Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number. Untersucht wurde die instationäre laminare Mischkonvektion längs eines vertikalen, in einem porösen Medium eingebetteten Zylinders unter kombinierten Auftriebseffekten von thermischer und spezieller Diffusion. Der Einfluß der Permeabilität des Mediums sowie des magnetischen Feldes wurden in die Betrachtung einbezogen. Die partiellen Differentialgleichungen mit drei unabhängigen Variablen, welche die Strömung beschreiben, wurde numerisch anhand des Schemas der endlichen Differenzen in Verbindung mit der Technik der Quasilinearisation gelöst. Berechnungen für die beschleunigte, verzögerte und oszillierende Geschwindigkeitsverteilung der freien Strömung sind durchgeführt worden. Untersucht wurden ebenfalls die Effekte der Permeabilität des Mediums, der Auftriebskräfte, der transversalen Krümmung, des magnetischen Feldes auf die Oberflächenreibung sowie die Wärmeund Stoffübertragung. Es wurde festgestellt, daß die Geschwindigkeit mehr Einfluß auf die Oberflächenreibung als auf die Wärmeund Stoffübertragung hat. Die Oberflächenreibung sowie die Wärme- und Stoffübertragung werden durch die Auftriebskräfte und die Krümmungsparameter verbessert. Die Wärmeübertragung ist stark abhängig von den Parametern der viskosen Dissipation und der Prandtl-Zahl; die Stoffübertragung von der Schmidt-Zahl.

High sensitive Static fiber Bragg grating strain sensing using lasers locked to relative frequency reference

A novel high sensitive fiber Bragg grating (FBG) strain sensing technique using lasers locked to relative frequency reference is proposed and analyzed theoretically. Static strain on FBG independent of temperature can be measured by locking frequency of diode laser to the mid reflection frequency of matched reference FBG, which responds to temperature similar to that of the sensor FBG, but is immune to strain applied to the same. Difference between light intensities reflected from the sensor and reference FBGs (proportional to the difference between respective pass band gains at the diode laser frequency) is not only proportional to the relative strain between the sensor and reference FBGs but also independent of servo residual frequency errors. Usage of relative frequency reference avoids all complexities involved in the usage of absolute frequency reference, hence, making the system simple and economical. Theoretical limit for dynamic and static strain sensitivities considering all major noise contributions are of the order of 25 (p epsilon) / root Hz and 1.2 n epsilon / root Hz respectively.

Global solutions describing the collapse of a spherical or cylindrical cavity

The collapse of a spherical (cylindrical) cavity in air is studied analytically. The global solution for the entire domain between the sound front, separating the undisturbed and the disturbed gas, and the vacuum front is constructed in the form of infinite series in time with coefficients depending on an ldquoappropriaterdquo similarity variable. At timet=0+, the exact planar solution for a uniformly moving cavity is assumed to hold. The global analytic solution of this initial boundary value problem is found until the collapse time (=(gamma–1)/2) for gamma le 1+(2/(1+v)), wherev=1 for cylindrical geometry, andv=2 for spherical geometry. For higher values of gamma, the solution series diverge at timet — 2(beta–1)/ (v(1+beta)+(1–beta)2) where beta=2/(gamma–1). A close agreement is found in the prediction of qualitative features of analytic solution and numerical results of Thomaset al. [1].

Vertical uplift capacity of horizontal anchors

The method of characteristics coupled with a log-spiral failure surface was used to develop a theory for vertical uplift capacity of shallow horizontal strip anchors in a general c-phi soil. Uplift-capacity factors F(c), F(q) and F(gamma), for the effects of cohesion, surcharge, and density, respectively, have been established as functions of embedment ratio lambda and angle of friction phi. The extent of the failure surface at the ground has also been determined. Comparisons made with existing test results support the predictive capability of the theory, and comparisons with the analysis proposed by Meyerhof and Adams show the proposed analysis provides slightly more conservative predictions of pullout capacity.

Combined convection in power-law fluids along a nonisothermal vertical plate in a porous medium

The problem of combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5 to 2.0.

