Variable Viscosity Parameter Research Articles

Influence of variable viscosity and local thermal non-equilibrium on nanofluid flow stability in an inclined porous channel

This study delves into the influence of local thermal non-equilibrium and changing viscosity on the stability of nanofluid flow in an inclined porous channel. The flow in the porous region governs Brinkman’s equation as well as a three-field model for temperature, with each field constitute the fluid, particle, and solid-matrix phases individually. Eigenvalue problem for a perturbed state is obtained using a normal mode analysis, and the problem is afterwards solved by the utilization of the Chebyshev spectral collocation method. Impact of various local thermal non-equilibrium parameters, critical Rayleigh number, and associated wavenumber are graphically displayed. Increasing values of the modified thermal capacity ratios, modified thermal diffusivity ratios, variable viscosity parameter, and channel inclination decrease the system’s stability for the interphase heat transfer parameter, which means these parameters destabilize the flow. Flow is most unstable when the channel is vertically oriented and the variable viscosity parameter ([Formula: see text]) = 0.5.

Influence of the Reynolds viscosity model and induced magnetic field on a thin Casson fluid film flow between two rotating disks with cross-diffusion effects

In models of fluid dynamics, the magnetic field is essential for preserving the stability of flow streams and found applications in magnetic resonance imaging, magnetic levitation, and geophysical exploration. Recognizing the significance of this magnetic influence, we aim to investigate the behavior of flow within a three-dimensional squeezed film of Casson fluid situated between two rotating disks, under the influence of an induced magnetic field and the Reynolds viscosity model. The study also meticulously examines the heat and mass transfers, taking into account the effects of thermo-diffusion and diffusion-thermo. The resulting torque on both the upper and lower surfaces is analyzed and presented in a tabulated format. The normalized system of equations is transformed into a set of first-order differential equations, which are then solved using the bvp4c numerical solver in MATLAB. The impacts of various parameters are graphically illustrated in two different scenarios ( ϒ = 0.0 , 0.5 ) , i.e., constant and variable viscosity. It is observed that when the variable viscosity parameter is set to zero, the azimuthal velocity profile experiences a more pronounced increase as the rotational parameter rises. Conversely, the azimuthal magnetic profile exhibits a more significant decrease when considering the influence of the variable viscosity parameter. Finally, the results are compared with previous studies in the literature for a limiting case, and error is reduced between 0.000003% and 0.000002%.

Pulsatile flow of Casson hybrid nanofluid between ternary-hybrid nanofluid and nanofluid in an inclined channel with temperature-dependent viscosity

This study presents a mathematical model for layered non-miscible liquid flow in an inclined channel subject to a pulsatile pressure gradient. The Casson hybrid nanofluid (hnf) is sandwiched between the layers of Newtonian ternary hybrid nanofluid (t-hnf) and nanofluid (nf). Additionally, the impact of temperature-dependent viscosity is taken into consideration. Multiwall carbon nanotubes, molybdenum disulfide, and silver are considered nanoparticles, with water and kerosene oil as base fluids. The governing partial differential equations are transformed into coupled non-linear ordinary differential equations (ODEs) using the perturbation technique. The resulting ODEs are solved numerically using MATHEMATICA software with the help of the shooting technique associated with the Runge-Kutta fourth-order scheme. The behaviors of numerous sundry parameters against velocity, temperature, concentration, and shear stress are depicted graphically and in tabular form. The outcomes of the study reveal that if the viscosity is held constant, then the fluid’s velocity is initially low and gradually increases as the viscosity variation parameter rises. The velocity of fluid flow is higher when a Newtonian fluid occupies the middle region of the channel than when Casson fluid does. The increase in the nanoparticle shape factor, at both boundaries, results in an increase in the rate of heat transfer.

