Variable Viscosity Fluid Research Articles

FRACTAL FRACTIONAL MODEL OF RADIATIVE HEAT AND MASS TRANSFER CHARACTERISTICS OF TIME DEPENDENT FLOW WITH VARIABLE VISCOSITY, INDUCED MAGNETIC FIELD, DUFOUR AND SORET EFFECTS: AN ENTROPY GENERATION

: In this article, the Caputo Fabrizio fractal fractional order derivatives operator with an exponential kernel was employed to examine the radiative heat and mass transfer characteristics of time dependent flow with variable fluid viscosity, induced magnetic field, Soret and Dufour effects. The local mathematical model for the flow problem is formulated by take into account the impacts of thermal radiation, heat source, and viscous dissipation. The governing equations in-terms of fractal fractional model with an exponential kernel were solved numerically using finite difference method. The influence of flow variables such as induced magnetic field, concentration field, entropy rate, thermal field, and velocity field profiles against the pertinent parameters are discussed through graphs. Increase the values of magnetic Prandtl number results to rises of induced magnetic field. Higher Dufour number significantly grows the thermal field. The fractal fractional parameters enhance the velocity field, thermal field, Bejan number, entropy rate, concentration field and induced magnetic field profiles. The velocity field profiles recede with higher values of fluid variable viscosity parameter whereas the thermal field and induced magnetic field has an opposite effect. Larger Soret number amplifies the concentration field. Increase of Brinkman number, thermal radiation parameter, and magnetic Prandtl number intensifies the entropy generation rate. Increases of Brinkman number, magnetic Prandtl number, Soret number and Dufour number leads to a decrease of Bejan number whereas Bejan number rises with an increase of thermal radiation parameter and heat source

Thin film flow of chemically reactive nonlinear thermally radiative magnetized variable viscosity fluid over a stretchable surface with non-uniform heat source/sink and Fick’s mass flux theory

The study of thin film flow over a stretching sheet holds significant importance from an industrial perspective due to its relevance in various manufacturing and engineering processes. In the present investigation, we delved into the combined influence of non-uniform heat source/sink on the governing heat and mass transfer equations in a thin liquid film on a permeable stretching surface. We have considered the nonlinear thermal radiation and implemented convective-type boundary conditions. Our analysis examined the effects of crucial physical parameters, including non-uniform heat source/sink, thermal radiation, chemical reaction, magnetic parameter , Prandtl number, Schmidt number, and unsteadiness parameter in the range [−3.5, 2.0], [−2, 5], [0, 1], [0.3, 4.0], [1, 7], [0.8, 1.7], [0.7, 2.0], respectively. It is found that a non-uniform heat source/sink mitigated the temperature gradient, while an elevation in the Schmidt number intensified the mass transfer rate. The validation process enhanced the robustness and reliability of our numerical simulations.

Natural convective and Cattaneo–Christov model for couple stress nanofluid at the middle of the squeezed channel with sensor surface

The aim of this work is to present a natural convective and squeezing flow model of two-dimensional couple stress nanofluid which is flowing on the sensory surface with variable fluid viscosity. The fluid flowing on a microcantilever sensory surface and squeezing is happening at free stream. The sensor is also useful to detect the movement of fluid and the variations in thermal and solutal rates. The Cattaneo–Christov model is adopted along with nanoparticle and chemical reaction to explore the transmission of heat and mass rates. The analysis of heat transmission in non-Newtonian couple stress fluid flowing on squeezed sensory surface by using the Cattaneo–Christov heat conduction model has various industrial and scientific applications including the polymer processing, wastewater treatment, chemical reactors, biomedical flows, cooling and heating processes in industries, heat exchangers, microfluidics, oil and gas industries. All the assumptions are applied in the basic governing laws laws and then we get the model of the partial differential equations. The governing model of equations is transmuted into ordinary differential equations form via the transformations and then the numerical results of these ODE’s are examined with a well-defined numerical technique “Shooting Method”. For higher inputs of couple stress, squeezing index and permeability velocity, the fluid’s internal velocity decreases. Because of the Prandtl number and thermal relaxation coefficient, the heat transfer mechanism slows down. Mass transfer increases for greater inputs of the thermal diffusivity coefficient and decreases due to concentration relaxation. Further, the numerical dependency of emerging parameters on the skin friction is illustrated in tabular form. The parametric effects on the model (velocity, temperature and concentration) are introduced using numerical values shown in the table.

