Power-law Nanofluid Research Articles

Coupled flow and heat transfer of power-law nanofluids on non-isothermal rough rotary disk subjected to magnetic field

We study the coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subjected to a magnetic field. The problem is formulated in terms of specified curvilinear orthogonal coordinate system. An improved BVP4C algorithm is proposed, and numerical solutions are obtained. The influence of volume fraction, types and shapes of nanoparticles, magnetic field and power-law index on the flow, and heat transfer behavior are discussed. The obtained results show that the power-law exponents (PLE), nanoparticle volume fraction (NVF), and magnetic field inclination angle (MFIA) have almost no effects on velocities in the wave surface direction, but have small or significant effects on the azimuth direction. The NVF has remarkable influences on local Nusselt number (LNN) and friction coefficients (FC) in the radial direction and the azimuth direction (AD). The LNN increases with NVF increasing while FC in AD decreases. The types of nanoparticles, magnetic field strength, and inclination have small effects on LNN, but they have remarkable influences on the friction coefficients with positively correlated heat transfer rate, while the inclination is negatively correlated with heat transfer rate. The size of the nanoparticle shape factor is positively correlated with LNN.

Thermal management for conjugate heat transfer of curved solid conductive panel coupled with different cooling systems using non-Newtonian power law nanofluid applicable to photovoltaic panel systems

Thermal performance features for a coupled conjugate thermo-fluid system with different cooling configurations (flat channel (F-C), grooved channel (G-C) and impinging jets (I-J)) are explored numerically by using non-Newtonian nanofluid. The numerical work is performed for different Reynolds numbers (100≤Re≤300), index of power law (0.8≤n≤1.2), height (0.1H≤b≤0.6H) and number (2≤N≤9) of corrugation in the G-C system, number (2≤Nj≤9) and distance (5w≤sx≤25w) between jets in the I-J flow system. Different volume fractions (0≤ϕ≤0.04) and particle sizes (20nm≤dp≤80nm) of nanoparticles are used. When systems operating at the highest and lowest Re are compared, 9 K, 11 K and 8 K temperature reduction are achieved for F-C, G-C and I-J cooling systems. However, I-J flow system at higher Re is very effective on the thermal performance improvement when shear thickening fluid is used. For the G-C flow system, increasing the height and number of the corrugation waves resulted in improvement in the thermal performance. Up to 46% increment in the Nu number (average) and reduction of 6.5 K in the average surface temperature are achieved with varying the height of the corrugation while these values are 17% and 1.6 K when wave number is increased. The average Nu number rises by about 32% and temperature drops by about 6.5 K when jet number is varied from 3 to 11, while these values are obtained as 8% and 4 K for when distance between jets are varied from sx=5w to sx=25w. For F-C, G-C and I-J flow systems, average Nu rises by about 15.5% and 14.5% and 16.3% for shear thinning fluid while they become 16.6%, 9.94% and 12.8% for shear thickening fluid at the highest solid volume fraction. As the nanoparticle size is increasing, there is 6% and 7% reduction in the average Nu number. Thermal performance estimations are made with four inputs and four outputs system by using artificial neural networks.

Forced Convection of Non-Newtonian Nanofluid Flow over a Backward Facing Step with Simultaneous Effects of Using Double Rotating Cylinders and Inclined Magnetic Field