MHD Natural Convection and Sensitivity Analysis of Ethylene Glycol Cu-Al2O3 Hybrid Nanofluids in a Chamber with Multiple Heaters: A Numerical Study of Lattice Boltzmann Method

The present work investigates the magnetohydrodynamic (MHD) convective heat transport of hybrid nanofluids in a chamber with multiple heaters (such as hot microchips). The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) and graphics processing unit (GPU) computing are used here. The present study is important due to its relevance to real-world applications, the use of advanced simulation techniques, the consideration of hybrid nanofluids, the inclusion of magnetohydrodynamics, and the identification of critical parameters influencing heat transfer. Thermally homogeneous blocks are set at the bottom of a rectangular enclosure filled with ethylene glycol Cu-Al2O3 hybrid nanofluids with temperature-dependent viscosity. The cold temperature of the enclosure’s left and right walls and the bottom and top surfaces is kept at adiabatic conditions. The numerical outcomes for the various parameters Rayleigh number (104≤Ra≤106), volume fraction (0.00≤ϕ≤0.04), Hartmann number (0≤Ha≤60), and viscosity variation parameter (0≤ε∗≤5) are presented in terms of streamlines, isotherms, and the peripheral local and average Nusselt numbers for the heated chips. The results demonstrated that inside the chamber, the Rayleigh number (Ra), the Hartmann number (Ha), and the volume fraction of nanoparticles (ϕ) have the highest impact on the heat transfer rate for hybrid nanofluid. For increased Ha from 0 to 20, while ϕ=0.0 and Ra=106, average Nusselt number decreased with 13.65%. For the same case, if the volume fraction was increased to ϕ=0.04, then the average Nusselt number decreased 14%. Finally, a sensitivity analysis was done to analyze the system’s correctness and effectiveness to determine the significance of the specified parameters.

Stefan flow of nanoliquid passing a plate surface with changeable fluid properties

This article describes the significance of ‘Stefan suction/blowing’ on the forced flow of nanoliquid past the surface of a ‘plate’ with temperature-obeying ‘thermal conductivity’ and ‘fluid viscosity’ with ‘zero nanoparticle flux’ at the ‘plate’ that has not till been attended by anyone and thus it points to the originality of present investigation and here lies the novelty of our work. Nanofluid flow is modeled with the help of ‘Buongiorno's two-phase model’ which contains the instantaneous virtue of thermophoresis diffusion and Brownian movement. This investigation shows that the speed of heat transport is remarkably augmented by the variable ‘thermal conductivity’ and variable ‘viscosity parameters’ which is the main contribution of this research. Due to changeable viscosity, reducing nature of velocity as well as the reducing nature of concentration of the nanoparticles near the ‘plate’ are observed. Due to Stefan's blowing parameter, fluid velocity augments but ‘temperature’ is observed to reduce for mounting values of Stefan's blowing parameter. 3.2 % reduction in skin-friction coefficient is noted when variable viscosity parameter reduces from -6 to -8. Moreover, 7.1 % reduction in heat transfer as well as mass transfer is noted when the variable thermal conductivity parameter rises from 0.2 to 0.4. The consequence of this inspection exposes a variation of exciting diversity which claims extra exploration of the present study.

Bioconvective flow of Maxwell nanoparticles with variable thermal conductivity and convective boundary conditions

Owing to recent development in the thermal sciences, scientists are focusing towards the wide applications of nanofluids in industrial systems, engineering processes, medical sciences, enhancing the transport sources, energy production etc. In various available studies on nanomaterials, the thermal significance of nanoparticles has been presented in view of constant thermal conductivity and fluid viscosity. However, exponents verify that in many industrial and engineering process, the fluid viscosity and thermal conductivity cannot be treated as a constant. The motivation of current research is to investigates the improved thermal aspects of magnetized Maxwell nanofluid attaining the variable viscosity and thermal conductivity. The nanofluid referred to the suspension of microorganisms to ensure the stability. The insight of heat transfer is predicted under the assumptions of radiated phenomenon. Additionally, the variable thermal conductivity assumptions are encountered to examine the transport phenomenon. Whole investigation is supported with key contribution of convective-Nield boundary conditions. In order to evaluating the numerical computations of problem, a famous shooting technique is utilized. After ensuring the validity of solution, physical assessment of problem is focused. It is claimed that velocity profile boosted due to variable viscosity parameter. A reduction in temperature profile is noted due to thermal relaxation constant.