Investigating the Role of Stator Slot Indents in Minimizing Flooded Motor Fluid Damping Loss

This research examines how fluid damping loss affects the operation of a two-pole, 5.5 HP (4 kW) induction machine (IM) within the context of different slot opening configurations developed for downhole water pump applications. Since these motors operate with their cavities filled with fluid, the variations in fluid viscosity and density, compared to air, result in the occurrence of damping losses. Furthermore, this loss can be attributed to the motor’s stator and rotor surface geometry, as the liquid within the motor cavity moves unrestrictedly within the motor housing. This study involves the examination of the damping loss in a 24-slot IM under different stator slot indentations. The investigation utilizes computational fluid dynamics (CFD) finite element analysis (FEA) and is subsequently validated through experiments. The aim of this work is to emphasize the significance of fluid damping loss in submerged machines. Results reveal that the damping loss exceeds 8% of the motor output power when the stator surface has indentations, and it diminishes to 3.2% of the output power when a custom wedge structure is employed to eliminate these surface indentations.

Evaluation of erosion of AISI 1045 carbon steel due to non-cohesive microparticles

Erosion behavior of AISI 1045 carbon steel was investigated using slurry solutions with different viscosities (1 cP, 3 cP, and 8 cP) containing 5 wt% silica sand as erodent particles. Tests were carried out using a slurry pot apparatus with various rotational velocities and at three mounting angles (30°, 60°, and 90°). The qualitative and quantitative analysis was performed using the Taguchi design method, paint modeling, image processing, and microscopic imaging techniques. The results indicate that the erosion process in the slurry flow is significantly influenced by fluid viscosity. There is a notable decrease in erosion wear rate as fluid viscosity increases. An analysis of variance (ANOVA) test was conducted, concluding that viscosity and rotational speed are the significant factors influencing the weight loss of carbon steel. The results demonstrate that each factor has a major impact on the response; velocity (47.20 %) is the primary factor contributing to R, followed by viscosity (38.20 %). The erosive wear mechanism changed considerably with the variation in fluid viscosity and impact angles. As viscosity increases, the cutting and pitting erosion wear mechanism shift to sliding wear with the development of micro-perforation sites.

Influence of Marangoni convection, viscous dissipation, and variable fluid viscosity of nanofluid flow on stretching surface analytical analysis

AbstractThe current research paper investigates the viscous dissipation, influence of Marangoni convection (MC), and the variable fluid viscosity of nanofluid flow on stretching surfaces. The flow system takes into account variable viscosity with the impact of MC. Furthermore, velocity and temperature slips at the stretching surface are also considered in this study. To convert a collection of NLPDE to a NODE, we applied appropriate transformations. We utilize Homotopy analysis method (HAM) to solve this set of equations. The effects of temperature, tangential, and radial velocities on numerical perceptions involving Marangoni convection, nanoparticle volume friction, porosity parameter, Eckert number (EN) and heat source input factors are shown. A physical description is used to simulate and evaluate the structures of flow features such as velocity and temperature profiles in response to changes in developing factors. Based on the given result, we can observe that the temperature profile increases as EN and the heat source parameter increase, and that the velocity profile decreases as MC increases and increases with the porosity parameter.

Instability thresholds for penetrative porous convection with variable viscosity fluids

A comprehensive investigation discerning different viscosity-temperature variations on the onset of porous penetrative convection modeled through quadratic density-temperature law is undertaken. The fluid viscosity is assumed to vary linearly, quadratically and exponentially with temperature. The variable viscosity results in a coupling between stream function and temperature in the Darcy momentum balance equation. The linear instability of the basic state is analyzed numerically by examining small-amplitude disturbances in velocity and temperature fields. By carrying out numerical computations for a wide range of parametric regimes, it is established that the principle of exchange of stabilities (PES) is valid. The critical values of the Darcy-Rayleigh number and of the wave number are obtained. The analysis reveals that the combined influence of variable viscosity and the density-maximum characteristic is to expedite the onset of porous convection much faster compared to their isolation presence. The size of the convection cell decreases with an increase in the Darcy-modified Rayleigh number linked to the quadratic density variant. The outcomes obtained under the limiting cases are shown to exhibit consistency with previously published findings.

