Power-law Nanofluid Research Articles

Exploring the Thermal Behavior of Cu-water and CuO-water Power-law Nanofluids on a Rotating Circular Disc: A Computational Analysis

The current theoretical investigation focuses on the thermal behavior of a power-law nanofluid flow on a rotating circular disc. In which nanofluid is made by taking colloidal suspension of copper (Cu) and copper oxide (CuO) nanoparticles in a base fluid like water. A theoretical investigation is conducted by formulating a mathematical model of a power-law fluid (which exhibits shear thickening and thinning effects) along with the Tiwari and Das model. A similarity transformation is employed to transform the nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs) and these ODEs are then numerically solved using the shooting technique. The study's findings are analyzed graphically by plotting radial, tangential, and axial velocity profiles, temperature profiles, Nusselt number, and skin friction coefficients to show how various factors affect the fluid's flow and heat transfer. It is revealed that drag force reduces in Cu-water nanofluid as compared to CuO-water nanofluid for all types of fluids (Newtonian, pseudoplastic, and dilatant fluids) and Nusselt number becomes high in Cu-water nanofluid for both Newtonian and dilatant fluids as compared to CuO-water nanofluid but in case of pseudoplastic reverse behavior is observed. Heat transfer rate in Cu-water dilatant and pseudoplastic nanofluids increases up to 20.4% and 12.5% with respect to base fluid and in CuO-water dilatant and pseudoplastic water nanofluids, it increases up to 18.6% and 15.2%.

Optimizing solar collector through constructal design of Y-shaped networks with power-law nanofluid flow

Solar energy is a plentiful and renewable resource; therefore, its use through clean energy technologies is necessary to reduce the consumption of fossil fuels and their consequent impact on the environment. Solar thermal energy can be harnessed to collect thermal energy through solar collectors for domestic or industrial use. In this work, a Y-shaped duct network was developed for a solar collector with a disc-shaped body. The shape and size of the network were defined using the constructal design method to harvest greater thermal energy from exposure to irradiance. For this purpose, the working fluid was a nanofluid composed of nanoparticles and a base fluid with non-Newtonian behavior, as described by the power-law model. The properties of the nanofluid were described using theoretical models that depend on the volume fraction of the nanoparticles in the base fluid. The aspect ratio of each element in the network was defined under the condition of minimum thermal resistance. For the shear-thinning nanofluid with a volume fraction of 0.04, the thermal resistance was reduced by 5.5% with an aspect ratio 5.8% lower than that of the pure base fluid. The minimum thermal resistance of the Y-shaped network arrangement occurs for shear-thinning fluids, whereas thermal resistance increases for shear-thickening fluids. This effect can be observed at different levels of branching and in pumping power. Results show that increasing the volume fraction of the nanofluid and base fluid with shear-thinning behavior aids in achieving minimal thermal resistance more easily with a smaller network. The above offers new design options for devices optimized to improve solar harvesting and thermal management, through shape, structure and rheological characteristics.

Comparative study of radiation effect on titanium dioxide power-law nanofluid over a thin needle with cancer treatment applications: a quadratic regression model

Comparative study of radiation effect on titanium dioxide power-law nanofluid over a thin needle with cancer treatment applications: a quadratic regression model

A parallel computational study of power-law non-Newtonian nanofluid in a C-shaped enclosure by multiple-relaxation-time lattice Boltzmann simulation

ABSTRACT This study aims to numerically examine the heat transfer and entropy generation of non-Newtonian power-law nanofluids in a C-shaped cavity filled with porous media considering the Brinkman-Forchheimer extended Darcy model (BFEDM). The graphics processing unit (GPU) based multiple-relaxation-time lattice Boltzmann method (MRT-LBM) was used through computing unified device architecture (CUDA) C/C++ platform. It is a known fact that the fluid viscosity varies with the shear rate and nanoparticle sizes and the thermal conductivity also varies with the fluid temperature. However, the extension of such phenomena needs to be further investigated to understand any specific threshold in heat transfer application. To leverage such characteristics, it is permissible to add certain input parameters. As a result, the power-law indices ( n ), the Darcy number ( Da ), the volume fraction of nanoparticles ( ϕ ), the Rayleigh number ( Ra ), and the fixed porosity ( ε = 0.4 ) were the five key parameters considered to analyze the numerical results. The GPU-based numerical code was validated with the available benchmark results, and good agreements were obtained. The results showed that the average rate of heat transfer in terms of the average Nusselt number ( Nu ‾ ) increased due to an increase in Ra due to the enhanced buoyancy force and a reduction in the .