Effects of rotation and temperature‐dependent viscosity on thermal convection in Oldroydian fluid saturating porous media: A modified stability analysis

AbstractThe onset of thermal convection in an incompressible Oldroydian fluid‐saturating porous media is examined to study the combined impact of uniform rotation and temperature‐dependent viscosity. A characteristic equation from the basic hydrodynamic equations governing the Brinkman–Oldroyd model is derived using linear stability theory and modified Boussinesq approximation. For various combinations of stress‐free and slip‐free boundaries, the expressions for the Darcy–Rayleigh numbers for both non‐oscillatory as well as oscillatory convection with linear and exponential temperature‐dependent viscosity are derived, using the “weighted residual method.” The effects of rotation, variable viscosity parameter, strain retardation and stress relaxation time parameters and other fluid parameters on non‐oscillatory and oscillatory convection are investigated numerically and the results are presented graphically. From the analysis, it is found that overstability is the preferred mode of onset of convection. The rotation, the coefficient of specific heat variations (due to temperature variation), and the strain retardation time have a stabilizing influence on the stability of the system, whereas the stress relaxation imparts a destabilizing effect. Additionally, it is noticed that the variable viscosity parameter and Brinkman‐Darcy number stabilize the system for each set of boundary conditions.

HARK formulation for entropy optimized convective flow beyond constant thermophysical properties

Background and objectiveOhmic heating has a pivotal role in food processing industry. For example, Ohmic heating in chocolate industry for cocoa beans shell is significant substrate for bioactive compounds recovery sustainability. In addition, the Soret and Dufour effects have importance in chemical and petroleum processes involving separation treatments, convective movements in lakes and solar ponds, solidification, humidity migration in building, drying processes, crystal growth and many others. In view of such applications here we discuss the hydromagnetic mixed convection flow with variable thermophysical properties. Formulation for Reiner-Rivlin material is made. Entropy generation in presence of dissipation, magnetohydrodynamics and radiation are discussed. Thermal relation consists of heat generation and dissipation. Soret and Dufour outcomes are under consideration. Ohmic heating is attended. Binary chemical reactive flow has been accounted. Convective conditions are implemented. MethodologyBy utilization of appropriate variables, we get the ordinary differential equations. ND-solve method is implemented to provide computations. ResultsEvaluation of different variables for flow, concentration, entropy rate and temperature are studied. Analysis of surface drag force and solutal and thermal transport rates via influential variables are examined. An augmentation in velocity is noted for variable viscosity and material parameters. Reverse effect holds for thermal field and flow with variation in magnetic variable. An intensification in thermal distribution and entropy is found through radiation and thermal Biot number. A reverse impact is observed for concentration through Schmidt and Soret numbers. Higher variable mass diffusivity parameter correspond to improves concentration and entropy rate. Brinkman number has increasing trend for entropy rate.

Unsteady magneto porous convective transport by micropolar binary fluid due to inclined plate: An inclusive analogy

In this investigation, the consequence of viscous dissipation on the unstable magneto porous convective transport by a micropolar binary fluid due to an inclined surface with viscous dissipation and thermal radiation is examined. Viscous dissipation plays a noteworthy role in industrial applications. The governing PDEs are converted to combined ODEs with the Boussinesq approximation using a similarity analysis. The obtained non-linear ODEs are resolved using the shooting method with “ODE45 MATLAB” coding assistance. The numerical outcomes are revealed graphically for various dimensionless parameters and numbers, including temperature, concentration, velocity, and micro-rotation. The temperature, micro-rotation, and velocity fields escalate with increasing Eckert numbers. The radiation parameter and variable viscosity parameter increase the flow rate of the fluid. Increasing radiation parameters, suction parameters, and Prandtl numbers lessen the fluid temperature. The buoyancy parameters have symmetrical impacts on the velocity and microrotation of fluid particles in the cooling and heating modes. Improving Eckert number, inclined angle, Schmidt number, Prandtl number, and magnetic parameter reduces skin friction. The heat transmission rate escalates in quantity due to larger Prandtl number values. Rising Prandtl, Eckert, and Schmidt numbers accelerate the mass transfer rate. The current research result is compared to previously published article's result with good agreement.