The forced convection of non-Newtonian nanofluid for a backward-facing flow system was analyzed under the combined use of magnetic field and double rotating cylinders by using finite element method. The power law nanofluid type was used with different solid volume fractions of alumina at 20 nm in diameter. The effects of the Re number (100≤Re≤300), rotational Re number (−2500≤Rew≤3000), Ha number (0≤Ha≤50), and magnetic field inclination (0≤γ≤90) on the convective heat transfer and flow features were numerically assessed. The non-Newtonian fluid power law index was taken between 0.8 and 1.2 while particle volume fractions up to 4% were considered. The presence of the rotating double cylinders made the flow field complicated where multiple recirculation regions were established near the step region. The impacts of the first (closer to the step) and second cylinders on the heat transfer behavior were different depending upon the direction of rotation. As the first cylinder rotated in the clockwise direction, the enhancement in the average heat transfer of 20% was achieved while it deteriorated by approximately 2% for counter-clockwise directional rotation. However, for the second cylinder, both the rotational direction resulted in heat transfer augmentation while the amounts were 14% and 18% at the highest speeds. Large vortices on the upper and lower channel walls behind the step were suppressed with magnetic field effects. The average Nu number generally increased with the higher strengths of the magnetic field and inclination. Up to 30% increment with strength was obtained while this amount was 44% with vertical orientation. Significant impacts of power law fluid index on the local and average Nu number were seen for an index of n = 1.2 as compared to the fluid with n = 0.8 and n = 1 while an average Nu number of 2.75 times was obtained for the flow system for fluid with n = 1.2 as compared to case for fluid with the n value of 0.8. Further improvements in the local and average heat transfer were achieved with using nanoparticles while at the highest particle amount, the enhancements of the average Nu number were 34%, 36% and 36.6% for the fluid with n values of 0.8, 1 and 1.2, respectively.

Group theoretical analysis for unsteady magnetohydrodynamics flow and radiative heat transfer of power-law nanofluid subject to Navier's slip conditions.

The present work covers the flow and heat transfer model for the Power-law nanofluid in the presence of a porous medium over a penetrable plate. The flow is caused by the impulsive movement of the plate embedded in Darcy’s porous medium. The flow and heat transfer models are examined with the effect of linear thermal radiation in the flow regime. The Rosseland approximation is utilized for the optically thick nanofluid. The governing partial differential equations are solved using Lie symmetry analysis to find the reductions and invariants for the closed-form solutions. These invariants are then utilized to obtain the exact solutions for the shear-thinning, Newtonian, and shear-thickening nanofluids. In the end, all solutions are plotted for the Cu-water nanofluid to observe the effect of different emerging flow and heat transfer parameters.

Heat transfer and entropy generation in two layered electroosmotic flow of power-law nanofluids through a microtube

Motivated towards investigating thermal performance in two-nanofluid systems through a microtube, the heat transfer and entropy generation in electroosmotic flow of two-power-law nanofluids considering viscous dissipation and Joule heating effect are studied. Since the circular wall effect triggers distinct thermal features between inner and peripheral flows, both liquids are represented by power-law nanofluid model. Based on two-layer flow analysis, the two-layer energy equation in cylindrical coordinate is presented, from which the semi-analytical solutions are solved. The temperature profiles, Nusselt number and entropy generation are evaluated at different parameters including flow behavior index of two nanofluids (n1, n2), electrokinetic width near the solid interface (λ1) and that near the liquid interface (λ2), nanoparticle volume fraction (ϕ), Brinkman number (Br) and Joule heating parameter (S), thereby the resulting interactive influence of the parameters above is assessed. Compared to that of inner power-law nanofluid, the nanoparticle volume fraction and the properties associated with peripheral power-law nanofluid play significant role. The results offer theoretical guide to the design and optimization of thermal performance in two-liquid microfluidics, thermal mixing and electronics cooling.

Insight into the dynamics of non-Newtonian carboxy methyl cellulose conveying CuO nanoparticles: significance of channel branch angle and pressure drop

Abstract Branching channels are commonly emerged in a considerable variety of engineering applications, in which most of the fluids present non Newtonian behavior, such as in chemical processes. It is noted that in the material forming process, when one suspends nanoparticles in a basic non Newtonian fluid, a completely new non Newtonian fluid is formed with different rheological characteristics from the former ones. In our present numerical research, considering the side branches inclined at varying angles, we focus on the fluid flow and heat transfer of the laminar power-law nanofluid in a rectangular branching channel under the influences of generalized Reynolds number. Both the consistency coefficient and power-law index of the non Newtonian nanofluid, different from those of the base fluid, are described by empirical formula, dependent on the nanoparticle quantity. Finite element method is applied in the research. It is found that a smaller branch angle α can cause a larger fluctuation in pressure near the branched region. Furthermore, negative pressures exist both in the main and side branch with some certain inclination angle. Above all, the new extensive results of velocity contours, temperature, concentration contours along with pressure drop of the changing rheological models provide detailed information for studies on non Newtonian nanofluids in many intricate industrial applications.