A modification of explicit time integrator scheme for unsteady power-law nanofluid flow over the moving sheets

This paper introduces an exponential time integrator scheme for solving partial differential equations in time, specifically addressing the scalar time-dependent convection-diffusion equation. The proposed second-order accurate scheme is demonstrated to be stable. It is applied to analyze the heat and mass transfer mixed convective flow of power-law nanofluid over flat and oscillatory sheets. The governing equations are transformed into a dimensionless set of partial differential equations, with the continuity equation discretized using a first-order scheme. The proposed time integrator scheme is employed in the time direction, complemented by second-order central discretization in the space direction for the momentum, energy, and nanoparticle volume fraction equations. Quantitative results indicate intriguing trends, indicating that an increase in the Prandtl number and thermophoresis parameter leads to a decrease in the local Nusselt number. This modified time integrator is a valuable tool for exploring the dynamics of unsteady power-law nanofluid flow over moving sheets across various scenarios. Its versatility extends to the examination of unstable fluid flows. This work improves engineering and technological design and operation in nanofluid dynamics. Improving numerical simulations’ precision and computational efficiency deepens our comprehension of fundamental physics, yielding helpful information for enhancing systems that rely on nanofluids.

Natural Convection of a Power-Law Nanofluid in a Square Cavity with a Vertical Fin

Natural Convection of a Power-Law Nanofluid in a Square Cavity with a Vertical Fin

Numerical investigation of the flow characteristics involving dissipation and slip effects in a convectively nanofluid within a porous medium

Abstract The aim of the present research is to discuss the numerical aspects of heat-mass transfer in power-law nanofluids on an stretched surface. In addition, the novelty in this research lies in its thorough exploration and incorporation of parameters such as viscous dissipation, slip velocity, and convective boundary conditions into the analysis. This distinguishes the study from previous work and underscores its originality. For non-Newtonian fluids, a power-law model is employed, while the nanofluid system associate the influences of thermophoresis and the Brownian motion. The fluid’s thermal conductivity is considered to change based on temperature, while the concentration of nanoparticles at the surface is maintained at a constant level. A heated fluid situated beneath the lower surface can act as a heat convection mechanism source. A process of similarity transformation is employed to simplify the equations related to the mass, momentum, thermal energy, and nanoparticle concentration into nonlinear ordinary differential equations. These equations are then treated numerically with the help of the shifted Chebyshev polynomials of the sixth order and the spectral collocation method. The proposed technique reduces the existing problem into a system of algebraic equations formulated as a constrained optimization challenge. Subsequently, the optimization technique is applied to determine the unknown coefficients of the series solution. Graphical representations depict the impacts of nanofluid parameters. A quantitative assessment is presented in a tabular format to illustrate a comparison with previously published results for specific scenarios, revealing a notable level of agreement.

Numerical treatment of the radiated and dissipative power-law nanofluid flow past a nonlinear stretched sheet with non-uniform heat generation

The main aim of this paper is to investigate the effect of non-uniform heat generation and viscous dissipation on the boundary layer flow of a power-law nanofluid over a nonlinear stretching sheet. Within the thermal domain, the analysis considers both thermal radiation and variable thermal conductivity. Through the use of similarity transformations, the governing boundary layer equations are transformed into a system of ODEs. The spectral collocation method (SCM) with shifted Vieta-Lucas polynomials (VLPs) is implemented to give an approximate expression for the derivatives and then use it to numerically solve the proposed system of equations. By employing this technique, the system of ODEs is converted into a system of nonlinear algebraic equations. The dimensionless temperature, concentration, and velocity are graphically presented and analyzed for various values of the relevant governing parameters. Through the presented graphical solutions, we can see that the main outcomes indicate that an increase in the power law index, thermal conductivity parameter, and radiation parameter leads to a noticeable decrease in the local Nusselt number, with reductions of around 0.05 percent, 0.23 percent, and 0.11 percent, respectively. In contrast, the Prandtl parameter demonstrates an opposing effect, elevating the local Nusselt number by about 0.1 percent. We validated the accuracy of the numerical solutions by comparing them in some special cases with existing literature.