Natural Convection of Variable Viscosity Fluid in a Partially Porous Cube Having Heat-generating Element Under Local Thermal Non-Equilibrium Model

Natural Convection of Variable Viscosity Fluid in a Partially Porous Cube Having Heat-generating Element Under Local Thermal Non-Equilibrium Model

Further thoughts on buoyancy-induced instability of a variable viscosity fluid saturating a porous slab

The stability of buoyant flow in a vertical porous layer bounded by impermeable-isothermal boundaries is studied insofar as the variability of fluid viscosity with temperature is concerned. The flow is governed by modified Darcy's law with two different forms of viscosity–temperature relationships namely, quadratic and exponential. The modal analysis is carried out with a velocity–temperature formulation of the governing equations for the perturbations. The temperature-dependence of the viscosity forbids the energy analysis of Gill [“A proof that convection in a porous vertical slab is stable,” J. Fluid Mech. 35, 545–547 (1969)] in embarking upon any definite conclusion on the stability of fluid flow even under the limit of an infinite Prandtl–Darcy number, and consequently, the stability eigenvalue problem is solved numerically. Types of temperature-dependent viscosity laws are found to demonstrate conflicting behavior on the stability characteristics of the base flow. The results show that the base flow is linearly stable if the viscosity varies with temperature quadratically. On the contrary, instability emerges for an exponential type of variation in viscosity beyond a certain range of values of the corresponding viscosity parameter depending on the Prandtl–Darcy number. It is established that an increase in the value of the viscosity parameter is to decrease the critical Darcy–Rayleigh number markedly and thereby destabilizes the fluid flow.

Impacts of variable viscosity and chemical reaction on Ohmic dissipative fluid flow in a porous medium over a stretching sheet with thermal radiation

AbstractThis study investigates the chemical reaction influence on heat transfer flow of viscous Newtonian fluid over a moving surface under the intensity of nonuniform heat source/sink. Variable fluid viscosity and ohmic heating effects are considered in the model equation. The uniqueness of the present investigation is to scrutinize the significance of nonuniform heat source/sink and ohmic heating on the heat transfer flow of optically thin radiative fluid in a permeable medium. The flow equations of continuity, momentum, thermal and solutal fields are converted by invoking relevant dimensionless variables. Also, the converted nonlinear equations are analyzed numerically by using the fourth order Runge–Kutta Fehlberg approach. The significance of model parameters are scrutinized and discussed in detail via graphs and tables. The important findings of this study are the effects of Joule heating , viscous dissipation parameter , variable fluid property parameter and radiation parameter on fluid flow, energy profile and solutal field. The results show that the thermal field depreciates as the Prandtl number increases but escalates against higher values of Joule heating parameter and Brinkman number. Also, the outcome of this study reveals that an enhancement in the values of variable viscosity parameter declines velocity distribution. Concentration distributions behave as a growing function of the Soret number and diminishing function of the Schmidt number. Furthermore, contrasting this study with existing results reveals excellent agreement.

Overlapping grid SQLM for third-grade modified nanofluid flow deformed by porous stretchable/shrinkable Riga plate

Abstract The improvement in thermal performance of fluid and the control of energy loss are equitably significant. Therefore, the purpose of this study is to analyze entropy generation, stagnation point flow, and thermal characteristics of non-Newtonian third-grade modified hybrid nanofluid generated by a stretchable/shrinkable Riga plate in a porous medium with varying flow viscosity. In this analysis, a modification of hybrid nanofluid is considered by using pure water as a base fluid and three various nanomaterials (aluminium oxide, copper, and nickel) as nanoparticles in the characterization of heat transfer. Furthermore, the contribution of heat source/sink and viscous dissipation are accounted for in the model. The suited transformations are enforced to remodel the governing mathematical equations to produce ordinary differential equations that are conveniently tackled via spectral quasilinearization method (SQLM) along with the overlapping grid idea to yield numerical solutions. The preference of this approach over others has been justified through discussion of error bound theorems, residual and solution errors, computational time, and conditioning of matrices. The physical significance of disparate governing parameters on flow variables, velocity gradient, thermal rate, and entropy generation are scrutinized through graphs and tables. Crucial findings of the study include that temperature of the modified hybrid nanofluid enhances quickly (better thermal conductor) than temperature of single nanofluid, hybrid nanofluid, and conventional third-grade fluid for higher Biot number, variable viscosity, and heat source parameters. Mass suction enhances fluid flow and physical quantities of interest, but suppresses the fluid temperature. An increase in variable fluid viscosity, modified Hartmann number, and third-grade parameters enhances the wall drag coefficient while lowering the rate of heat transfer, and the opposite is true for porous media. More entropy is generated in the system by high variable fluid viscosity, suction, viscous dissipation, modified Hartman number, and non-Newtonian parameters. Owing to high velocity and temperature associated with modified hybrid nanoparticles, modified hybrid technology is recommended in enhancing the physical attributes of the fluid with minimal cost effects. In engineering and industrial point of view, this study can contribute significantly in thermal improvement of the working fluid.