Analysis of entropy generation in a power-law nanofluid flow over a stretchable rotatory porous disk

A theoretical entropy generation analysis is conducted by applying the MHD and nonlinear thermal radiation effects contained in porous material for a steady three-dimensional power-law nanofluid flow near the stagnation point region. With the assistance of a thermally radiated non-uniform heat source /sink subject to convective boundary conditions, the heat transformation phenomenon is explored within the boundary layer over the stretchable rotatory disk. Multi-wall carbon nanotubes (MWCNTs) are incorporated in the ethylene glycol (C2H6O2) as a base fluid. The proposed problem of fluid flow is mathematically modeled. The governing nonlinear partial differential equations (PDEs) are lessened to highly mixed nonlinear ordinary differential equations (ODEs) after the utilization of appropriate transformations. The effects of several classes of relevant parameters upon total entropy generation and Bejan number profiles are investigated by numerically addressing the ODEs with the purpose of a well-known Keller Box method. Furthermore, the skin friction coefficients and local Nusselt number are calculated for shear-thinning and shear-thickening behaviors of the power-law fluid. Also, the total entropy generation increases for the Brinkman number and the permeability parameter but decreases for the material parameter, whereas the Bejan number has different behavior from entropy generation.

Effects of using phase change material and non‐Newtonian power law nanofluid on different sides of a double pipe heat exchanger for phase change dynamics and energy performance improvements

AbstractIn this study, the effects of using phase change material (PCM) and non‐Newtonian power law (PL) fluid on the performance features of a double pipe heat exchanger were numerically assessed with finite element technique. PCM and PL fluid were used in different sides of the heat exchanger while impacts of cold side fluid Re number, nanoparticles loading amount, and PL index of fluid on the dynamics characteristics of phase change process, and thermal performance were examined. There is a reduction of 71.5% in the full phase transition time (td) when cases with Re = 100 and Re = 300 are compared while cold fluid exit temperature rises by about 5.8 K with PCM‐installed heat exchanger as compared to non‐PCM configuration at Re = 300. As cases with different PL indices (n) between n = 0.8 and n = 1.2 are compared, the value of td rises by about 34%. For different nanoparticle loading, variation of td depends upon the PL index and its value rises with higher n at the highest solid volume fraction. The particle size has also impacts on the variation of td and exit temperatures which is more pronounced for power n values. A polynomial regression model is used for the estimation of td.

Effect of Hall current on the flow and heat transfer of non-Newtonian power-law nanofluid in the presence of Cattaneo–Christov heat flux and free stream

The nanofluids are a recent challenging task in a nanotechnology field used in heat transfer enhancement for base fluids. The major purpose of this research is to examine the influences of Hall current on the non-Newtonian power-law nanofluid on an exponentially extending surface. Implementation in the Cattaneo–Christov heat flux and the free stream is performed to analyze the thermal relaxation features. Entropy generation evaluation and Bejan number during the convection flow are investigated. The Runge–Kutta–Fehlberg method is employed to resolve the transformed governing nonlinear equations. The impacts of the key physical factors on the profiles of primary and secondary velocities, temperature and entropy generation are discussed across the graphs. The local skin-friction coefficients, Nusselt and Sherwood numbers are demonstrated in a tabular form under the impacts of key physical parameters. Two different types of power-law indicators including pseudoplastic fluid [Formula: see text] and dilatant fluid [Formula: see text] are conducted. The results indicated that the flow speed decreases at dilatant fluid compared to pseudoplastic fluid due to higher viscosity. Increasing Hall current parameter powers the axial and secondary velocity profiles. Thermophoresis parameter powers the profiles of the temperature, nanoparticle volume fraction and local entropy generation. The dilatant fluid [Formula: see text] gives higher values of [Formula: see text] and [Formula: see text] compared to the pseudoplastic fluid [Formula: see text].

