On the case when steady converging/diverging flow of a non-Newtonian fluid in a round cone permits an exact solution

This communication considers the steady converging/diverging flow of a non-Newtonian viscous power-law fluid in a round cone. The motion is driven by a sink/source of mass at the origin. It is shown that the problem permits exact similarity solution for a particular value (n=4/3) of the fluid index. In this case a complete set of governing equations can be reduced to an ordinary differential equation, which is solved numerically for different values of the main non-dimensional parameters (the cone angle and the dimensionless sink/source intensity).     

Improvement of mass source/sink for an immersed boundary method

An improved immersed boundary method using a mass source/sink as well as momentum forcing is developed for simulating flows over or inside complex geometries. The present method is based on the Navier–Stokes solver adopting the fractional step method and a staggered Cartesian grid system. A more accurate formulation of the mass source/sink is derived by considering mass conservation of the virtual cells in the fluid crossed by the immersed boundary. Two flow problems (the decaying vortex problem and uniform flow past a circular cylinder) are used to validate the proposed formulation. The results indicate that the accuracy near the immersed boundary is improved by introducing the accurate mass source/sink. Copyright © 2006 John Wiley & Sons, Ltd.     

Removal of unwanted fluid

This work is concerned with the removal of unwanted fluid through the source–sink pair. The source consists of fluid issuing out of a nozzle in the form of a jet and the sink is a pipe that is kept some distance from the source pipe. Of concern is the percentage of source fluid sucked through the sink. The experiments have been carried in a large glass water tank. The source nozzle diameter is 6 mm and the sink pipe diameter is either 10 or 20 mm. The horizontal and vertical separations and angles between these source and sink pipes are adjustable. The flow was visualized using KMnO₄ dye, planer laser induced fluorescence and particle streak photographs. To obtain the effectiveness (that is percentage of source fluid entering the sink pipe), titration method is used. The velocity profiles with and without the sink were obtained using particle image velocimetry. The sink flow rate to obtain a certain effectiveness increase dramatically with lateral separation. The sink diameter and the angle between source and the sink axes don’t influence effectiveness as much as the lateral separation.     

The flow of magnetohydrodynamic Maxwell nanofluid over a cylinder with Cattaneo–Christov heat flux model

A theoretical analysis is performed for studying the flow and heat and mass transfer characteristics of Maxwell fluid over a cylinder with Cattaneo–Christov and non-uniform heat source/sink. The Brownian motion and thermophoresis parameters also considered into account. Numerical solutions are carried out by using Runge–Kutta-based shooting technique. The effects of various governing parameters on the flow and temperature profiles are demonstrated graphically. We also computed the friction factor coefficient, local Nusselt and Sherwood numbers for the permeable and impermeable flow over a cylinder cases. It is found that the rising values of Biot number, non-uniform heat source/sink and thermophoresis parameters reduce the rate of heat transfer. It is also found that the friction factor coefficient is high in impermeable flow over a cylinder case when compared with the permeable flow over a cylinder case.     

Effect of non-uniform heat source on MHD heat transfer in a liquid film over an unsteady stretching sheet

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a laminar liquid film over a flat impermeable stretching sheet in the presence of a non-uniform heat source/sink. The basic unsteady boundary layer equations governing the flow and heat transfer are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformation. Numerical solutions of the resulting boundary value problem are obtained by the efficient shooting technique. The effects of magnetic and the non-uniform heat source/sink parameters on the dynamics are discussed. Findings of the paper reveal that non-uniform heat sinks are better suited for effective cooling of the stretching sheet. Skin friction coefficient and the local Nusselt number are also explored for typical values of magnetic and non-uniform heat source/sink parameters. The results are in excellent agreement with the earlier published works, under some limiting cases.     

Unsteady two-dimensional rotation of a viscous fluid for steady source flow

We obtain the solution of the Navier-Stokes equations for one class of unsteady axisymmetric two-dimensional rotational flows for the case of a line source or sink of constant intensity in the fluid.     