Blottner finite difference analysis for non-Darcy flow of variable viscosity power-law nanofluids over a truncated cone with Arrhenius activation energy

Examining the behaviors of power-law nanofluid flow and the rate of heat transfer over different surfaces has received great attention due to its numerous industrial applications, such as polymer solutions, molten plastics, pulps, and foods. Also, the investigators focused on the case of constant viscosity, while in several practical situations, the dynamic viscosity of the power-law suspension is variable. So this study aims to examine non-similar solutions for the coupled flow of power-law non-Newtonian nanofluids over a truncated cone. The dynamic viscosity is varied according to the Reynolds viscosity model, and an exponential decaying form is considered for the internal heat generation. The non-Darcy model, where the quadratic drag is significant, is applied to formulate this situation, and the medium's permeability is varied according to the modified Ostwald-de-Waele power law model. Both the Arrhenius activation energy and non-linear thermal radiation impacts are considered. The solution methodology is based on the effective finite differences method with the Blottner scheme. The significant outcomes revealed that the rise in the power-law index n accelerates the flow and boosts the heat transfer rate. The values of the local Nusselt number in the case of the Darcy flow are higher than those of the non-Darcy case. Additionally, considering the case of variable dynamic viscosity, it is recommended to enhance the heat transfer rate. Furthermore, the rate of the heat transfer is enhanced by 29.1% viscosity parameter δ is varied from 0 to 0.5.

Radiative flow of temperature-dependent viscosity power-law nanofluids over a truncated cone saturated heat generating, porous media: Impacts of Arrhenius energy

In this paper, the coupled flow of the pseudo-plastic, dilatant/Newtonian nanofluids along truncated cones is treated using a set of non-similar solutions. The dynamic viscosity is assuming to be a variable and depending on flow region temperature. The non-Darcy model where the quadratic drag is significant is applied to formulate this situation and the medium's permeability is varied according to the modified Ostwald-de-Waele power law model. Both of the Arrhenius activation energy and non-linear radiation flux impacts are assumed. The converted system is treated using the effective finite differences analyses with Blottner scheme. The major outcomes disclosed that the temperature and nanoparticles distributions are higher in case of the pseudo-plastic nanofluids while the dilatant nanofluids types gives the higher rates of the heat and mass transfer. The Darcy flow case causes higher values of the Nusselt number comparing to the non-Darcy case. Further, presence of the activation energy supports the convective situation and enhances the Nusselt and Sherwood coefficient.

Computer simulation of two phase power-law nanofluid of blood flow through a curved overlapping stenosed artery with induced magnetic field: entropy generation optimization

PurposeThe purpose of this study is to determine the impact of two-phase power law nanofluid on a curved arterial blood flow under the presence of ovelapped stenosis. Over the past couple of decades, the percentage of deaths associated with blood vessel diseases has risen sharply to nearly one third of all fatalities. For vascular disease to be stopped in its tracks, it is essential to understand the vascular geometry and blood flow within the artery. In recent scenarios, because of higher thermal properties and the ability to move across stenosis and tumor cells, nanoparticles are becoming a more common and effective approach in treating cardiovascular diseases and cancer cells.Design/methodology/approachThe present mathematical study investigates the blood flow behavior in the overlapped stenosed curved artery with cylinder shape catheter. The induced magnetic field and entropy generation for blood flow in the presence of a heat source, magnetic field and nanoparticle (Fe3O4) have been analyzed numerically. Blood is considered in artery as two-phases: core and plasma region. Power-law fluid has been considered for core region fluid, whereas Newtonian fluid is considered in the plasma region. Strongly implicit Stone’s method has been considered to solve the system of nonlinear partial differential equations (PDE’s) with 10–6 tolerance error.FindingsThe influence of various parameters has been discussed graphically. This study concludes that arterial curvature increases the probability of atherosclerosis deposition, while using an external heating source flow temperature and entropy production. In addition, if the thermal treatment procedure is carried out inside a magnetic field, it will aid in controlling blood flow velocity.Originality/valueThe findings of this computational analysis hold great significance for clinical researchers and biologists, as they offer the ability to anticipate the occurrence of endothelial cell injury and plaque accumulation in curved arteries with specific wall shear stress patterns. Consequently, these insights may contribute to the potential alleviation of the severity of these illnesses. Furthermore, the application of nanoparticles and external heat sources in the discipline of blood circulation has potential in the medically healing of illness conditions such as stenosis, cancer cells and muscular discomfort through the usage of beneficial effects.

