High-viscosity oil flow in a formation with a hydraulic fracture under the action of a high-frequency electromagnetic field

The results of numerical investigations of high-viscosity oil flow in a low-permeability reservoir under high-frequency electromagnetic action in combination with hydraulic fracturing are presented. The fluid flow toward a solitary vertical sand-filled fracture with high permeability, much higher than the permeability of the formation, is considered. The electrophysical and thermal characteristics of the formation and fracture both saturated with formation fluid are assumed to be identical. The unsteady fluid pressure, temperature and viscosity fields near the hydraulic fracture are calculated and the efficiencies of high-viscosity oil extraction are compared for different electromagnetic radiation powers and “cold” fluid withdrawal.     

Dissipative heating in shear plow of the asthenosphere

The problem of the dissipative heating of a fluid under a solid plate moving at constant velocity is considered. Dissipative heating is associated with the viscous friction of the layers of fluid, whose velocity outside the region of disturbances is zero. The viscosity of the fluid is assumed to depend exponentially on the temperature. The temperature of the plate is assumed to be constant.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–57, March–April, 1985.     

Linear and weakly nonlinear variable viscosity convection in spherical shells

A theoretical study of linear and weakly nonlinear thermal convection in a spherical shell is performed. The Boussinesq fluid is of infinite Prandtl number and its viscosity is temperature dependent. The linear stability eigenvalue problem is derived and solved by a shooting method assuming isothermal, stress-free boundaries, a self-gravitating fluid, and corresponding to two heating models. The first is heating from below, and the second is a model of combined heating from below and within, such that convection is described by a self-adjoint linear stability formulation. In addition, nonlinear, hemispherical, axisymmetric convection is computed by a finite volume technique for a shell with 0.5 aspect ratio. It is shown that 2-cell convection occurs as transcritical bifurcation for a viscosity constrast across the shell up to about 150. Motions with four cells are also possible. As expected, the subcritical range is found to increase with increasing viscosity contrast, even when the linear operator is self-adjoint.This research was supported by the AT&T Foundation.     

Effects of non-uniform heating on a variable viscosity Rayleigh�CB��nard problem

This study presents a natural convection problem with a temperature-dependent viscosity fluid, driven by buoyancy and influenced by horizontal temperature gradients. A numerical linear stability analysis of the stationary solutions is studied. The horizontal temperature gradients tend to localize motion near the warmer zones and favour pattern formation in the direction perpendicular to the gradient. In fact, the problem is almost 2D in the uniform heating case, but becomes totally 3D in the non-uniform heating case.     

Radiation Effect on MHD Free Convection Flow of a Gas Past a Semi-infinite Vertical Plate with Variable Viscosity

The radiation effect in the presence of a uniform transverse magnetic field on steady free convection flow with variable viscosity is investigated. The fluid viscosity is assumed to vary as the reciprocal of a linear function of temperature. Boundary layer equations are derived. The resulting approximate non-linear ordinary differential equations are solved linearly and nonlinearly by shooting methods. The velocity and temperature profiles are shown, and the skin friction on the plate and heat transfer coefficient are presented and discussed. The results of the present study show that in the presence of magnetic field, as the radiation parameter increases the temperature increases, but the velocity decreases.     

Noncontact manipulation of microflow by photothermal control of viscous force

In this paper, we investigate a potential of local control of the viscous force in a microfluidic device for a noncontact microflow manipulation method. Photothermal effect and temperature dependence of the liquid viscosity play a key role to induce an inhomogeneous viscosity distribution in the flow field in a microchannel. Absorption of focused laser beam generates the local change in the viscosity of liquid corresponding to the temperature change. The velocity and temperature fields are measured by the micron-resolution particle image velocimetry and laser-induced fluorescence, respectively. Measurement results indicate that the local reduction of the fluid viscosity due to the temperature rise can cause the change of the flow structure in the microchannel. At the focused area of heating laser beam, namely high temperature area, the flow velocity was increased. The accompanying fluid behavior around the heated region was also recognized. In addition, the agreement between the experimental results and numerical simulation clarifies that the primary factor for the change of the microflow structure is the locally controlled viscous force.     