Temperature-Transient Analysis for Matrix Linear Flow Toward Infinite-Conductivity Hydraulically Fractured Wells

SummaryThis work presents novel analytical temperature-transient solutions for matrix linear flow toward an infinite-conductivity hydraulically fractured well producing under specified constant rate (CR) or constant bottomhole pressure (CBHP) production. The solutions apply to the single-phase flow of a slightly compressible fluid with constant viscosity (e.g., undersaturated oil reservoirs with irreducible water saturation or liquid-dominated geothermal reservoirs). They include the effects of conduction, convection, the Joule-Thomson (J-T) expansion of fluids and adiabatic expansion of the total rock and fluid system, and fluid loss fracture damage and assume constant rock and fluid physical and thermophysical properties with pressure and temperature. They are obtained by using Laplace (for CR) and Boltzmann (for CBHP) transformations. To validate the analytical solutions, an in-house numerical solution is also developed. It solves the mass and thermal energy balance equations coupled simultaneously and accounts for the variation of rock and fluid properties with pressure and temperature. The in-house simulator was validated by using a commercial reservoir simulator. Results indicate that the fracture surface temperature is decreasing with a square root of time for CR production but is constant for CBHP production. The temperature responses for both modes of production are controlled by the adiabatic expansion of the rock and fluid properties and the thermal diffusivity of the rock. The effect of thermal conductivity plays a significant role in both production modes as the matrix permeability decreases. The fracture damage has different signatures on temperature transients depending on the mode of production. The approximate analytical solutions show the information content of temperature-transient data acquired from an infinitely conductive hydraulically fractured well under matrix linear flow. They are simple and can be used to perform matrix linear-flow analysis jointly with pressure and rate transient data to estimate the physical and thermophysical properties of the rock and fluids. We also propose a simple correction to fluid viscosity variation as input for the analytic solutions to accurately estimate the physical and thermophysical parameters in case drawdowns are significant.

Fluid properties of an unsteady MHD free stream flow over a stretching sheet in presence of radiation

AbstractVariable fluid properties with thermal radiation in an unsteady magnetohydrodynamics free stream incompressible flow over a stretching sheet has been considered. The thermal diffusivity and viscosity of the fluid varies linearly with temperature. The governing partial differential equations are moulded to ordinary differential equations using time‐dependent similarity variables and the stream function. RKF technique with shooting method has been implement to find the solution numerically. In the current analysis the impact of unsteadiness, magnetic field, radiative parameter, variable fluid viscosity and thermal diffusivity parameter on heat and flow behavior with the free stream parameter have been studied. Transition point observed in the velocity profiles with an change in unsteadiness parameter and the effect of magnetic field is reduced in the presence of free stram velocity. The velocity and the temperature gradient are computed on the surface and their outcomes with different parameters have been analyzed in the results shown graphically and in tabular form.

