Effects Of Various Dimensionless Parameters Research Articles

Effects of first-order chemical reactions on the dispersion coefficient associated with laminar flow through the lungs

This paper aims to look into the determination of effective area-average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute undergoes first-order chemical reaction both within the fluid and at the boundary. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. To understand the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Finite Difference Method. The resultant equation shows how the dispersion coefficient is influenced by the first-order chemical reaction. The effects of various dimensionless parameters e.g. Da (the Damkohler number), α (phase partitioning number) and Γ (dimensionless absorption number) on dispersion are discussed. One of the results exposes that the dispersion coefficient may approach its steady-state limit in a short time at a high value of Damkohler number (say Da ≥ 10) and a small but nonzero value of absorption rate (say Γ ≤ 0.5).

Effect of thermo diffusion and chemical reaction on convective heat and mass transfer flow of a rotating micro polar fluid with hall effect past a vertical plate

In this paper, we investigate the effect of combined influence of Hall effect chemical reaction thermo diffusion and rotation on Hydro magnetic convective Heat & mass transfer flow of a micro polar fluid through a porous medium bounded by a semi-infinite porous plate in the presence of heat generating sources. The dimensionless grouping equations for this investigation on solved using small perturbation approximation. The effects of various dimensionless parameters entering to the problem on the velocity & temperature concentration micro rotation profiles across the boundary layer are investigated to graphs. Also the result of the couple stress coefficient, the rate of heat & mass transfer at the wall are evaluated for different variations of the parameters.

Falling film flow of a viscoelastic fluid along a wall

In this paper, we study the heat transfer in the fully developed flow of a viscoelastic fluid, a slag layer, down a vertical wall. A new constitutive relation for the stress tensor of this fluid is proposed, where the viscosity depends on the volume fraction, temperature, and shear rate. For the heat flux vector, we assume the Fourier's law of conduction with a constant thermal conductivity. The model is also capable of exhibiting normal stress effects. The governing equations are non‐dimensionalized and numerically solved to study the effects of various dimensionless parameters on the velocity, temperature, and volume fraction. The effect of the exponent in the Reynolds viscosity model is also discussed. The different cases of shear‐thinning and shear‐thickening, cooling and heating, are compared and discussed. The results indicate that the viscous dissipation and radiation (at the free surface) cause the temperature to be higher inside the flow domain. Copyright © 2013 John Wiley & Sons, Ltd.

Convective–radiative radial fins with convective base heating and convective–radiative tip cooling: Homogeneous and functionally graded materials

This paper studies a radial fin of uniform thickness with convective heating at the base and convective–radiative cooling at the tip. The fin is assumed to experience uniform internal heat generation. The exposed surfaces of the fin lose heat by simultaneous convection and radiation to the surroundings. Two types of fin materials are investigated: homogeneous material and functionally graded material (FGM). For the homogeneous material, the thermal conductivity is assumed to be a linear function of temperature, while for the FGM fin the thermal conductivity is modeled as a linear function of the dimensionless radial coordinate. The analysis is conducted using the differential transformation method (DTM). The accuracy of DTM is verified by comparing the results for the simplified versions of the present model with an exact analytical solution derived here. Once the accuracy of DTM is authenticated, the method is used to generate results for the general problem formulated here. These results illustrate the effects of various dimensionless parameters on the thermal performance of homogeneous material fins and FGM fins.

Effect of Heat and Mass Transfer on Unsteady MHD Oscillatory Flow of Jeffrey Fluid in a Horizontal Channel with Chemical Reaction

The effect of heat transfer on unsteady MHD oscillatory flow of Jeffrey fluid in a horizontal channel with chemical reaction has been studied. The temperature prescribed at plates is uniform and asymmetric. A perturbation method is employed to solve the momentum and energy equations. The skin frictions, the Nusselt numbers and Sherwood are evaluated using perturbation technique. The effects of various dimensionless parameters on velocity and temperature profiles are considered and discussed in details through graphs and tables. It is found that, the velocity u increases with increase in Gr, Gc, N and Re. The velocity also increases with decrease in λ1,Ha, Sc and ω. The velocity only decreases with increase in Pe. It is also observed that the temperature θ decreases with increase in N, Re and ω. Decrease in Schmidt number Sc, chemical parameter Kc and frequency of oscillation ω increase the species concentration or the concentration boundary layer thickness of the flow field.