Magnetohydrodynamics and viscosity variation in couple stress squeeze film lubrication between rough flat and curved circular plates

A simplified mathematical model has been developed for understanding combined effects of surface roughness, viscosity variation and couple stresses on the squeeze film behaviour of a flat and a curved circular plate in the presence of transverse magnetic field. The Stokes (1966) couple stress fluid model is included to account for the couple stresses arising due to the presence of microstructure additives in the lubricant. In the context of Christensen’s (1969) stochastic theory for the lubrication of rough surfaces, two types of one-dimensional roughness patterns (radial and azimuthal) are considered. The governing modified stochastic Reynolds type equations are derived for these roughness patterns. Expressions for the mean squeeze film characteristics are obtained. Numerical computations of the results show that the azimuthal roughness pattern on the curved circular and flat plate results in more pressure buildup whereas performance of the squeeze film suffers due to the radial roughness pattern. Further the Lorentz force characterized by the Hartmann number, couple stress parameter and viscosity variation parameter improve the performance of the squeeze film lubrication as compared to the classical case (Non-magnetic, Newtonian case and non-viscous case).

Computation of non-Newtonian quadratic convection in electro-magneto-hydrodynamic (EMHD) duct flow with temperature-dependent viscosity

Motivated by novel developments in smart non-Newtonian thermal duct systems, a theoretical study has been presented in this article for electro-magneto-hydrodynamic (EMHD) buoyancy-driven flow of a fourth-grade viscoelastic fluid in a vertical duct with quadratic convection. The viscosity of the fourth-grade fluid model is assumed to be temperature-dependent, and the Reynolds exponential model is deployed. Viscous heating and Joule dissipation effects are included. The duct comprises a pair of parallel electrically insulated vertical flat plates located a finite distance apart. Via suitable scaling transformations, a nonlinear boundary value problem is derived for the momentum and heat transport. A homotopy perturbation method (HPM) solution is obtained coded in Mathematica symbolic software. There is a considerable enhancement in wall skin friction with an increment in fourth-grade fluid parameter, Brinkman number, electrical field parameter, thermal buoyancy parameter, and quadratic thermal convection parameter. However, skin friction is strongly reduced with a rise in variable viscosity parameter, Hartmann (magnetic) number, and electromagnetic heat generation to conduction ratio. Nusselt number magnitudes are elevated with increase in variable viscosity parameter, thermal buoyancy parameter, and quadratic thermal convection parameter, whereas they are significantly suppressed with increment in fourth-grade fluid parameter, Brinkman number, and Hartmann magnetic number.

Influence of exponential heat source, variable viscosity and shape factor on a hybrid nanofluid flow over a flat plate when thermal radiation and chemical reaction are significant

The significance of hybrid nanofluid flow over a flat plate lies in its ability to enhance heat transfer, improve energy efficiency, enable temperature control, and provide surface protection. For instance, hybrid nanofluids can provide a protective coating on the surface of a flat plate due to the presence of nanoparticles. This coating can offer improved corrosion resistance, erosion resistance, and anti-fouling properties. Consequently, it can extend the lifespan of the flat plate and reduce maintenance requirements. In this study, we examined how several characteristics, such as variable viscosity, chemical reaction, thermal radiation and shape factor of nanoparticles, affect the flow of a hybrid nanofluid (H[Formula: see text]) through a flat plate. The equations required to represent the problem have been turned into a system of nonlinear ordinary differential equations, and this system has been unraveled by means of the bvp4c solver. Outcomes are provided for three instances related to shape factor i.e. Platelet, Cylinder and Spherical. Using Multiple Linear Regression (MLR), we investigated how physical parameters of concern together with friction factor, are affected by a variety of parameters. It is remarked that the fluid’s velocity lessens as the variable viscosity parameter enhances. It is discovered that the temperature profile increases with the rise in exponential heat source parameter ([Formula: see text]). It is discovered that when [Formula: see text], the Nusselt number declines by 0.03588 (Platelet shape), 0.03562 (Cylinder shape), and 0.03489 (Spherical shape). It has been noted that magnetic field parameter (Mg) reduces the coefficient of skin friction. At [Formula: see text], the skin friction coefficient is seen to drop at a rate of 1.15018 (Platelet shape), 1.14871 (Cylinder shape), and 1.14476 (Spherical shape). There is an enhancement in the Sherwood number with the rise in Schmidt number (St) and chemical reaction parameter (Cr). At [Formula: see text] the Sherwood number is seen to rise at a rate of 0.248303 (Platelet shape), 0.248344 (Cylinder shape), and 0.248447 (Spherical shape). Furthermore, it is detected that the fluid’s temperature rises as the thermal radiation parameter enhances and the entropy generation increases as the variable viscosity parameter increases.