Numerical simulation on double diffusion natural convection of a power-law nanofluid within double wavy cavity

In the present paper, the effect of double diffusion natural convection fluid flow inside the double wavy enclosure using the mesh-free method is investigated. The enclosure is filled with nanofluid whose base fluid is non-Newtonian. The results are obtained for the variation in Brownian motion parameter (0.2–0.8), buoyancy ratio parameter (0.2–1), power-law index (0.2–1), thermophoresis parameter (0.2–0.8), Rayleigh number (103–105), and Lewis number (1–5) on mass and heat transfer. It is explored that the mass and heat transfer rate increases with increase in the Rayleigh number and buoyancy ratio. Heat transfer rate decreases with increase in the thermophoresis parameter, Lewis number, Brownian motion, and power-law index, whereas mass transfer rate increases. Such type of enclosure has direct application in heat exchanger devices, the double-wall thermal insulation system, and microelectronic devices. Parallel implementation with the hybrid [EFGM (element free Galerkin method)/FEM (finite element method)] method has been used for the reduction of the running cost to ensure efficiency, which is the novel contribution of the author.

Group Invariant Solutions for Flow and Heat Transfer of Power-Law Nanofluid in a Porous Medium

The present work covers the flow and heat transfer model for the power-law nanofluid in the presence of a porous medium over the penetrable plate. The flow is caused by the impulsive movement of the plate embedded in Darcy’s type porous medium. The flow and heat transfer model has been examined with the effect of linear thermal radiation and the internal heat source or sink in the flow regime. The Rosseland approximation is utilized for the optically thick nanofluid. To form the closed-form solutions for the governing partial differential equations of conservation of mass, momentum, and energy, the Lie symmetry analysis is used to get the reductions of governing equations and to find the group invariants. These invariants are then utilized to obtain the exact solution for all three cases, i.e., shear thinning fluid, Newtonian fluid, and shear thickening fluid. In the end, all solutions are plotted for thecu-water nanofluid and discussed briefly for the different emerging flow and heat transfer parameters.

Jet Impingement Heat Transfer of Confined Single and Double Jets with Non-Newtonian Power Law Nanofluid under the Inclined Magnetic Field Effects for a Partly Curved Heated Wall

Single and double impinging jets heat transfer of non-Newtonian power law nanofluid on a partly curved surface under the inclined magnetic field effects is analyzed with finite element method. The numerical work is performed for various values of Reynolds number (Re, between 100 and 300), Hartmann number (Ha, between 0 and 10), magnetic field inclination (γ, between 0 and 90), curved wall aspect ratio (AR, between 01. and 1.2), power law index (n, between 0.8 and 1.2), nanoparticle volume fraction (ϕ, between 0 and 0.04) and particle size in nm (dp, between 20 and 80). The amount of rise in average Nusselt (Nu) number with Re number depends upon the power law index while the discrepancy between the Newtonian fluid case becomes higher with higher values of power law indices. As compared to case with n = 1, discrepancy in the average Nu number are obtained as −38% and 71.5% for cases with n = 0.8 and n = 1.2. The magnetic field strength and inclination can be used to control the size and number or vortices. As magnetic field is imposed at the higher strength, the average Nu reduces by about 26.6% and 7.5% for single and double jets with n greater than 1 while it increases by about 4.78% and 12.58% with n less than 1. The inclination of magnetic field also plays an important role on the amount of enhancement in the average Nu number for different n values. The aspect ratio of the curved wall affects the flow field slightly while the average Nu variation becomes 5%. Average Nu number increases with higher solid particle volume fraction and with smaller particle size. At the highest particle size, it is increased by about 14%. There is 7% variation in the average Nu number when cases with lowest and highest particle size are compared. Finally, convective heat transfer performance modeling with four inputs and one output is successfully obtained by using Adaptive Neuro-Fuzzy Interface System (ANFIS) which provides fast and accurate prediction results.