Finite-difference analysis of natural convection flow of a viscous fluid in a porous channel with constant heat sources

The fully developed natural convection flow of a viscous fluid in a porous channel is modeled and studied numerically. The walls are kept at constant temperatures. The effects of various dimensionless parameters emerging in the model are studied graphically. It has been noted that the velocity and temperature both depend on the heat source and the free convection parameters.

Magnetohydrodynamics flow of a Burgers’ fluid in an orthogonal rheometer

The magnetohydrodynamics flow of an electrically conducting, incompressible Burgers’ fluid in an orthogonal rheometer is investigated. An exact solution is obtained. The effects of various dimensionless parameters existing in the model on the velocity field, vorticity and traction are studied graphically. It is noted that boundary layers form for a variety of reasons. It form as the Reynolds number increases. Also, as the Weissenberg number increases a distinct boundary layer formation is observed. It can develop at low Reynolds number provided the Weissenberg number is sufficiently high, however, it is not possible in the case of a Newtonian fluid. It is shown that no torque is exerted by the fluid on one of the disks. Results are compared with Oldroyd-B fluid.

Numerical simulation of the dispersion in oscillating flows with reversible and irreversible wall reactions

This is a study on the mass transport of a solute or contaminant in oscillating flows through a circular tube with a reactive wall layer. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. The short-time dispersion characteristics are numerically investigated, incorporating the coupling effects between the flow oscillation, sorption kinetics, and retardation due to phase partitioning. The effects of various dimensionless parameters e.g., Da (the Damköhler number), α (phase partitioning number), Γ(dimensionless absorption number), and δ(dimensionless Stokes boundary layer number) on dispersion are discussed. In particular, it is found that there exist trinal peaks of the breakthrough curves in some cases.

Effect of Magnetic Field on Entropy Generation Due to Laminar Forced Convection Past a Horizontal Flat Plate

Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow past a horizontal plate was numerically investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effect of various dimensionless parameters, such as Hartmann number (Ha), Eckert number (Ec), Prandtl number (Pr), Joule heating parameter (R) and the free stream temperature parameter (θ∞) on the entropy generation characteristics is analyzed. The dimensionless governing equations in Cartesian coordinate were solved by an implicit finite difference technique. The solutions were carried out for Ha2=0.5-3, Ec=0.01-0.05, Pr=1-5 and θ∞=1.1-2.5. It was found that, the entropy generation increased with increasing Ha, Ec and R. While, increasing the free stream temperature parameter, and Prandtl number tend to decrease the local entropy generation.

Kinetics of competitive polymerization in bidisperse seed systems using oil‐soluble initiators: Calculation of effect of various dimensionless parameters

AbstractExpressions for calculating the stationary state distribution of radicals in a bidisperse seed system initiated by oil‐soluble initiators were developed. Dimensionless parameters were used throughout, thus making it possible to obtain general trends without introducing specific numerical values. Desorption and reabsorption of radicals, aqueous phase termi‐nation, partition of the initiator into the aqueous phase, and a possible generation of single radicals are taken into account. The radical entry and exit rate coefficients are formulated in terms of power laws with respect to particle diameter. No discrimination of the various radical species and their origin is made. The derivation is based on a probabilistic stationary state analysis leading to third‐order recurrence relations that are solved using confluent, hypergeometric Kummer functions. A selection of curves illustrating the effect of various dimensionless parameters on the calculated average number of radicals per particle, the order of volume growth with respect to the particle diameter, and relative rates are given. © 1995 John Wiley & Sons, Inc.

Modelling of dislocation mobility controlled brittle-to-ductile transition

The phenomenon of brittle-to-ductile transition (BDT) is known to be controlled by the competition between cleavage fracture and dislocation activity at crack tips, but the transition could be determined by one of the two successive processes, dislocation nucleation or dislocation motion. In this paper a model is developed to study the BDT controlled by dislocation mobility. The model material is assumed to undergo elastic rate-dependent plastic deformation, with the plastic strain rate scaled with dislocation velocity. An isotropic plasticity theory is used. The BDT is assumed to occur when the crack tip is shielded by the surrounding plastic zone such that it never reaches the critical stress intensity for cleavage fracture. The crack tip shielding due to plastic deformation is evaluated using the finite element method. The dimensionless groups that affect the BDT are identified, and a parametric study is performed to reveal the effects of various dimensionless parameters. Numerical results using the specific material properties of Si single crystals are compared with experimental data. Good agreements are obtained. Some interesting features of the BDT behaviour are predicted by our computer simulations which require further confirmation by experimental studies.