Entropy generation analysis of non-miscible couple stress and Newtonian fluid in an inclined porous channel with variable flow properties: HAM Analysis

The aim of this study is to investigate the entropy production characteristics of two non-miscible fluids in an inclined porous channel with temperature-dependent thermal conductivity and viscosity. The porous region of the channel is divided in two regions. In region-1 and region-2, the Couple stress and Newtonian fluid take place due to constant pressure gradient, respectively, under the influence of a uniform magnetic field. Here, the Darcy–Brinkman model is used for the flow of immiscible fluid through the porous media. In this work, we used a semi-analytical method named as homotopy analysis method (HAM) to solve the coupled nonlinear ordinary differential equations. The goal of the considered problem is to examine the consequences of a variety of thermophysical parameters, including Hartmann number, varying viscosity parameter, varying thermal conductivity parameters, and Grashof number on the characteristics of entropy generation, Bejan number distribution, thermal behavior and flow characteristics of non-miscible couple stress and Newtonian fluid passing through a porous channel. The novel aspect of this study is the formation of entropy and Bejan number as a result of non-miscible Newtonian and couple stress fluids with varying thermal conductivity and viscosity in porous media. In terms of rheological investigation, a semi-analytical simulation for changeable thermal and flow properties in an immiscible Newtonian and couple stress fluid via an inclined porous channel is a brand-new concept, and the behaviors of such flows have not been examined yet. From this study, it is concluded that on raising the variable thermal conductivity, Hartmann number and the permeability of the porous medium, the flow velocity, thermal characteristics and entropy generation number decrease. The authors also come to the significant conclusion that non-miscible Newtonian and couple stress fluids have larger entropy production numbers, flow velocities, and temperature profiles for higher values of Grashof number, variable viscosity parameter, and couple stress parameter. The findings of this work have also been graphically validated through the previously established work. The results of the present analysis can be used in petroleum industry, lubrication theory, etc.

Analysis of activation energy and microbial activity on couple stress nanofluid with heat generation

This investigation includes the performance of the Couple Stress Nanofluid with microbial activity, activation energy incorporation of thermal conductivity, heat generation, variable viscosity and other parameters. We used some suitable similarity transformations to convert the governing partial differential equations and the initial boundary conditions of our model into the coupled structure of ordinary differential equations and final boundary conditions. Furthermore, the Spectral Quasi Linearization Method (SQLM) was used to numerically solve these ordinary differential equations with boundary conditions, generating the reassuring impacts of various parameters taken in our model. The graphical representation for the flow, temperature, solute and microbial distribution was analyzed with activation energy, heat generation and other interesting parameters. The impact of variable viscosity and thermal conductivity with the Prandtl number for the local skin friction, Nusselt, Sherwood, and the microbial density numbers was included and reflects the favorable results. The comparison table is also included to validate our model. The rising values of the activation energy parameter enhances the solute and microbe profiles, while rising of bio-convection Rayleigh number and Reynolds numbers discriminates the heat profiles, but enhances the solute profile. The microbial profile of the model falls for the rising values of the microbe reaction parameter.