Effect of magnetic field on the binding energy of a hydrogenic donor in a vertical bar z vertical bar(2/3) quantum well

We have calculated the binding energy of a hydrogenic donor in a quantum well with potential shape proportional to \z\(2/3) as a function of the width of the quantum well and the barrier height under an applied uniform magnetic field along the a axis. As the well width decreases, the binding energy increases initially up to a critical well width (which is nearly the same for all magnetic fields) at which there is a turnover. The results are qualitatively similar to those of a hydrogenic donor in a rectangular well. We have also calculated [rho(2)](1/2) and [z(2)](1/2) for the donor electron. [rho(2)](1/2) is found to be strongly dependent on the magnetic field for a given well width and weakly dependent on the well width and the barrier height, for a given value of magnetic field [z(2)](1/2) is weakly dependent on the applied magnetic field. The probability of finding the donor electron inside the well shows a rapid decrease as the well width is reduced at nearly the well width at which the binding energy shows a maximum.

Mixed convection heat transfer from the bottom tip of a cylinder spinning about a vertical axis in a saturated porous medium

The present work is a numerical study of heat transfer characteristics from the bottom tip of a cylinder spinning about a vertical axis in an infinitely saturated porous medium. The problem is axisymmetric. The non-dimensionalized governing equations are solved using the SIMPLER algorithm on a staggered grid. The influence of rotational Reynolds numbers and Darcy numbers on the heat transfer for a Grashof number of 104 and Prandtl number of 7.0 is studied. It is found that for very high Darcy numbers, over a wide range of rotational Reynolds numbers, the heat transfer takes place mainly due to conduction. The convective heat transfer takes place for lower Darcy numbers and for higher rotational Reynolds numbers. Moreover, there is a rapid increase in the overall Nusselt number below a certain Darcy number with increase in the rotational Reynolds numbers. The effect of the Darcy number and the rotational Reynolds number on the heat transfer and fluid flow in the porous medium is depicted in the form of streamline and isotherm plots. The variation of the overall Nusselt number with respect to the Darcy number for various rotational Reynolds numbers is plotted. The variation of the local Nusselt number with respect to the radial coordinate at the heated tip of the vertical cylinder is plotted for various Darcy and rotational Reynolds numbers.

Natural Convection Heat Transfer From an Isothermal Vertical Surface to a Stable Thermally Stratified Fluid

Natural convection from an isothermal vertical surface to a thermally stratified fluid is studied numerically. A wide range of stratification levels is considered. It is shown that at high levels of ambient thermal stratification, a portion at the top of the plate absorbs heat, while a horizontal plume forms around a location where the plate temperature equals the ambient temperature. The plume is shown to be inherently unsteady, and its transient nature is investigated in detail. The effect of the temperature defect in striating the plume is discussed. Average Nusselt number data are presented for Pr = 6.0 and 0.7.

Obliquely incident water waves against a vertical cliff

Utilizing the commutativity property of the Cartesian coordinate differential operators arising in the boundary conditions associated with the propagation of surface water waves against a vertical cliff, under the assumptions of linearized theory, the problem of obliquely incident surface waves is considered for solution. The case of normal incidence, handled by previous workers follow as a particular limiting case of the present problem, which exhibits a source/sink type behavior of the velocity potential at the shore-line. An independent method of attack is also presented to handle the case of normal incidence.

Solubilization of n-decane into n-decyl-polyoxyethylene surfactants: A cavity forming free energy based model

The present paper reports the results of a theoretical study of the forces and factors driving the solubilization of n-alkane solubilizates into the micellar core of some non-ionic surfactants, based on a micellar model which includes the cavity forming free energy as a component of micellization. The solubilizate is n-decane and the non-ionic surfactants considered are n-decyl-polyoxyethylene surfactants. The extent of solubilization, i.e. the mole fraction of the solubilizate within the core has been calculated. The results indicate that the incorporated solubilizate has more translational and rotational degrees of freedom as compared to those of the tail parts of the surfactants present in the core. This drives the total free energy of aggregation after solubilization into a more favourable direction. The results are in fair agreement with the experimental results.

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T Wpropx lambda and surface injectionv Wpropx(lambda–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.