by conventional analytical and numerical calculations. Due to the small dimensions, laminar flow is expected and the mass transfer is supposed to be dominated by diffusion. A detailed CFD-study by CFDRC-ACE+ of simple static mixers shows a deviation from strictly laminar flow in a wide range of Re numbers and channel dimensions. The static mixers under test have a T-Profile with rectangular cross sections and characteristic dimensions of 50 to 400 μm. The mean flow velocity is varied from 0,01 m/s to 5 m/s, which are typical values for chemical and biological applications, chemical analysis, and microfluidics with acceptable pressure losses. With increasing flow velocity and increasing Re numbers the flow starts to develop a vortex at the entrance of the mixing channel. With further increasing velocity the flow tends to instabilities, which causes the break up of the flow symmetry. With the onset of the vortex formation and with the occurrence of the flow instabilities the mass transfer is enhanced by the exchange of fluid elements. The laminar diffusion model cannot describe this mixing effect. A simple analytical model for first calculations is proposed.

The aim here is to investigate the effects of convective heat and mass transfer in the flow of Eyring-Powell fluid past an inclined exponential stretching surface. Mathematical formulation and analysis have been performed in the presence of Soret, Dufour and thermal radiation effects. The governing partial differential equations corresponding to the momentum, energy and concentration are reduced to a set of non-linear ordinary differential equations. Resulting nonlinear system is computed for the series solutions. Interval of convergence is determined. Physical interpretation is seen for the embedded parameters of interest. Skin friction coefficient, local Nusselt number and local Sherwood number are numerically computed and examined.