Nonsteady sink and source in a rotating fluid

The effect of the Coriolis force on the nonsteady two-dimensional sink or source flow has been studied theoretically. With the assumptions of incompressibility and invisddity of fluid, the equations governing the flow are still non-linear. However, a set of analytical and exact solutions is obtained for the velocity and pressure distributions. The result shows that no significant vortex flow can be induced by a source flow, the circulation produced there mainly is because the observer is moving with the rotating system; however, a sink will always induce a vortex, the strength of circulation in the sink flow is simply in proportion to the rotating speed of the system and the time integrated sink strength. As the system is under a constant rotating speed, the circulation will vanish only when the time integrated sink strength vanishes. Several special cases of sink strength are examined and their results are presented in this paper. The purpose of this study is mainly to relate the strength of circulation with the strength of sink and source. Consequently, it- can be applied to the weather forecast for hurricanes or tornadoes.     

Improvement of mass conservation and reduction of spurious oscillations for the local DFD method

By introducing a mass source/sink term into the continuity equation, the mass-conservation property of the local domain-free discretisation (DFD) method is improved to reduce the spurious oscillations in the simulation of moving-boundary problems. The mass source/sink term is constructed by evaluating the mass flux through the solid part of the control volume split by the immersed boundary. Additionally, some special treatments are given for the multi-valued nodes associated with thin bodies. The introduction of source/sink term has also been extended to three-dimensional problems. Unlike the ghost-cell immersed boundary method, coupling the mass source/sink algorithm with the local DFD method is implemented on triangular and tetrahedral meshes. Compared to the hybrid reconstruction formulation, the properties of the original local DFD method can be preserved better. Numerical experiments for two- and three-dimensional moving-boundary problems show that the present mass source/sink treatment can reduce spurious oscillations effectively.     

Compression and outflow of an asymptotically thin perfectly rigid-plastic spherical layer

The axisymmetric meridional flow of an incompressible perfectly rigid-plastic medium between two concentric rough spheres is studied in the case of a sink. The outer sphere is fixed, whereas the surface of the inner sphere is uniformly expanded. An asymptotic integration of a boundary value problem with a natural small geometric parameter is performed.     

Unsteady Motion of a Gas in a Strip

An exact solution is constructed, which describes a gas glow in a strip between a rectilinear source and sink. With time, the strip turns and expands. In the case of consistent boundary conditions, the flow in the strip is continuous. If the consistency constraints are violated, a shock wave is formed inside the strip.     

The steady-state flow of a rarefied gas from a spherical source or sink

The method of characteristics is used to solve problems in the steady-state flows of a rarefied gas on the basis of approximating the kinetic equations. Numerical results are given for the solution of the problem of the flow from a spherical source or sink using the generalized Kruk equation [1] and approximating the Boltzmann equation by the method proposed by the author [2, 3], Various flow conditions are discussed: flow into a vacuum, flow into a flooded volume, flow from a sink.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 58–66, March–April, 1971.     

Heat transport of hybrid nanomaterial in an annulus with quadratic Boussinesq approximation

The convective heat transfer of hybrid nanoliquids within a concentric annulus has wide engineering applications such as chemical industries, solar collectors, gas turbines, heat exchangers, nuclear reactors, and electronic component cooling due to their high heat transport rate. Hence, in this study, the characteristics of the heat transport mechanism in an annulus filled with the Ag-MgO/H_2O hybrid nanoliquid under the influence of quadratic thermal radiation and quadratic convection are analyzed. The nonuniform heat source/sink and induced magnetic field mechanisms are used to govern the basic equations concerning the transport of the composite nanoliquid. The dependency of the Nusselt number on the effective parameters(thermal radiation, nonlinear convection,and temperature-dependent heat source/sink parameter) is examined through sensitivity analyses based on the response surface methodology(RSM) and the face-centered central composite design(CCD). The heat transport of the composite nanoliquid for the spacerelated heat source/sink is observed to be higher than that for the temperature-related heat source/sink. The mechanisms of quadratic convection and quadratic thermal radiation are favorable for the momentum of the nanoliquid. The heat transport rate is more sensitive towards quadratic thermal radiation.     