Three-dimensional flow of a power-law nanofluid within a cubic domain filled with a heat-generating and 3D-heterogeneous porous medium

Three-dimensional flow of a power-law nanofluid within a cubic domain filled with a heat-generating and 3D-heterogeneous porous medium

Unsteady thermal Maxwell power law nanofluid flow subject to forced thermal Marangoni Convection

In the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film.

Numerical study and error estimation in power-law nanofluid flow over vertical frustum of a cone

The aim of this article is to analyze the mixed convective Ostwald–de Waele power-law nanofluid flow over vertical frustum of a cone in a non-Darcy porous medium using an efficient numerical technique. The involved power-law nanofluid model utilizes water as the base fluid, and Ti-alloy (Ti6Al4V) and multi-wall carbon nanotubes (MWCNTs) as the nanoparticles. The solution of resultant non-similarity equations subjected to boundary conditions is described using the local non-similarity technique along with an efficient spectral local linearization method. The error estimation is provided to show the efficiency of above-mentioned solution procedure. A detailed explanation about the impact of nanoparticle volume fraction on the dimensionless velocity and temperature profiles along with heat transfer rate and skin friction coefficient is also provided for both the opposing and aiding flow cases. On comparison of the present results in particular cases with the relevant published data, it is assured that this method gives highly accurate outcomes for this kind of very complex fluid flow problems. The domination of dilatant nanofluid over pseudo-plastic nanofluid in both the aiding and opposing flow cases is noticed for velocity profiles, and the velocity is decreased with an increment in the nanoparticle volume fraction. Also, the variation in profiles with a streamwise coordinate $$\xi$$ shows non-similar nature of the problem. The use of Ti-alloy and MWCNTs in this work makes it very profitable in various important sectors like aerospace and medical sector.

Theoretical investigation of a single vapor bubble during Al2O3/H2O nanofluids in power-law fluid affected by a variable surface tension

This article analyzes the growth of the vapor bubble in a novel model of power-law nanofluids (Al2O3/H2O) under a new effect of variable surface tension. The governing equations of the rising vapor bubble flow model are formulated and converted to a single equation describing the bubble dynamics behavior. By employing the model of Plesset and Zwick method, we investigate a new model of equations within power-law nanofluids to examine the effect of different physical parameters such as initial superheating liquid, critical bubble radius, and thermal diffusivity on the vapor bubble formation. Furthermore, the effects of surface tension behavior with the initial bubble radius, time, and initial rate of bubble radius are examined. It is found that the growth of the vapor bubble radius increases with the increase of initial superheating liquid, critical bubble radius, and thermal diffusivity. In addition, the connection between shear stress and shear rate is analyzed in detail. Using appropriate values for the physical parameters, the behavior of solutions of the vapor bubble is discussed. Based on the conducted simulation analysis, the behavior of the solutions is found to be more accurate than those in the previous studies. Besides, the obtained results demonstrate that the vapor bubble in power-law nanofluids grows slower than in pure water.