Unsteady Power Law Nanofluid Flow Subjected to Electro-Magnetohydrodynamics with Active and Passive Nanoparticles Flux

The heat and mass transfer characteristics of power-law nanofluid flow over a stretching sheet embedded in a porous medium with active and passive control of wall mass fluxes are explored in this research. Additionally, the formulation incorporates electromagnetohydrodynamic (EMHD), Brownian movement, and thermophoresis aspects in the flow problem. The solutions of formulated boundary layer fluid flow equations are represented via tabular and graphical demonstrations to study the impact of the leading parameters. MATLAB inbuilt bvp4c solver is utilized for numerical simulation of presented fluid flow theories. Physical elaboration of the graphs is given to recognize the influence of fluid flow, heat, and mass transport mechanisms in different rising conditions. Results show that the implication of magnetic field, unsteadiness, and porous medium restricts the fluid flow velocity while the electric field enhances it. Active control of nanoparticles dominates the velocity, temperature, and concentration profiles more than passively controlled conditions. The significance of the power-law index enclosed in the current study shows that the performance of pseudoplastic fluids (n < 1) is improved than that of dilatant fluids (n > 1).

Power-Law Nanofluid Magnetohydrodynamics Combined Convection in the Presence of Heat Absorption/Generation: A Lattice Boltzmann Analysis to Compute Thermal Performance Index

Endeavors to improve the performance of thermal systems have always been of great noticed due to their extremely high importance in industrial and engineering applications. For this intention, in the existing simulation, several effective strategies have been evaluated to determine the amount of heat transfer and entropy formation caused by the combined convection of non-Newtonian nanofluid with particles Brownian motion. Based on the findings via LBM simulation, it has been observed that changing the position and speed direction on the chamber wall helps to control the flow characteristics, and thus significantly changes the thermal performance of the system. The least effect of the magnetic field in reducing the value of the Nusselt number in all the positions of applying the speed belongs to the state where the wall direction is aligned with the force of gravity. In the case where the middle part of the vertical wall has speed, the formed flow power inside the chamber is 29% and 45% higher than when the first third and the last third of the wall have speed. The presence of a strong magnetic field leads to the reduction of convection effects, which is more evident for moving up the vertical wall. When the middle part of the wall has speed, if the magnetic field is applied to the middle part of the chamber to the highest value, the reduction of the average Nusselt number is about 35% and 39% more than the case when the magnetic field is applied to the first third and the last third of chamber. To have a higher average Nusselt number value, reducing the fluid power-law index and enhancing the Reynolds number value are effective strategies. To control the effects of the magnetic field, it is very effective to reduce the shear force on the chamber wall and expose the fluid flow to the heat absorption/production phenomenon. By reducing the value of fluid power-law index, the effect of magnetic field and heat absorption/production becomes more evident. In Re=200, the reduction of the thermal performance index for enhancing the Hartmann number value to the highest value is about 39% for n = 0.45, while this effect is about 31% and 24% for n = 0.7 and n = 0.95, respectively. By exposing the current to heat production, the effect of the magnetic field is reported to be about 55% higher than in other cases. Although heat production enhances the amount of Be value by about 66% compared to the heat absorption mode, it leads to an increase in the thermal performance index. The highest value of the system thermal performance index (0.82) can be achieved by upward moving the middle part of the chamber wall in the absence of magnetic field for heat absorption mode at the lowest power-law index and the highest Reynolds number value.

