Single-phase Nanofluid Research Articles

A new similarity solution with stability analysis for the three-dimensional boundary layer of hybrid nanofluids

Purpose The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties. Design/methodology/approach The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed. Findings The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only. Originality/value The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

Thermal convection in a chamber filled with a nanosuspension driven by a chemical reaction using Tiwari and Das’ model

PurposeThe purpose of this paper is to study numerically the steady thermal convection in a chamber filled with a nanoliquid affected by a chemical reaction using the single-phase nanofluid approximation.Design/methodology/approachWater was considered as a host fluid while nanoparticles are aluminum oxide. Homogeneous reactions are analyzed. The nonlinear partial differential equations describing the considered problem are simulated using the finite difference technique.FindingsThe results of streamlines, isotherms, isoconcentrations, nanofluid flow rate, mean Nusselt and Sherwood numbers are discussed. The data demonstrate that the mean Sherwood number increases with the homogeneous reaction rate. Further, nanofluid flow rate can be increased with nanoparticles concentration for high Rayleigh numbers owing to the homogeneous chemical reaction inside the cavity.Originality/valueSearching the existent references illustrates that the homogeneous-heterogeneous reactions influence on the nanoliquid motion and energy transport within enclosures has not been investigated before. The results of this paper are completely original and the numerical results of the present paper were never published by any researcher.

MHD hybrid nanofluid flow over a permeable stretching/shrinking sheet with thermal radiation effect

Purpose This study aims to investigate the heat transfer characteristic of the magnetohydrodynamic (MHD) hybrid nanofluid over the linear stretching and shrinking surface in the presence of suction and thermal radiation effects. Design/methodology/approach Mathematical equations are transformed into pairs of self-similarity equations using similarity transformation. Boundary value problem solver (bvp4c) in MATLAB was adopted to solve the system of reduced similarity equations. In this study, the authors particularly examine the flow and heat transfer properties for different values of suction and thermal radiation parameters using single-phase nanofluid model. A comparison of the present results shows a good agreement with the published results. Findings It is noticed that the efficiency of heat transfer of hybrid nanofluid (Cu-Al2O3/H2O) is greater than the nanofluid (Cu/H2O). Furthermore, it is also found that dual solutions exist for a specific range of the stretching/shrinking parameter with different values of suction and radiation parameters. The results indicate that the skin friction coefficient and the local Nusselt number increase with suction effect. The values of the skin friction coefficient increases, but the local Nusselt number decreases for the first solution with the increasing of thermal radiation parameter. It is also observed that suction and thermal radiation widen the range of the stretching/shrinking parameter for which the solution exists. Practical implications In practice, the investigation on the flow and heat transfer of MHD hybrid nanofluid through a stretching/shrinking sheet with suction and thermal radiation effects is very important and useful. The problems related to hybrid nanofluid has numerous real-life and industrial applications, for example microfluidics, manufacturing, transportation, military and biomedical, etc. Originality/value In specific, this study focused on increasing thermal conductivity using a hybrid nanofluid mathematical model. This paper is able to obtain the dual solutions. To the best of author’s knowledge, this study is new and there is no previous published work similar to present study.

Design of nanofluid-cooled heat sink using topology optimization

The paper presented topology optimization of 2D and 3D Nanofluid-Cooled Heat Sink (NCHS). The flow and heat transfer problem in the NCHS was treated as a single-phase nanofluid based convective heat transfer model. The temperature-dependent fluid properties were taken into account in the model due to the strong temperature-dependent features of nanofluids. An average temperature minimum problem was studied subject to the fluid area and energy dissipation constraints by using the density method. In the method, the design variable is updated according to the gradient information obtained by an adjoint based sensitivity analysis process. The effects of the energy dissipation constraint, temperature-dependent fluid properties and nanofluid characteristics on optimal configurations of NCHS were numerically investigated with following conclusions. Firstly, branched flow channels in the optimal configuration increased with the rise of the allowed energy dissipation. Secondly, temperature-dependent fluid properties were significant for obtaining the appropriate optimal results with best cooling performance. Thirdly, heat transfer performances of optimal configurations were enhanced by reducing the nanoparticle diameter or increasing the nanoparticle volume fraction. Fourthly, the optimal configuration for nanofluid had better cooling performance than that for its base fluid.