Mixed Convection of Cu–H2O Nanofluid in a Darcy–Forchheimer Porous Medium Microchannel with Thermal Radiation and Convective Heating

Heat transfer and convective flow of Cu–H2O nanofluid in a microchannel with thermal radiation has many attributes in engineering, industries, and biomedical sciences including cooling of electronics, drug delivery, cancer therapy, optics, missiles, satellites, and lubricants. Therefore, this paper aims to investigate the hydrodynamical behaviors and heat transfer characteristics of Cu–H2O nanofluid through a porous medium microchannel with thermal radiation and convective heating. The highly non-linear partial differential equations that govern the momentum and energy equations are formulated, non-dimensionalized, transformed into ordinary differential equations and solved numerically via the fourth order Runge-Kutta integration scheme. Consequently, the numerical simulation reveals that the nanofluid velocity and temperature profiles show a rising pattern with increasing values of the pressure gradient parameter, variable viscosity parameter, Darcy number, thermal Grashof number and Eckert number. The temperature profile escalates with the Prandtl number however it diminishes with the Biot number, Forchheimer number, suction/injection Reynolds number and nanoparticles volume fraction. Furthermore, the thermal radiation parameter indicates a retarding effect on the temperature profile and hence, radiation quite effectively controls the microchannel temperature distribution which plays a significant role in cooling the flow transport system. The skin friction coefficient at both microchannel walls indicates a rising pattern with the suction/injection Reynolds number, thermal Grashof number, Eckert number and Darcy number. Moreover, at both microchannel walls the heat transfer rate enhances for large values of the suction/injection Reynolds number, thermal Grashof number, Eckert number, variable viscosity parameter and Darcy number whereas it decreases with the thermal radiation parameter, Forchheimer number and nanoparticles volume fraction. The Biot number reveals an opposite effect on the heat transfer rate at the left and right walls of the microvhannel.

Numerical investigation of heat and mass transfer of the Sisko fluid in a wire-coating process with variable fluid properties

The fundamental and essential objective of the wire coating process is to reduce the shear stress and extraction force exerted on the wire from the die in order to achieve practical benefits. Therefore, the purpose of the present work is to develop a mathematical model for the wire coating process withdrawal of the wire from the die. The Sisko fluid model and the temperature-dependent thermophysical properties are taken into consideration for modelling the constitutive equation. The basic equations governing the flow are solved with the aid of the numerical method. The impact of key factors is scrutinized. The influence of shear stress on the surface of the wire and fluid flow rate are delineated. The linear regression model is formulated to explore the significance of the relationship between the amount of force required to pull the wire and flow control variables. Moreover, the heat transfer rate and shear stress rate of molten polymer are modeled using quadratic correlation models obtained through the Central Composite Design (CCD) technique. To simultaneously achieve maximum heat transfer rate and minimum shear stress rate for the melt, the ideal values of the variable viscosity parameter, Sisko fluid parameter, and Brinkman number are determined. The study reveals that the required result occurs for a low level of the variable viscosity parameter, Sisko fluid parameter, and the Brinkman number. Additionally, a sensitivity analysis has been performed. The result reveals that the shear stress rate and heat transfer rate exhibit the highest sensitivity to variations in the viscosity parameter.

Cattaneo-Christov heat-mass flux model on mixed convection of Casson nanofluid in a porous medium microchannel with thermal radiation and chemical reaction

This article presents mixed convection of radiating and reacting Casson nanofluid in microchannel filed with a saturated porous medium with Cattaneo-Christov heat-mass flux model. The Buongiorno’s nanofluid flow model is used to study the effects of the Brownian motion and the thermophoresis whereas the Darcy-Forchheimer model is considered to examine the nanofluid and porous medium interaction. Thereafter, the highly nonlinear system of equations for momentum, energy and concentration are formulated and solved numerically by utilizing the Runge-Kutta-Fehlberg integration scheme with shooting technique. Consequently, the numerical simulation indicates that the Casson fluid parameter and the variable viscosity parameter play a great role in escalating the velocity field and temperature profile however chemical reaction, porous medium, radiation, thermal relaxation time and convective heating control over the temperature profile. Besides, an increase in the thermal relaxation time causes more transfer of heat from the hot microchannel wall to the fluid and thus, fluid temperature distribution is higher for Hence, the Cattaneo-Christov heat flux model is constructive in cooling process as compared to that of the classical Fourier’s law of heat conduction. Furthermore, heat and mass transfer rates are enhancing because of the thermal radiation and solutal Grashof number at both sides of the microchannel walls. Also, the current findings are compared with that of the existing literature and a sound agreement was established.