Mathematical model for a thermal cooling system with variable viscosity and thermal conductivity over a rotating disk

Mathematical models involving rotation of the disks and the flow of fluid over these serve as a prototypical representation of electronic devices including rotational components. The rotation results in substantial heat generation and the excessive heat buildup can affect performance and reliability, and can cause failure. Therefore efficient cooling mechanisms are essential to dissipate the generated heat and maintain the devices’ temperature within safe operating limits. In this research paper, the focus is on investigating the magnetohydrodynamic (MHD) slip flow and heat transfer of power-law nanofluid over an infinite rotating disk. The study incorporates numerical methods to analyze the system, considering the variable thermal conductivity and viscosity as a function of velocity gradients, and employing velocity slip conditions at the boundary. To facilitate the analysis, the similarity transformation technique is applied, which effectively reduces the governing boundary value problem to a set of nonlinear ordinary differential equations (ODEs). The research explores the dependence of the velocity and temperature profiles on various parameters, including the nanofluid volume concentration parameter, power-law index, magnetic parameter, and velocity slip parameters. Through the numerical results, the influence of these parameters on the flow and heat transfer characteristics is presented and thoroughly discussed. The outcomes of the study are presented in the form of graphs and tables, providing valuable insights into the behavior of the power-law nanofluid flow and heat transfer over the rotating disk.

Mathematical Modeling of Pseudoplastic Nanofluid Natural Convection in a Cavity with a Heat-Generating Unit and Solid Finned Heat Sink

The power-law nanofluid natural convection in a chamber with a thermally generating unit and a solid ribbed structure has been studied in this work. A mixture of carboxymethylcellulose with water and copper nanoparticles is a working fluid illustrating pseudoplastic properties. The effective properties of the nanoliquid have been described by experimental correlations reflecting the temperature effect. The governing equations have been formulated on the basis of the conservation laws of mass, momentum and energy employing non-primitive parameters such as stream function and vorticity. The defined boundary value problem has been worked out by the finite difference technique using an independently developed calculation system. The Rayleigh number is fixed for analysis (Ra = 105). The paper analyzes the influence of the nanoparticles volume fraction, an increase in which reduces the temperature in the case of the one edge presence. An analysis of the rib height has shown that its growth leads to a weakening of the convective heat transfer, but at the same time, the source temperature also decreases. Increasing the number of fins from 1 to 3 also helps to reduce the average temperature of the heat-generated element by 15%.

An effects of mass transpiration and inclined MHD on nanoboundary layer of an ostwald-de waele fluid due to a shrinking boundary

This paper examines the power-law nanofluid flows due to a shrinking sheet with mass transpiration under inclined MHD. The governing partial differential equations are similarly transformed into nonlinear ordinary differential equations and solved analytically. The mathematical model through analytical solutions graphically shows that the flow's dynamics depending on the Chandraselhar number, mass transpiration, nanofluid and inclined angle parameters. The main findings and methods of the present work includes the closed-form exact solutions are examined for some special cases and one of them is an algebraic solution. Specific and quantitative analytical solutions provide important understanding to the boundary layer flow for power-law nanofluid. The present study reveals that the magnetic field significantly increases the magnitude of the skin friction and mass transpiration. Cu-H2O nanofluid is used to examine the entaire calculation. Nanofluids are suspensions of nanoparticles in fluids that show significant enhancement of their properties at modest nanoparticle concentration.

Spatial–temporal analysis of magnetohydrodynamics flow and energy flux of power-law nanofluid in a confined domain

Energy flux analysis of power-law fluid is a novel contribution to recent developments in computational fluid dynamics. The study of the unsteady two-dimensional flow with double diffusive effect inside a complex enclosure exhibits great potential in optimizing the heat transfer rate due to the wavy nature of the side walls. The enclosure is confined with the flow circulation due to the thermal and solutal gradients acting along the left and right wavy walls. The computational time and accuracy in results are estimated and compared by implementing the finite volume method and element-free Galerkin technique. The results are obtained in terms of streamlines, isotherms, isoconcentrations, average Nusselt number, Sherwood number, and total entropy generation due to the effect of conventional parameters, namely, power-law index, Rayleigh number, buoyancy ratio parameter, thermophoresis parameter, Brownian motion parameter, and Lewis number with a fixed Prandtl number throughout the computation. The optimized double-diffusive natural convection analysis is based on entropy generation and a calculated Bejan number. The novelty of this paper lies in the implementation of a mesh-free approach, which may be useful for the further analysis of elliptical/semi-elliptical structures.