A FEM-DFN model for the interaction and propagation of multi-cluster fractures during variable fluid-viscosity injection in layered shale oil reservoir

To investigate the height growth of multi-cluster fractures during variable fluid-viscosity fracturing in a layered shale oil reservoir, a two-dimensional finite element method (FEM)-discrete fracture network (DFN) model coupled with flow, stress and damage is proposed. A traction-separation law is used to describe the mixed-mode response of the damaged adhesive fractures, and the cubic law is used to describe the fluid flow within the fractures. The rock deformation is controlled by the in-situ stress, fracture cohesion and fluid pressure on the hydraulic fracture surface. The coupled finite element equations are solved by the explicit time difference method. The effects of the fracturing treatment parameters including fluid viscosity, pumping rate and cluster spacing on the geometries of multi-fractures are investigated. The results show that variable fluid-viscosity injection can improve the complexity of the fracture network and height of the main fractures simultaneously. The pumping rate of 15 m 3 /min, variable fluid-viscosity of 3-9-21-36-45 mPa s with a cluster spacing of 7.5 m is the ideal treatment strategy. The field application shows that the peak daily production of the application well with the optimized injection procedure of variable fluid-viscosity fracturing is 171 tons (about 2.85 times that of the adjacent well), which is the highest daily production record of a single shale oil well in China, marking a strategic breakthrough of commercial shale oil production in the Jiyang Depression, Shengli Oilfield. The variable fluid-viscosity fracturing technique is proved to be very effective for improving shale oil production.

EMHD Nanofluid Flow with Radiation and Variable Heat Flux Effects along a Slandering Stretching Sheet.

Nanofluids have gained prominence due to their superior thermo-physical properties. The current paper deals with MHD nanofluid flow over a non-linear stretchable surface of varying thickness in the presence of an electric field. We investigated the effects of nanometer-sized copper (Cu) particles in water (base fluid) as a nanofluid, as well as non-linear thermal radiation, variable fluid viscosity, Joule heating, viscous dissipation, and non-uniform heat flux. The current study's aim is influenced by the immense applications in industry and machine building. It has been observed that linear stretching sheets have been extensively used in heat transfer research. Moreover, no effort has been made yet to model a non-linear stretching sheet with variable thickness. Furthermore, the effects of electromagnetohydrodynamics (EMHD) boundary-layer flow of a nanofluid with the cumulative impact of thermal radiation, variable viscosity, viscous dissipation, Joule heating, and variable heat flux have been investigated. Sheets with variable thicknesses are practically significant in real-life applications and are being used in metallurgical engineering, appliance structures and patterns, atomic reactor mechanization and paper production. To investigate the physical features of the problem, we first examined the model and identified all the physical properties of the problem. This problem has been formulated using basic laws and governing equations. The partial differential equations (PDEs) that govern the flow are converted into a system of non-dimensional ordinary differential equations (ODE's), using appropriate transformations. The Adam-Bashforth predictor-corrector technique and Mathematica software are utilized to numerically solve the resulting non-dimensionalized system. The interaction of various developing parameters with the flow is described graphically for temperature and velocity profiles. It is concluded that the velocity of nanoparticles declines as the intensity of the magnetic field increases. However, the temperature of the nanomaterials rises, as increasing the values of the electric field also increases the velocity distribution. The radiation parameter enhances the temperature field. The temperature of the fluid increases the occurrence of space- and time-dependent parameters for heat generation and absorption and radiation parameters.

Scaling of Transient Natural Convection Cooling in Side-Cooled Cavity: The Effect of Variable Viscosity

The transient natural convection of variable and constant viscosity fluids in a side cooled cubical cavity is studied experimentally. The convective flow in the cavity is visualized by the shadowgraph technique. The fluid was initially preheated and enough time is allowed to assure uniform temperature distribution. Temperature difference is introduced by a sudden cooling of the two side walls. The results indicate that the transient flow development is characterized by the following distinct processes: the initial growth of the vertical boundary layer and horizontal intrusions, the interaction of the horizontal intrusions and the stratification. New scaling relations are introduced to include the effect of the viscosity variation with temperature. The new suggested scalings showed good agreement with the measurements based on the shadowgraph images.