Flow and heat transfer of hybrid nanofluid over a permeable shrinking cylinder with Joule heating: A comparative analysis

The objectives of the present study are (i) to observe the duality of solutions, and (ii) to investigate the flow and heat transfer of the hybrid nanofluid past a shrinking cylinder in the appearance of Joule heating. The single phase nanofluid model with modified thermophysical properties are used for the mathematical model. The similarity transformation simplifies the model (PDEs) into similarity (ordinary) differential equations. bvp4c solver is used to compute the reduced equations. For the validation part, the analytical solution is developed using an exact analytical method and compared with the numerical values for several cases. First and second solutions are observable for the shrinking cylinder case only if suction parameter is applied. Meanwhile, only the first solution is found to be stable from the stability analysis. The application of high suction strength make the reduced heat transfer rate is lower for hybrid nanofluid (Cu-Al2O3/water) than alumina-water nanofluid but, opposite result is found for the skin friction coefficient. The addition of curvature parameter (flat plate to cylinder) can quicken the separation process of boundary layer. This results are conclusive to the pair of alumina and copper only.

Significance of Joule heating and viscous heating on heat transport of MoS2–Ag hybrid nanofluid past an isothermal wedge

The problem of flow and heat transport of magneto-composite nanofluid over an isothermal wedge has not been addressed in the literature up to yet. Thus, this article features the laminar transport of Newtonian composite nanomaterial (C2H6O2–H2O hybrid base liquid + MoS2–Ag hybrid nanoparticles) in the presence of exponential space- and temperature-dependent heat source past an isothermal wedge. An incompressible and electrically conducting fluid is assumed. The effects of Joule heating and viscous heating are also accounted. Single-phase nanofluid model and boundary layer approximation are utilized to govern the equations of flow and heat transport phenomena. The solution of the simplified coupled system of dimensionless constraints is obtained by using the Runge–Kutta–Fehlberg method based on the shooting technique. Detailed analysis of active quantities of interest has been presented and discussed. The interesting physical quantities (friction factors and Nusselt number) are estimated. Also, the slope of the data point is calculated in order to estimate the amount of decrease/increase in physical quantities.

Inclined magneto: convection, internal heat, and entropy generation of nanofluid in an I-shaped cavity saturated with porous media

A numerical investigation of entropy generation due to MHD-free convective of Cu–water nanofluid in a porous I-shaped cavity is reported. The cavity is under Darcy law with inclined uniform magnetic field. The cavity is cooled from the top and a part of bottom wall subjected to uniform heat flux, while the other parts of walls of the cavity are adiabatic. Mathematical pattern formulated employing the single-phase nanofluid approach in governing equations the problem has been solved by finite difference technique. Prime efforts have been concentrated on the impacts of the pertinent parameters on the fluid flow and heat transfer inside the cavity. Numerical data have been plotted in the form of streamlines, isotherms, and average Nusselt numbers. The results show that the Nu number decreases via increasing the Ha number. It increases when the Ra number is increased. The maximum and minimum values of Nusselt occur at B = 0.2 and B = 0.8, respectively. Exerting an angle for magnetic flux leads to the improvement in thermal performance for all amount of B. The effects of Ha, nanofluid volume fraction, heat source size, location and angle of magnetic field on heat transfer, entropy generation, and thermal performance are completely studied and discussed.

Entropy generation and nanofluid mixed convection in a C-shaped cavity with heat corner and inclined magnetic field

A numerical simulation of entropy generation due to MHD mixed convective of water-copper nanofluid in a C-shaped cavity with a heated corner is performed. The cavity is subjected to an inclined uniform magnetic field, and the top wall of the cavity is adiabatic and moves with a constant velocity. The governing equations are formulated by employing the single-phase nanofluid approach and the resulting equations have been solved by the Finite Volume Method (FVM). Impacts of the pertinent parameters on the fluid flow and heat transfer inside the cavity have been presented graphically. The numerical data have been plotted in the portrait of streamlines, isotherms and the average Nusselt numbers. The effects of volume fraction, Hartmann number, and the aspect ratio on the entropy generation and mixed convection of the C-shaped cavity are investigated. It is found that for an aspect ratio = 0.1, increasing the nanofluid volume fraction causes an increment in the heat transfer. At low volume fractions and Hartmann numbers, the outcomes manifest a better thermal performance. Generally, the rate of entropy generation increases by increasing both the Hartmann number and the volume fraction.