The effects of temperature-dependent fluid properties on free convective flow along a semi-infinite vertical plate by the presence of radiation

The effects of temperature-dependent density, viscosity and thermal conductivity on the free convective steady laminar boundary layer flow by the presence of radiation for large temperature differences, are studied. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. The fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The usual Boussinesq approximation is neglected due to the large temperature difference between the plate and the fluid. The nonlinear boundary layer equations, governing the problem under consideration, are solved numerically by applying an efficient numerical technique based on the shooting method. The effects of the density/temperature parameter n, the thermal conductivity parameter , the viscosity/temperature parameter _r and the radiation parameter F are examined on the velocity and temperature fields as well as the coefficient of heat flux and the shearing stress at the plate.     

Analytical and numerical solutions of electro-osmotically driven flow of a third grade fluid between micro-parallel plates

Electro-osmotic flow of a third grade fluid between micro-parallel plates is considered. The equations of motion are derived and made dimensionless. Approximate analytical solutions are obtained by perturbation techniques. Constant viscosity and temperature dependent viscosity (Reynolds model) cases are treated separately. Numerical solutions of the equations are also obtained. Influences of non-Newtonian parameter, Joule heating effect, viscosity index and electro-kinetic effect on the velocity and temperature profiles are shown. Approximate and numerical solutions are contrasted.     

The developing heat transfer and fluid flow in micro-channel heat sink with viscous heating effect

The numerical modeling of the conjugate heat transfer and fluid flow through the micro-heat sink was presented in the paper, considering the viscous dissipation effect. Three different fluids with temperature dependent fluid viscosity are considered: water, dielectric fluid HFE-7600 and isopropanol. The square shape of the cross-section is considered with D _h  = 50 μm with a channel length L = 50 mm. As most of the reported researches dealt with fully developed fluid flow and constant fluid properties in this paper the thermal and hydro-dynamic developing laminar fluid flow is analyzed. Two different heat transfer conditions are considered: heating and cooling at various Br. The influence of the viscous heating on local Nu and Po is analyzed. It was shown that for a given geometry the local Po and Nu numbers are strongly affected by the viscous heating. Moreover the Po number attains the fully developed value as the external heating is equal with the internal viscous heating.     

Temperature field at time of pulse current discharge in metal structure with elliptical embedding crack

Theoretical analysis is made on the temperature field at the time of pulse current discharge in a metal structure with an elliptical embedding crack. In finding the temperature field, analogy between the current flow through an elliptical embedding crack and the fluid flow through a barrier is made based on the similarity principle. Boundary conditions derived from this theory are introduced so that the distribution of current density and the temperature field expressions can be obtained. The study provides a theoretic basis to the applications of stopping spatial crack with electromagnetic heating.     

Numerical simulation of forced convection in a duct subjected to microwave heating

In this paper, forced convection in a rectangular duct subjected to microwave heating is investigated. Three types of non-Newtonian liquids flowing through the duct are considered, specifically, apple sauce, skim milk, and tomato sauce. A finite difference time domain method is used to solve Maxwell’s equations simulating the electromagnetic field. The three-dimensional temperature field is determined by solving the coupled momentum, energy, and Maxwell’s equations. Numerical results show that the heating pattern strongly depends on the dielectric properties of the fluid in the duct and the geometry of the microwave heating system.     