A numerical study of natural convection from a localized heat source in the lower plenum of a fast breeder reactor under failed conditions

A comprehensive numerical study has been done to investigate two-dimensional, steady state, conjugate natural heat convection in the hemi spherical lower plenum of a fast breeder reactor under failed conditions. The continuity, momentum and energy equations are solved over the entire domain, using the corresponding properties for the solid and fluid regions. The control volume approach is employed in order to discretize the governing equations for their numerical solution. A parametric study has been done to study the variation of the velocity vectors and isotherms for different constant temperature of the heat source, simulating different heat generation rates. The actual problem in a nuclear reactor involves a volumetric heat generation in the debris falling over the heat shield plate under failed conditions of the reactor and heat is removed by a decay heat exchanger serving as a sink. In this study we have reduced this transient problem to a quasi-steady problem with a prescribed temperature on the heat shield plate. This makes the problem more tractable. The fluid flow pattern, variation of the temperature along the axis in and around the heat source are presented to show the overall heat transfer characteristics inside the plenum.     

Thermal stresses in an isotropic trimaterial interacted with a pair of point heat source and heat sink

A general analytical solution for an isotropic trimaterial interacted with a point heat source is provided in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solutions to heat conduction and thermoelasticity problems for three dissimilar media are first derived. A rapidly convergent series solution for both the temperature and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. As a numerical illustration, the distributions of thermal stresses along the interface are presented for various material combinations and for different positions of the applied heat source and heat sink.     

Convection of Maxwell fluid over stretching porous surface with heat source/sink in presence of nanoparticles: Lie group analysis

The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into coupled nonlinear ordinary differential equations. The ordinary differential equations are solved numerically by the Bvp4c with MATLAB, which is a collocation method equivalent to the fourth-order mono-implicit Runge-Kutta method. Furthermore, more attention is paid to the effects of the physical parameters, especially the parameters related to nanoparticles, on the temperature and concentration distributions with consideration of permeability and the heat source/sink.     

Magnetoconvection in a vertical channel with heat source or sink

The problem of steady, laminar mixed convective flow and heat transfer of an electrically conducting fluid through a vertical channel with heat source or sink is analyzed. The effects of viscous and Ohmic dissipations are included in the energy equation. Both walls are kept either at the same or different temperatures such as isothermal-isothermal, isoflux-isothermal and isothermal-isoflux conditions. Analytical solutions are found using regular perturbation technique and numerical solutions are found using finite difference method. A selected set of graphical results illustrating the effects of various parameters involved in the problem on the flow as well as flow reversal situation and Nusselt numbers are presented and discussed. It is also found that both the analytical and numerical solutions agree very well for small values of the perturbation parameter.     

A Cauchy integral approach to Hele-Shaw problems with a free boundary: The case of zero surface tension

In this paper, we study a nonlinear and nonlocal free-boundary dynamics — the Hele-Shaw problem without surface tension when the fluid domain is either bounded or unbounded. The key idea is to use a global quantity, the Cauchy integral of the free boundary, to capture the motion of the boundary. This Cauchy integral is shown to be linear in time. The free boundary at a fixed time is then recovered from its Cauchy integral at that time. The main tool in our analysis isCherednichenko's theorem concerning the inverse properties of the Cauchy integrals.As products of our approach, we establish the short-time existence and uniqueness of classical solutions for analytic initial boundaries. We also show the non-existence of classical solutions for all smooth but non-analytic initial boundaries when there is a sink at either a finite point or at infinity. When the fluid domain is bounded, all solutions except the circular one break down before all the fluid is sucked out from the sink. Regularity results are also obtained when there is a source at a finite point or at infinity.     

Performance characteristics of HFC-134a and HFC-410A refrigeration system using a short-tube orifice as an expansion device

In the present article, the effect of heat source temperature, heat sink temperature, short-tube orifice diameter and short-tube orifice length on the performance characteristics of HFC-140A and HFC-134a refrigeration system using a short-tube orifice as expansion device, i.e., mass flow rate, cooling capacity, compressor pressure ratio, power consumption, and second law efficiency are experimentally studied. The short-tube orifices diameters ranging from 0.849 to 1.085 mm with length ranging from 10 to 20 mm are used in this examination. The test run are done at heat source temperature ranging between 16.5 and 18.5°C, and heat sink temperature ranging between 30 and 35°C. The results show that the tendency of second law efficiency is increased as the short-tube orifice diameter and heat source temperature are enhanced, but it is decreased by increasing the short-tube orifice length and heat sink temperature. Under the similar conditions, the mass flow rate, cooling capacity, and compressor power consumption obtained from HFC-410A are higher than those obtained from HFC-134a.     

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.