MHD thermogravitational convection and thermal radiation of a micropolar nanoliquid in a porous chamber

This work studies the thermogravitational transmission and thermal radiation of micropolar nanoliquid within a porous chamber in the presence of the uniform magnetic influence. The model includes the single-phase nanofluid approach, local thermal equilibrium approximation and Darcy law for the processes within the porous structure. The Galerkin finite element method with the structured non-uniform mesh is used to calculate the formulated equations. The key characteristics are the Darcy–Rayleigh number Ra = 10–1000, Darcy number Da = 10−5–10−1, porosity ε = 0.1–0.9, nanoparticles concentration φ = 0–0.04, radiation parameter Rd = 0–2, vortex viscosity characteristic Δ = 0–2, and Hartmann number Ha = 0–50. It has been ascertained the energy transport intensification with thermal radiation parameter, Darcy–Rayleigh number, porosity and nanoparticles concentration. Also, the results indicate that the average Nusselt number reduces with an increment of the Hartmann number for high values of the Rayleigh number, while for low magnitudes of the Rayleigh number a weak change of the average Nusselt number can be found.

Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis

Background and objectiveThe hydrodynamic stability of nanofluids of one phase is investigated in this paper based on linear stability theory. The overall thrust here is that the linear stability features of nanofluids can be estimated from their corresponding working fluid, at least in special circumstances. MethodsThe approach uses the adjusting parameter to make assertions about stability. This is possible by certain correlations between the resulting eigenvalues. ResultsIt is shown that as the nanoparticles are added, the mean flow of nanofluids is slightly modified and the resulting eigen space of nano disturbances is built on the corresponding pure flow eigen space of perturbations. Several fluid dynamics problems are revisited to verify the usefulness of the obtained correlations. ConclusionThe presented approach in this work serves us to understand the stabilizing/destabilizing effects of nanofluids as compared to the standard base fluids in terms of stability of viscous/inviscid and temporal/spatial senses. To illustrate, the critical Reynolds number in a traditional boundary layer flow is shown to be pushed to higher values with the dispersed nanoparticles in a working fluid, clearly implying the delay in transition from laminar to turbulent state.

Entropy formation analysis of MHD boundary layer flow of nanofluid over a porous shrinking wall

In the current paper, we investigate the entropy analysis of MHD boundary layer flow of copper (Cu)-water based nanofluid along with the porous shrinking wall. Heat transfer analysis is also taken into account with the thermal radiation effects. The single phase nanofluid model is used for the analysis of the effective thermal conductivity. Mathematical modeling is performed to change the physical system into a set of mathematical equations which are further simplified by using suitable variables. Exact solutions for the velocity and temperature profiles are computed and interpreted for diverse physical of interest. It is depicted that by enhancing the magnitude of solid volume fraction and velocity slip parameter of nanoparticles the velocity profile is increased. The results indicate an increment in the Hartman number increases the temperature and thermal boundary layer thickness. It is observed that the entropy generation profile is enhanced by increasing the value of Brinkman number and Reynolds number. The irreversibility parameter is decreasing function of Brinkman number.

Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium

Purpose This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

Flow and heat transfer of couple stress nanofluid sandwiched between viscous fluids

PurposeThe purpose of this study is a numerical analysis of steady-state heat transfer behavior of couple-stress nanofluid sandwiched between viscous fluids. It should be noted that this research deals with the development of a cooling system for the electronic devices.Design/methodology/approachStokes model is used to define the couple-stress fluid and the single-phase nanofluid model is used to define the nanofluid transport processes. The fluids in all regions are assumed to be incompressible, immiscible and the transport properties in all the three layers are assumed to be constant. The governing coupled linear ordinary differential equations are made dimensionless by using appropriate fundamental quantities. The exact solutions obtained for the velocity and temperature fields are evaluated numerically for various model parameters.FindingsThe results are demonstrated using different types of nanoparticles such as copper, silver, silicon oxide (SiO2), titanium oxide (TiO2) and diamond. The investigations are carried out using copper–water nanofluid for different values of couple-stress parameter a with a range of 0 = a = 12, solid volume fraction ϕ with a range of 0.0 ≤ ϕ ≤ 0.05, Eckert number Ec with a range of 0.001 ≤ Ec ≤ 6 and Prandtl number Pr with a range of 0.001 ≤ Pr ≤ 6. It was found that the Nusselt number increases by increasing the couple stress parameter, Eckert number and Prandtl number and it decreases with a growth of the solid volume fraction parameter. It was also observed that using SiO2–water nanofluid, the optimal Nusselt number is obtained. Further, using copper, silver, diamond and TiO2, nanoparticles and water as a base fluid does not show any significant changes in the rate of heat transfer. The couple-stress parameter enhances the velocity and temperature fields whereas the solid volume fraction suppresses the flow field for both Newtonian and couple-stress fluid.Originality/valueThe originality of this work is to analyze the heat transfer behavior of couple-stress nanofluid sandwiched between viscous fluids. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer and flow structures in nanofluids and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.