Nonisothermal steady flow of a viscoplastic liquid between two coaxial rotating cylinders

Rotational viscosimeters are widely used to determine liquid viscosity. The technique for processing the experimental data is based fundamentally on the analytic solution of the problem of isothermal flow of a viscous liquid between two rotating cylinders.If in the course of the experiment the heat released due to the internal friction leads to significant heating, then the processing of the experimental results using the equations obtained on the assumption of isothermocity of the flow may lead to large errors. The dissipative heating may be reduced by reducing the angular velocity of rotation of the cylinder; however extensive reduction of the angular velocity is not desirable, since this leads to an increase of the measurement relative error. In addition, there is the possibility of conducting the experiments with a wide variation of the angular velocities in order to identify the structural-rheological peculiarities of the liquid. In the latter case we must be able to separate the purely thermal effects from the influence of the rheological factors. All these questions are discussed in detail in [1]. The authors of [1] obtained the solution of the problem of nonisothermal flow of a Newtonian fluid between two rotating cylinders and gave a technique for processing the experimental data which takes account of the dissipative heating of the fluid. The present paper pursues the same objective for a visco-plastic fluid.An attempt to solve the problem of nonisothermal flow of a viscoplastic fluid was made by Dzhafarov in [2], where the problem was solved in two versions. In the first version it was considered that the viscosity varies hyperbolically with the temperature and the gap between the cylinders is small in comparison with the radius of the inner cylinder. As a result of the linearization of the equations of motion and heat balance, it turned out that in fact the problem of Couette flow of a viscoplastic fluid was solved rather than the original problem. In this case, naturally, such a characteristic of the flow of a viscoplastic fluid in an annular gap as the possibility of the formation of an elastic zone was not covered. In the second version the problem was solved under the assumption that the viscosity is independent of the temperature and the angular velocity is small.In the present study the problem is solved without the limitations discussed above on the angular velocity, the fluid visoosity, and the gap between the cylinders. In this case we consider two types of temperature boundary conditions: a) constant temperatures are specified on the surfaces of the cylinders, which in the general case may be different; and b) a constant temperature is given on the surface of the outer cylinder and the inner cylinder is thermally insulated.     

Effects of thermal radiation and variable fluid viscosity on stagnation point flow past a porous stretching sheet

Similarity analysis is performed to investigate the structure of the boundary layer stagnation-point flow and heat transfer over a stretching sheet subject to suction. Fluid viscosity is assumed to vary as a linear function of temperature. Thermal radiation term is considered in the energy equation. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. With the help of them the partial differential equations corresponding to momentum and energy equations are transformed into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing values of the ratio of the free stream velocity to the stretching velocity. Velocity increases with the increasing temperature dependent fluid viscosity parameter when the free-stream velocity is less than the stretching velocity but opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. Temperature at a point of the surface is found to decrease with increasing thermal radiation.     

Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity

This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip velocity.The fluid viscosity and the thermal conductivity are assumed to be the functions of temperature.The equations governing the flow are solved numerically by the Chebyshev spectral method for some representative value of various parameters.In comparison with the previously published work,the excellent agreement is shown.The effects of various parameters on the velocity,the microrotation velocity,and the temperature profiles,as well as the skin-friction coefficient and the Nusselt number,are plotted and discussed.     

Heat transfer in flow of nonlinear fluids with viscous dissipation

The rotational flow of viscoplastic fluids between concentric cylinders is examined while dissipation due to viscous effects through the energy balance. The viscosity of fluid is simultaneously dependent on shear rate and temperature. Exponential dependence of viscosity on temperature is modeled through Nahme law, and the shear dependency is modeled according to the Carreau equation. Hydrodynamically, stick boundary conditions are applied, and thermally, both constant temperature and constant heat flux on the exterior of cylinders are considered. The governing motion and energy balance equations are coupled adding complexity to the already highly correlated set of differential equations. Introduction of Nahme number has resulted in a nonlinear base flow between the cylinders. As well, the condition of constant heat flux has moved the point of maximum temperature toward the inner cylinder. Taking viscous heating into account, the effects of parameters such as Nahme and Brinkman numbers, material time and pseudoplasticity constant on the stability of the flow are investigated. Moreover, the study shows that the total entropy generation number decreases as the fluid elasticity increases. It, however, increases with increasing Nahme and Brinkman numbers.     

