Projection operator theoretical approach to unsteady convective diffusion phenomena.

A solution is given for unsteady state concentration profiles in an infinitely long composite cylinder resulting from a step‐change in concentration in a large reservoir surrounding the cylinder. The composite cylinder consists of an inner cylinder with diffusivity D1 surrounded by a permeable tube with diffusivity D2 and has interfacial mass transfer resistances at the cylinder‐tube and tube‐reservoir interfaces. Numerical values are given for the first eight roots and various coefficients of the solution for physical properties typical of tubular (hollow fiber) membranes. These results can be used in the analysis of data from unsteady state mass transfer experiments to determine the permeability of homogeneous tubular membranes. A simple, approximate method for data analysis is suggested for the rapid estimation of the permeability of both homogeneous and asymmetric (skinned) tubular membranes.

Solved Problems in Transport Phenomena

Solved Problems in Transport Phenomena

An approximate analysis of the weakly guiding cladded acoustic fiber consisting of a core and infinite thick cladding both with hexagonal crystal symmetry is presented. The crystalline Z axis is parallel to the fiber axis. Weak guidance conditions require that the stiffness constants of the core are slightly less than those of the cladding, and the density of the core and cladding are almost the same. Approximate dispersion and cutoff equations are derived for all pure guided modes. Dispersion curves of several lower-order guided torsional, radial-axial and flexural modes are evaluated using both exact and approximate formulas and they are in good agreement. A simple approximate dispersion equation for leaky (longitudinal-type) modes is also obtained.

In this work we study various aspects of the projection operators technique and application of projection operators to description of open quantum systems.

Purpose This paper aims to examine the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid along a stretching sheet. The thermal conductivity is taken in a temperature-dependent fashion. With the aid of Cattaneo–Christov double-diffusion theory, relaxation-retardation double-diffusion model is advanced, which considers not only the effect of relaxation time but also the influence of retardation time. Convective heat transfer is not ignored. Additionally, experiments verify that with sodium carboxymethylcellulose (CMC) solutions as base fluid, not only the flow curve conforms to Oldroyd-B model but also thermal conductivity decreases linearly with the increase of temperature. Design/methodology/approach The suitable pseudo similarity transformations are adopted to address partial differential equations to ordinary differential equations, which are computed analytically through homotopy analysis method (HAM). Findings It is worth noting that the increase of stagnation-point parameter diminishes momentum loss, so that the velocity enlarges, which makes boundary layer thickness thinner. With the increase of thermal retardation time parameter, the nanofluid temperature rises that implies heat penetration depth boosts up and the additional time required for nanofluid to heat transfer to surrounding nanoparticles is less, which is similar to the effects of concentration retardation time parameter on concentration field. Originality/value This paper aims to explore the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid with variable thermal conductivity and relaxation-retardation double-diffusion model.

In this work the network simulation method (NSM) is proposed as a tool for solving the two-dimensional unsteady free convection and mass transfer flow of a viscous dissipative fluid along a semi-infinite vertical plate, taking into account the variation of the viscosity, thermal conductivity, and mass diffusivity with temperature. A spatial discretization, as in finite-difference schemes, is applied to the governing equations, with the time remains as a real continuous variable, and the different analogies (electrical-motion, electrical-thermal, and electrical-mass) developed in this work are applied to solve the problem in an adequate electric simulation program. The effect of variations in viscosity, thermal conductivity, and mass diffusivity with temperature is discussed. The effects of viscous dissipation and the Schmidt number are also studied.

We study the unsteady free convection and mass transfer of a non-Newtonian fluid past an infinite vertical plate in the presence of thermal diffusion. Closed form analytical solutions are obtained for the concentration and the temperature distributions by means of the Laplace transform technique on the assumption that the thermal conductivity, k, of the fluid is small. Consequences of the thermal diffusion effect (the Dufour term Df) are then discussed quantitatively. (Botswana Journal of Technology: 2002 11(1): 52-56)

In this paper, we have reported the effects of Hall current on magnetohydrodynamics (MHD) unsteady heat and mass transfer of Casson nanofluid flow through a vertical plate in the presence of radiation and chemical reaction. The model equations have been used for the Casson nanofluid and they include the effects of thermophoresis and Brownian motion. Then, the obtained model equations have been transformed into nondimensional form by the usual mathematical procedure of transformation and the resultant nondimensional couple of partial differential equations are solved by explicit finite difference technique. Then, the obtained results are plotted after stability test by using the graphical software tecplot-9 and these results indicate the fluid flow, temperature, and concentration distributions which are significantly invaded by the variation of different dimensionless parameters such as magnetic parameter, Schmidt number, thermal Grashof number, Lewis number, Prandtl number, mass Grashof number, Dufour number, thermophoresis parameter, Brownian motion parameter, chemical reaction, and radiation parameter on velocity, temperature, and concentration along with the skin friction coefficient, Nusselt number, and Sherwood number. Further, the results have been discussed also with the help of graphs. Furthermore, it is observed that with the increase of the Casson parameter, velocity puts down, whereas by increasing the heat generation parameter, the temperature profiles are decreased.

Unsteady heat and mass transfer from spheres

This paper presents numerical simulation of unsteady and periodic motion heat and mass transfer of a highly concentrated granular medium in a coaxial bunker. Mathematical model with variables vortex-stream functions was developed. Heat and mass transfer in highly concentrated granular materials at different time steps was studied for Re=0.25 and Pr=10 with periodically variable density of the heat flow.

Unsteady flow and mass transfer in models of stenotic arteries considering fluid-structure interaction

Thermodynamic analysis and a theory of unsteady-state process of thermal diffusion and diffusional thermal effect in gas mixtures are presented. A mathematical model for unsteady mass transfer process in gas mixtures is developed.

After decades of development, computational fluid dynamics (CFD), which solves fluid mechanics and, more generally, transport phenomena problems using numerical analysis, has become a main-stream tool in many areas of engineering practice [...]

The spectral task is solved for open prolate spheroid that made from homogeneous isotropic crystal and has small distance between its focuses. The approximate dispersion equation is obtained at satisfaction of the tangential component continuity conditions of electromagnetic field strengths for resonance oscillations on the spheroid surface. It allows to study spectral characteristics of resonance oscillations.