Free and circular jets cooled by single phase nanofluids

Abstract Nanofluids are widely known to enhance the heat transfer rate resulting in a cooled system. In the present paper, we show mathematically that the nanofluids indeed cool the system as the nanoparticles volume fraction is increased. The key role is explained for a two-dimensional laminar free nanofluid jet and for a circular axisymmetric free nanofluid jet issuing into the same nanofluid medium. Exact nanofluid flow results are obtained and, integral flux relations of momentum and thermal layers concerning five most studied nanofluids, respectively Ag, Cu, CuO, Al2O3 and TiO2, are derived. A shape factor is defined controlling the momentum layer thickness. By means of another shape factor representing the thermal layer thickness, the relevant energy equation enables one to identify the regimes of nanoparticle size leading to a coolant jet, without a need to solve the energy equation fully. Two recently popular nanofluid models, resulting in the same conclusion, are examined on the considered free nanofluid jets. Additionally, an exact temperature field associated with the laminar two-dimensional free jet of nanoparticles is obtained offering explicit support to the current approach.

Natural convection of magnetic hybrid nanofluid inside a double-porous medium using two-equation energy model

Porous media and nanofluids can be used for heat transfer enhancement in different industrial sectors. Very often technical systems consist of several porous layers. At the same time, hybrid nanofluids can be more effective in comparison with a nanofluid including only one kind of nanoparticles. The present study deals with a numerical analysis of MHD hybrid nanofluid natural convection heat transfer within the T-shaped cavity heated from the bottom and cooled from the upper chamber walls. Two different porous layers form the considered enclosure. The viscosity of the nanofluid depends on the magnetic field intensity. Governing equations written in dimensionless primitive variables using the extended Darcy–Brinkman–Forchheimer model for the porous medium, single-phase nanofluid model and local thermally non-equilibrium model were solved by the finite element method. Wide-range governing parameters impacts were examined to define the development of nanofluid flow and heat transfer inside the enclosure. Heat transfer enhancement can be gained for low values of the solid-liquid interface convection parameter, magnetic field viscosity parameter and high values of the thermal conductivity ratio.

Magneto-hydrodynamic natural convection of CuO-water nanofluid in complex shaped enclosure considering various nanoparticle shapes

PurposeThe purpose of this study is to peruse natural convection in a CuO-water nanofluid-filled complex-shaped enclosure under the influence of a uniform magnetic field by using control volume finite element method.Design/methodology/approachGoverning equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with the Koo–Kleinstreuer–Li correlation for the effective dynamic viscosity and the effective thermal conductivity have been solved numerically by control volume finite element method.FindingsEffects of various pertinent parameters such as Rayleigh number, Hartmann number, volume fraction of nanofluid and shape factor of nanoparticle on the convective heat transfer characteristics are analysed. It was observed that local and average heat transfer rates increase for higher value of Rayleigh number and lower value of Hartmann number. Among various nanoparticle shapes, platelets were found to be best in terms of heat transfer performance. The amount of average Nusselt number reductions was found to be different when nanofluids with different solid particle volume fractions were considered due to thermal and electrical conductivity enhancement of fluid with nanoparticle addition.Originality/valueA comprehensive study of the natural convection in a CuO-water nanofluid-filled complex-shaped enclosure under the influence of a uniform magnetic field by using control volume finite element method is addressed.