Analysis of couple stress nanofluid flow under convective condition in the temperature‐dependent fluid properties and Lorentz forces

AbstractIn recent years, a great deal of interest has been generated in modern micro‐ and nanotechnologies for micro/nano‐electronic devices. These technologies are increasingly utilizing sophisticated fluid media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro‐organisms. Motivated by bio‐nanofluid vertical channel oxygenators in medical engineering, in the current work, a mathematical model is developed to examine the flow of mixed convective couple‐stress nanofluids in a vertical channel with a transverse magnetic field, fluid viscosity that changes with temperature, and thermal conductivity. The non‐Newtonian model follows Brownian motion and heat spread by nanoparticles in a fluid under coupled stress. Highly linked, nonlinear regulating equations are translated into nondimensional equations using relevant variables. The governing equations are then turned into a form with no dimensions. The Keller‐box technique, a second‐order finite difference method for solving second‐order equations, is used to solve them numerically. On the other hand, the effects of different non‐Newtonian flow parameters, such as the couple stress fluid parameter, the magnetic parameter, the variable fluid viscosity, the variable thermal conductivity parameters, the Brinkman number, the nanofluid and buoyancy parameters, and the rate of chemical reaction parameter, are carefully studied. The velocity, temperature, and concentration fields are calculated over a wide range of possible values for the relevant parameters.

Consequences of thermal slip flow of non-Newtonian fluid with temperature-dependent thermal conductivity

The mixed convection thermal flow of Casson nanofluid has been addressed in the presence of variable flow features. The thermal conductivity and viscosity of the fluid are assumed to be variables. Additionally, the heat source and chemical reaction features for a problem are addressed. The porous-saturated space with the implementation of magnetic force endorsed the flow. The investigation is focused on using the slip boundary conditions. After implementing the dimensionless quantities, the expressions for the problem are achieved. A fifth-order Runge–Kutta (RK-5) numerical scheme is employed to simulate the solution. The physical dynamic of the problem against the parameters is addressed. The results are verified with already available reports to ensure the solution’s accuracy. It is claimed the consideration of variable thermal conductivity and fluid viscosity enhanced the thermal transportation phenomenon more effectively.

How far below the critical Rayleigh number can convection occur in temperature-dependent viscosity fluids?

We use 2D numerical simulations to study the onset of convection below the critical Rayleigh number in a basally-heated fluid with temperature-dependent viscosity. The existence of convection below the critical Rayleigh number has previously been demonstrated in variable-viscosity fluids. Under these, subcritical conditions, convection can be initiated by finite-amplitude perturbations and can assume a number of different steady-state planforms. We find the absolute minimum critical Rayleigh number and aspect ratio for the onset of subcritical convection in a broad range of viscosity contrasts. For various planetary bodies, the threshold for the onset of convection by finite-amplitude perturbations is about 40% below the critical Rayleigh number. The lowest viscosity contrast at which subcritical convection can occur is 1.3 × 102. The existence of subcritical regime extends the range of conditions under which convection can occur in planetary interiors and expands the assortment of possible convective planforms that can explain various surface features on planetary bodies.

Development of a Self-Viscosity and Temperature-Compensated Technique for Highly Stable and Highly Sensitive Bead-Based Diffusometry.

Brownian motion, which is a natural phenomenon, has attracted numerous researchers and received extensive studies over the past decades. The effort contributes to the discovery of optical diffusometry, which is commonly used for micro/nano particle sizing. However, the analysis uncertainty caused by the coupling relationship among particle diameter, temperature, and fluid viscosity usually poses a barrier to precise measurement. Preventing random background noise becomes the key to achieving a high level of accuracy in diffusometry detection. Recently, Janus particles have become known as an ideal tool for resolving the rotational Brownian motion. Followed by our previous study, the rotational Brownian motion and the translational Brownian motion can be separately measured using the Janus particles. Accordingly, a simple self-viscosity and temperature-compensated technique based on the delicate removal of temperature and fluid viscosity variations through particle tracking was first proposed in this study. Consequently, the translational Brownian motion was expressed in terms of particle trajectory, whereas the rotational Brownian motion was expressed in terms of the blinking signal from the Janus particles. The algorithm was verified simulatively and experimentally in temperature (10 °C to 40 °C) and viscosity-controlled (1 mPa·s to 5 mPa·s) fields. In an evaluation of biosensing for a target protein, IFN-γ, the limit of detection of the proposed self-compensated diffusometry reached 0.45 pg/mL, whereas its uncertainties of viscosity and temperature were 96 and 15-fold lower than the pure the rotational Brownian motion counterpart, respectively. The results indicated the low-uncertainty and high-accuracy biosensing capability resulting from the self-viscosity and temperature-compensated technique. This research will provide a potential alternative to future similar bead-based immunosensing, which requires ultra-high stability and sensitivity.