Numerical investigation of heat and mass transfer of variable viscosity Casson nanofluid flow through a microchannel filled with a porous medium

Thermal behaviours and hydrodynamics of non-Newtonian nanofluids flow through permeable microchannels have large scale utilizations in industries, engineering and bio-medicals. Therefore, this paper presents the numerical investigation of heat and mass transfer of variable viscosity Casson nanofluid flow through a porous medium microchannel with the Cattaneo-Christov heat flux theory. The highly nonlinear PDEs corresponding to the continuity, momentum, energy and concentration equations are formulated and solved numerically via the second order implicit finite difference scheme known as the Keller-Box method. Accordingly, the numerical simulations reveal that variable viscosity parameter, thermal Grashof number, solutal Grashof number, thermophoresis parameter, Schmidt number and Casson fluid parameter show increasing effects on both velocity and temperature of the nanofluid. Furthermore, the temperature profile escalates with increasing values of the Eckert number and the thermal relaxation time parameter. Thus, the Cattaneo-Christov heat flux model is beneficial in warming the transport system of microfluidics when compared to that of the classical Fourier heat conduction law. The temperature profile however, indicates a retarding behavior with increasing values of the Brownian motion parameter, Prandtl number and porous medium parameters namely Forchheimer number and porous medium shape parameter and hence, the porous medium quite effectively controls the nanofluid temperature distribution which plays substantial roles in cooling the transport system of microfluidics. Moreover, the concentration profile shows an increasing pattern with escalating values of the Prandtl number, Schmidt number and thermophoresis parameter but it demonstrates a decreasing trend with the Casson fluid, variable viscosity, thermal relaxation time and solutal relaxation time parameters. It is also observed that coefficient of the skin friction increases with increasing values of the pressure gradient parameter, Eckert number, Forchheimer number and injection/suction Reynolds number. Besides, the heat transfer rate at both walls of the microchannel enhances with rising values of the Eckert number, variable viscosity, parameter and injection/suction Reynolds number. The Casson fluid and thermal relaxation time parameters reveal opposite scenarios on the heat transfer rate at the left and right walls of the microchannel. In addition, the mass transfer rate at both walls of the microchannel shows an increasing pattern as the Eckert number, variable viscosity parameter, Schmidt number and suction/injection Reynolds number increase.

Slip effects on 3-D spinning dual-phase nanofluid flow over an exponentially stretching sheet with variable viscosity

This article's major goal is to describe the slip boundary condition and movement of a rotating, three-dimensional, steady flow of nanoparticles across a flexible surface. The dual-phase concept of nanofluid is utilized in physically existing models. The partial differential governing equations are split into ordinary differential equations by utilizing similarity transformations. The built-in solver bvp4c in MATLAB is used to evaluate the statistical solution. This study shows that velocity and temperature profiles depend on basic variables such as slip parameter, variable viscosity, stretching ratio, and rotation parameter. Tables display the numeric value of several parameters related to the Nusselt number and skin friction indices. Copper oxide and silver nanoparticles in a water base fluid are utilized for examination. According to the graphical representation, the variable viscosity parameter's velocity profile is growing while the slip parameter's decreasing and the temperature profile inclining for the slip parameter while declining for variable viscosity.

The stability of the nanofluid flow in an inclined porous channel with variable viscosity

The effect of variable viscosity on the stability of nanofluid flow in an inclined porous channel is investigated. The nanofluid model considers the consideration of thermophoresis and Brownian motion. In addition, the Brinkman model has been employed in the momentum equation. The eigenvalue problem for the perturbed state is obtained using normal mode analysis, and the spectral method is used to solve it. The influence of numerous parameters on the critical Rayleigh number and associated wavenumber are graphically displayed. It is noticed that the increasing impact of the Darcy number, Prandtl number, and porosity parameter increases the system’s stability, whereas the variable viscosity parameter and the channel’s inclination destabilize the flow. Also, the dynamics of the flow field, behavior of temperature, and volume fraction are presented through streamlines, isotherms, and isonanoconcentration at the critical level.