MHD natural convection of Cu/H2O nanofluid in a horizontal semi-cylinder with a local triangular heater

Purpose The purpose of this study is to investigate free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using control volume finite element method (CVFEM). Design/methodology/approach Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with Brinkman correlation for the effective dynamic viscosity and Hamilton and Crosser model for the effective thermal conductivity have been solved numerically by CVFEM. Findings The impacts of control parameters such as the Rayleigh number, Hartmann number, nanoparticles volume fraction, local triangular heater size, shape factor on streamlines and isotherms as well as local and average Nusselt numbers have been examined. The outcomes indicate that the average Nusselt number is an increasing function of the Rayleigh number, shape factor and nanoparticles volume fraction, while it is a decreasing function of the Hartmann number. Originality/value A complete study of the free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using CVFEM is addressed.

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das’ nanofluid model

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls (wavy and undulation numbers) are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.

The influence of thermal radiation on unsteady free convection in inclined enclosures filled by a nanofluid with sinusoidal boundary conditions

PurposeThe purpose of this study is a numerical analysis of transient natural convection in an inclined square cavity filled with an alumina-water nanofluid under the effects of sinusoidal wall temperature and thermal radiation by using a single-phase nanofluid model with empirical correlations for effective viscosity and thermal conductivity.Design/methodology/approachThe domain of interest includes the nanofluid-filled cavity with a sinusoidal temperature distribution along the left vertical wall. Horizontal walls are supposed to be adiabatic, while right vertical wall is kept at constant low temperature. Temperature of left wall varies sinusoidally along y-coordinate. It is assumed in the analysis that the thermophysical properties of the fluid are independent of temperature and the flow is laminar. The governing equations have been discretized using the finite difference method with the uniform grid. Simulations have been carried out for different values of the Rayleigh number, cavity inclination angle, nanoparticles volume fraction and radiation parameter.FindingsIt has been found that a growth of radiation parameter leads to the heat transfer enhancement and convective flow intensification. At the same time, an inclusion of nanoparticles illustrates a reduction in the average Nusselt number and fluid flow rate.Originality/valueThe originality of this work is to analyze unsteady natural convection in a square cavity filled with a water-based nanofluid in the presence of a sinusoidal temperature distribution along one wall. The results would benefit scientists and engineers to become familiar with the analysis of convective heat and mass transfer in nanofluids and the way to predict the properties of nanofluid convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.

Free convection of copper–water nanofluid in a porous gap between hot rectangular cylinder and cold circular cylinder under the effect of inclined magnetic field

Natural convection heat transfer of copper–water nanofluid in a porous gap between hot internal rectangular cylinder and cold external circular cylinder under the effect of inclined uniform magnetic field has been investigated. Domain of interest is a porous sector, where horizontal and vertical adiabatic borders are the external circular cylinder radii. Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the Brinkman-extended Darcy model for the porous medium, single-phase nanofluid model with Brinkman correlation for the nanofluid viscosity and Hamilton and Crosser model for the nanofluid thermal conductivity have been solved numerically by the control volume finite element method. Effects of the Rayleigh number, Hartmann number, Darcy number, magnetic field inclination angle, nanoparticles volume fraction, nanoparticles shape factor, nanoparticles material, nanofluid thermal conductivity and dynamic viscosity models and nanofluid electrical conductivity correlation on streamlines, isotherms, local and average Nusselt numbers have been studied. Obtained results have shown the heat transfer enhancement with the Rayleigh number, Darcy number, nanoparticles volume fraction and nanoparticles shape factor, while the heat transfer rate reduces with the Hartmann number and magnetic field inclination angle. At the same time, the average Nusselt number increases at about 16% when nanoparticles volume fraction rises from 0 till 4% for Ra = 105, Ha = 25, while for Ha = 0 one can find the heat transfer rate augmentation at about 9% for the same conditions. In the case of different nanofluid thermal conductivity and dynamic viscosity models, it has been found that KKL model reflects the heat transfer rate reduction with nanoparticles volume fraction, while for the Hamilton–Crosser–Brinkman model, the heat transfer rate increases. Comparison between the Maxwell correlation for the nanofluid electrical conductivity and the base fluid electrical conductivity illustrates an intensification of the convective heat transfer rate for high values of the Rayleigh number (Ra ≥ 104) in the case of Maxwell correlation for the nanofluid electrical conductivity. At the same time, the effect of the nanoparticles volume fraction becomes more significant when nanofluid electrical conductivity is a function of nanoparticles volume fraction.