Radial fuel-water transport in aquifer near an injection well

A new physico-mathematical approach is developed for modelling of fuel migration in an axisymmetric groundwater flow by considering the various dimensionless parameters governing the transport processes. The self-similar solution scheme developed for a time-dependent water injection rate describes the evolution of the fuel saturation in the aquifer near a single recharge well. It is found that the capillary forces prevent the fuel from being removed downstream by injecting water through the well. The time dependent saturation profiles calculated from several exact analytical solutions exhibit the effects of various dimensionless parameters in fuel migration in radial water flow.

Analytical Modeling of Calcium Carbonate Deposition for Laminar Falling Films and Turbulent Flow in Annuli: Part II—Multispecies Model

The present study proposes a multispecies transport model to predict calcium carbonate deposition. The model has been applied to predict the deposition flux, the mean fouling layer thickness, and the profile of local fouling thickness along a heated plate of a laminar falling film. Good agreement is found when comparing with experimental data. Similarly, the model is applied to predict the fouling layer in a turbulent annulus flow system and a good agreement of the predicted results is also found with recent experimental data. Finally, solutions in dimensionless forms are presented to show the effects of various dimensionless parameters on calcium carbonate deposition.

Transfer Function of a Class of Nonlinear Multidegree of Freedom Oscillators

Analytical and experimental studies were made of the dynamic response of a multidegree-of-freedom system with a geometric nonlinearity, which is encountered in many practical engineering applications. An exact solution was derived for the steady-state motion of a viscously damped two-degree-of-freedom oscillator with an unsymmetric geomtric nonlinearity, under the action of harmonic excitation. Experimental measurements of a distributed-parameter mechanical model under harmonic excitation verified the analytical findings. The effect of various dimensionless parameters on the system response was determined.

Modeling of solute transport in aggregated/fractured media including diffusion into the bulk matrix

In this paper the influence of mass-transfer resistance on solute transport and uptake in soils is stressed. The resistance is generally divided into three distinct stages: (1) diffusion of the component from the flowing water to the solid interface (external or film diffusion); (2) diffusion through the porous network of the aggregates (internal diffusion); and (3) the sorption process itself, when the component is bound to some sorption site in the micropores (ion-exchange, adsorption, etc). In the general case, all three steps can contribute to the overall sorption rate. The sorption process is usually rapid (third mass transfer resistance). Film diffusion (first mass transfer resistance) may be of importance at low velocities. The bulk of the present paper discusses the impact of internal diffusion (second mass transfer resistance) on ion-transport in soils. This effect can be very important since large internal surfaces become available for sorption. Mathematical models are formulated and solved analytically. In these models chemicals are transported by flow and dispersion in larger pores or cracks. In addition, diffusion-type equations are used to describe transfer of solute from the larger pores into the bulk soil matrix. The effects of various dimensionless parameters, taking into account transport distance, water velocity, flow porosity, film diffusion, diffusivity, sorption constant, reaction rate, longitudinal dispersion coefficient and aggregate radius are explored. The influences of aggregate shape and a particle size distribution are treated. It is shown that if the area-to-volume ratio of slabs, cylinders and spheres is the same, identical breakthrough curves are produced for short and long contact times. In the intermediate range the first breakthrough times are in the order of spheres < cylinders < slabs. Generally, compared to uniform aggregates (particles), the effect of size distribution is to delay the breakthrough. This is most pronounced for particle size distributions which are skewed towards smaller particles.

Dynamic Response of a Beam With a Geometric Nonlinearity

Analytical and experimental studies were made of the dynamic response of a system with a geometric nonlinearity, which is encountered in many practical engineering applications. An exact solution was derived for the steady-state motion of a viscously damped Bernoulli-Euler beam with an unsymmetric geometric nonlinearity, under the action of harmonic excitation. Experimental measurements of a mechanical model under harmonic as well as random excitation verified the analytical findings. The effect of various dimensionless parameters on the system response was determined.

Prediction of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis

The temperature distribution in spur gears operating in a state of thermal equilibrium is solved by using a finite element method. The effects of various dimensionless parameters on bulk temperature are shown. A table is provided which can be used to predict the bulk temperature on gear teeth, once the heat transfer coefficients and frictional heat input is estimated. Theoretical results for estimating heat transfer coefficients and frictional heat are also summarized. Presented as an American Society of Lubrication Engineers paper at the ASLE/ASME Lubrication Conference in Kansas City, Missouri, October 3–5, 1977