Magnetohydrodynamic convection-entropy generation of a non-Newtonian nanofluid in a 3D chamber filled with a porous medium

Magnetohydrodynamic (MHD) mixed convection in a 3D (three dimensional) lid-driven cavity loaded with a power-law nanofluid is examined. The bottom wavy wall is maintained at a hot temperature, while the upper lid is at a uniformly cold temperature. The vertical walls are kept in adiabatic conditions. The steady and three-dimensional flow of nanofluids is quantitatively studied utilizing thermophysical properties and the Galerkin Finite Element Method (GFEM). The findings were shown for a variety of Grashof numbers (Gr = 103-105), Hartmann numbers (Ha = 0–20), Reynolds numbers (Re = 10–500), power-law indexes (n = 0.8,1,1.6), and undulation numbers (N = 1–4). The influence of the various parameters on flow, heat transfer, and entropy generation is illustrated by the streamlines, isotherms, and isentropic contours. Higher Re, γ, N, φ, and lower Ha enhance the heat transfer. Entropy generation is mostly due to heat transfer but also fluid-friction and magneto effects contribute. Also, the increase in Re from 50 to 500 gives an enhancement in Nuav up to 87.5 %. Furthermore, the increase in power-law index (n) from 0.8 to 1 gives a reduction in Nusselt number up to 10.58 %.

Optimizing energy generation in power-law nanofluid flow through curved arteries with gold nanoparticles

The investigation of blood flow into curved arteries is fascinating and essential to prevent the advancement of vascular disease. Motivated by electro-kinetic manipulation, gold nanoparticles, and their size applications, a mathematical model is developed to explain blood flow, entropy generation, and electro-kinetic energy conversion (EKEC) efficiency in curved arterial flow. To make this study more realistic, a patient-specific overlapped stenosis condition and non-Newtonian (power-law fluid) blood flow model have been considered. The effects of a magnetic field, external heating, and chemical reactions are also included. The Stone’s strongly implicit scheme has been considered to solve the system of non-linear partial differential equations (PDE’s) in the” MATLAB” software. In this numerical investigation, an error tolerance of 10 − 6 has been considered for every iteration step under Stone’s scheme. The significance of various physical parameters, such as nanoparticle volume fraction (m), their size (dp), magnetic field intensity (M), inverse Debye length ( κ ¯ ), flow behavior index (Sc), heat source (H), and chemical reaction parameter (ξ) on the blood flow velocity, temperature, concentration, EKEC efficiency, and entropy generation have been explained graphically. This study also developed stream function contours to describe flow trapping patterns. The findings of this study conclude that the blood flow EKEC efficiency reduces with the presence of nanoparticles and stenosis in the artery. In addition, both flow velocity and entropy enhance by adopting large-size nanoparticles instead of small diametric nanoparticles. Clinical researchers and biologists may use the results of this computational study to forecast endothelial cell damage and plaque deposition in curved arteries with WSS profiles, by which the severity of these conditions can be reduced.

Wall jet nanofluid flow with thermal energy and radiation in the presence of power-law

The effectiveness of jet flow in the energy transfer process has made it very useful in industrial applications. These flows also have higher heat transfer coefficients than traditional cooling through convection. The appliances inclusive of the jet make effective use of fluid and enhance the heat transfer rate. The contemporary article investigates the jet flow of power-law nanofluid past a moving wall. The nanofluid is formed by suspending Cu and Al2O3 nanoparticles in water. Furthermore, the jet flow is analyzed in the presence of radiation, which is further assumed to be linear, and the application of Rosseland approximation is considered to be valid. Considering these aspects, the model is designed using partial differential equations (PDE), which are then converted to a system of non-linear ordinary differential equations (ODE) by implementing certain similarity transformations. Thus, the obtained system is solved using numerical methods, and the results are discussed with the help of graphs. The significant conclusions of the analysis were that the increase in the radiation parameter contributed to the increase in the temperature of the nanofluid. The increase in the Prandtl number reported a decrease in the amount of heat absorbed by the nanofluid.