Steady and transient liquid sphere heating in a convective gas stream

 A finite-difference scheme has been developed to solve the equations governing the laminar forced convection heat transfer around and inside a spherical fluid droplet moving steadily in another immiscible fluid for both steady and transient thermal conditions. For large values of the external flow Reynolds number (Re), results not available in the literature have been obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ^*). Detailed results over a wide range of viscosity ratio (μ^*) and for 200≤Re≤1000 are presented for the temperature profiles outside and inside the sphere, Nusselt number, the time required to attain a uniform surface temperature and the time required to reach the steady-state temperature. Results show that convective heating is dependent on the external flow Reynolds number (Re) and the interior-to-exterior viscosity ratio (μ^*) where increasing Re or decreasing μ^* result in increasing heat transfer rate convected to the liquid sphere. Received on 1 March 1999     

Particle image velocimetry and infrared thermography in a levitated droplet with nanosilica suspensions

Preferential accumulation and agglomeration kinetics of nanoparticles suspended in an acoustically levitated water droplet under radiative heating has been studied. Particle image velocimetry performed to map the internal flow field shows a single cell recirculation with increasing strength for decreasing viscosities. Infrared thermography and high speed imaging show details of the heating process for various concentrations of nanosilica droplets. Initial stage of heating is marked by fast vaporization of liquid and sharp temperature rise. Following this stage, aggregation of nanoparticles is seen resulting in various structure formations. At low concentrations, a bowl structure of the droplet is dominant, maintained at a constant temperature. At high concentrations, viscosity of the solution increases, leading to rotation about the levitator axis due to the dominance of centrifugal motion. Such complex fluid motion inside the droplet due to acoustic streaming eventually results in the formation of a ring structure. This horizontal ring eventually reorients itself due to an imbalance of acoustic forces on the ring, exposing larger area for laser absorption and subsequent sharp temperature rise.     

Free convection effects on a vertical cone with variable viscosity and thermal conductivity

The present paper deals with a flow of a viscous incompressible fluid along a heated vertical cone, with due allowance for variations of viscosity and thermal diffusivity with temperature. The fluid viscosity is assumed to be an exponential function of temperature, and the thermal diffusivity is assumed to be a linear function of temperature. The governing equations for laminar free convection of the fluid are transformed into dimensionless partial differential equations, which are solved by a finite difference method with the Crank–Nicolson implicit scheme. Dependences of the flow parameters on the fluid viscosity and thermal conductivity are obtained.     

Carreau fluid flow due to nonlinearly stretching sheet with thermal radiation,heat flux,and variable conductivity

A sophisticated theoretical and mathematical model is proposed. It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux, thermal radiation, and viscous dissipation. Despite the fact that some properties of the fluid do not depend on the temperature, the fluid thermal conductivity is assumed to depend on the temperature. Based on accelerating the fluid elements, some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena. The contribution in this study is that a similar solution is obtained, in spite of the high nonlinearity of the Carreau model,especially, with the heat flux, variable conductivity, and viscous dissipation phenomena.Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number. Likewise, the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter.Finally, the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results.     

Heat transfer in laminar pulsating flows of fluids with temperature dependent viscosities

The effect of time-dependent pressure pulsations on heat transfer in a pipe flow with constant temperature boundaries is analysed numerically when the viscosity of the pulsating fluid is an inverse linear function of the temperature. The coupled differential equations are solved using Crank-Nicholson semi-implicit finite difference formulation with some modifications.The results indicate local variations in heat transfer due to pulsations. They are useful in the design of heat exchangers working under pulsating flow conditions. The analytical results are presented for both heating and cooling. The conditions under which pulsating flows can augment the heat transfer are discussed. The results are applicable for heat exchangers with fluids of high Prandtl number.