Time-dependent power-law nanofluid with entropy generation

This work studies the time-dependent convective flow of non-Newtonian power-law fluid by vertical plate. Fluid flow is studied in the presence of thermal radiation. The Buongiorno model is employed to describe the features of nanofluid. Entropy generation and Bejan number are calculated. The flow, temperature and concentration are given by the system of partial differential equations (PDE’s). The system of PDE’s is transformed into dimensionless form by transformation and then solve implementing finite difference technique. Special emphasis is given to the outcomes of Prandtl number, Reynolds number, Eckert number, radiation parameter, thermophoresis, Brownian parameter, and Schmidt number. Velocity, temperature, concentration, skin friction, Sherwood and Nusselt numbers are graphically analyzed. Graphical results show that velocity of fluid enhanced for high Grashof number while shows opposite behavior for Reynold number. For the high estimation of the thermophoresis parameter and Brownian motion parameter temperature and concentration increase. For the higher value of the radiation parameter, the irreversibility of fluid particles increases while the Bejan number decreases.

A theoretical analysis of steady three-dimensional flow and heat transfer of Power-Law nanofluid over a stretchable rotating disk filled with gyrotactic microorganisms

The current research study investigates the steady three-dimensional flow and heat transfer of a power-law nanofluid in the presence of the uniformly applied magnetic field and nonlinear thermal radiation over the stretchable rotating disk filled with gyrotactic microorganisms. The physically modeled partial differential equations (PDEs) are lessened to combined nonlinear ordinary differential equations (ODEs) with appropriate transformation. The influence of several types of pertinent parameters upon the dimensionless distributions of velocity, temperature, the concentration of nanoparticles, and microorganisms are analyzed graphically by solving the ODEs with a well-known shooting method. The tabular comparison is provided for the verification between the present results with those in the literature. Also, the physical quantities of interest are calculated, and the effects are scrutinized. Furthermore, it is noticed that the emerging parameters have produced a significant influence upon the velocity components, temperature, concentration of nanoparticles, and motile density of microorganisms.

Nonlinear Radiation and Variable Viscosity Effects on Free Convection of a Power-Law Nanofluid Over a Truncated Cone in Porous Media With Zero Nanoparticles Flux and Internal Heat Generation

Abstract This study used numerical analysis to investigate the effects of nonlinear radiation and variable viscosity on free convection of a power-law nanofluid over a vertical truncated cone in porous media with Rosseland diffusion approximation considering zero nanoparticles flux and internal heat generation. The internal heat generation is of an exponential decaying form and the viscosity of the fluid is assumed to follow Reynolds viscosity model. The surface boundary conditions of vertical truncated cone is maintained at the uniform wall temperature (UWT) and the zero nanoparticle flux (ZNF) to cause the results to be more realistic and useful. The nanofluid model considered the effects of Brownian motion and thermophoresis. The nonsimilar governing equations are obtained by using a suitable coordinate transformation and then solved by Keller box method (KBM). Comparisons with previously published work obtained good agreement. Graphical and tabular presentations of numerical data for the dimensionless temperature profile and the local Nusselt number were presented for main parameters: dimensionless streamwise coordinate, thermophoresis parameter, Lewis number, radiation parameter, surface temperature parameter, viscosity parameter, power-law index of the non-Newtonian fluid, and internal heat generation coefficient. The local Nusselt number increased when the following parameters were increased: radiation parameter, surface temperature parameter, viscosity parameter, power-law index of the non-Newtonian fluid, and dimensionless streamwise coordinate. In contrast, the local Nusselt number decreased when the following parameters were increased: internal heat generation coefficient, thermophoresis parameter, and Lewis number. Besides, the physical aspects of the problem are discussed in details.

MHD mixed convective flow of power-law nanofluid in a lid-driven cavity with heat generation and chemical reaction effects: Buongiorno's model

The two-dimensional laminar MHD mixed convective flow of non-Newtonian power-law nanofluid in a lid-driven cavity with the presence of heat generation and chemical reaction effects is analysed. The nanofluid incorporates the effects of Brownian motion and thermophoresis using Buongiorno’s model. The governing equations in a vector form are transformed into non-dimensional form. Then, the dimensionless equations are solved numerically by finite element method (FEM) using automated solution technique which is FEniCS. The effects of different physical parameters on velocity, temperature, and nanoparticles volume fraction profiles are presented and discussed in this paper.