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The present article investigates the effect of second-order slip, chemical reaction and Soret and Dufour effects on MHD convective flow of an Oldroyd-B liquid toward a stretchy surface. Analysis of thermal relaxation time is made by using Cattaneo-Christov heat flux model. The effects of radiation and convective heating are also taken into account. The ordinary differential equations are retrieved by the help of suitable transformations of governing equations. The analytical solutions are observed by homotopy progress. The velocity, concentration and temperature field are analyzed for various pertinent parameters involved in the study. The graphical results of physical quantities of interest such as skin friction, local Nusselt number and local Sherwood number are presented. A comparative study with existing result indicates excellent agreement. [ABSTRACT FROM AUTHOR]

The aim of the present study is to analyze the convective flow and heat transfer of nanofluid in an inclined cavity filled with heat generating porous medium using the local thermal non-equilibrium model. The horizontal bottom wall of the cavity is maintained at a constant higher temperature while the left and right vertical walls are maintained at a constant lower temperature. The top wall is to be kept as adiabatic. The Darcy model is adopted for flow through the porous medium and the Boussinesq approximation is taken into account. The pores are saturated by a water-based nanofluid consisting of Cu nanoparticles. The governing equations are solved iteratively by finite difference based Alternating Direction Implicit (ADI) method. The results are discussed by various combinations of parameters involved in the study. The average heat transfer rate decreases when increasing the values of nanoparticle volume fraction for the case of high Rayleigh numbers. The heat transfer rate is enhanced by increasing values of the modified conductivity ratio and the porosity of the media. The results have possible applications in the heat-storage nanofluid-saturated porous systems. [ABSTRACT FROM AUTHOR]

The effects of subcooled flow boiling of nanofluids (Al2O3/water and Cu/water) through a vertical heated pipe are investigated numerically considering a number real flow factors such as uneven particle distributions and particle deposition on the wall surface. The results from the Eulerian-Eulerian two-phase model (liquid/nanofluid-gas) and those of the Eulerian-Lagrangian three-phase model (liquid-gas particles) are compared in detail. For the heat transfer coefficient prediction, the latter model gives about 6% error, whereas the Eulerian-Eulerian model gives about 12% error when it is compared with Chen's correlation. The uneven distribution of nanoparticles concentrations, i.e., lower near the tube wall and higher at the pipe center, is well predicted by the Eulerian-Lagrangian model. On top that, for the first time, the changes on heating surface wettability induced by nanoparticles deposition is included via user define functions. [ABSTRACT FROM AUTHOR]

A steady stagnation point flow of an incompressible Williamson nanofluid towards a horizontal linearly stretching/shrinking sheet with active and passive controls on the wall mass flux is numerically studied. The governing partial differential equations are reduced into a system of ordinary differential equations using a similarity transformation and are solved using the bvp4 c package in MATLAB. The velocity, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, reduced Nusselt number and reduced Sherwood number are graphically presented to visualize the effects of parameters involved in the study. Results show that temperature and nanoparticle volume fraction are decreasing functions of the stagnation parameter, r. It is also found that the diffusivity ratio $$N_{\mathrm{bt}}$$ and Lewis number Le have almost negligible effects on heat transfer rate in passive control. Increasing value of Williamson parameter $$\lambda$$ will increase the skin friction in both stretching and shrinking surfaces. [ABSTRACT FROM AUTHOR]

The axisymmetric flow of a nanoparticles-saturated fluid with existence of thermic radiation over a stretched sheet is investigated. The effects of zero (passive control) as well as nonzero fluxes (active control) of nanoparticles on the plate on distributions of temperature and volumetric fraction of nanoparticles are investigated together comparatively. Through the supposition of boundary layer, the Navier-Stokes equations are simplified hence converted into non-dimensional form by similarity transformation. A shooting technique is engaged to deal with the emerging nonlinear system of ordinary differential equations numerically in MATLAB software. Several distributions of velocity, thermal energy, and volumetric fraction of nanoparticles under zero/nonzero normal flux are graphically demonstrated. The impact of the parameters on the reduced coefficient of skin friction, Nur and Shr, are also investigated. The presence of thermic radiation under consideration of both zero and nonzero normal fluxes has significant effects on the intensification of the flow heat transfer. Thermophoresis enhances the heat conductivity performance in the case of zero fluxes of nanoparticles. [ABSTRACT FROM AUTHOR]

A numerical simulation of magneto-hydrodynamic mixed convection flow and heat transfer of Cu–water nanofluid in a square cavity filled with a Darcian porous medium with a partial slip is numerically investigated. The left and right walls of the cavity are moving up with a constant speed in vertical direction, and the partial slip effect is considered along these walls. The top and bottom walls of the cavity are assumed to be adiabatic. The right vertical wall of the cavity is assumed to be kept at a lower temperature, while the left vertical wall is kept at a higher temperature. The developed equations of the mathematical model are nondimensionalized and then solved numerically subject to appropriate boundary conditions by the finite-volume method. A parametric study is performed and a set of graphical results is presented and discussed to demonstrate interesting features of the solution. [ABSTRACT FROM PUBLISHER]

• MHD nanofluid squeezed flow within two parallel plates is studied. • Heat and mass transfer with chemical reaction is examined. • Differential Transformation Method is used to solve the equations. • The temperature decreases with rise in squeezing parameter and Hartmann number. • The mass transport enhances with enhance in squeezing parameter. This article presents the investigation relating to the mass and heat transfer characteristics of MHD copper–water unsteady incompressible nanofluid flow squeezed within two parallel plates in the presence of applied magnetic field and chemical reaction by employing a systematic method called Differential Transformation Method (DTM) and numerically solved using Runge–Kutta–Fehlberg method. The distinct feature is the inclusion of chemical reaction term of order greater than or equal to one. The governing nonlinear two-dimensional PDEs are altered into ODEs using similarity transformations. The flow, heat and mass transfer results thus found are validated with previous investigations. Effects of squeezing parameter, Eckert and Hartmann numbers on velocity, thermal and mass transfer profiles are analysed and the behaviour of squeeze number on skin friction, Sherwood and Nusselt numbers are dissertated and concluded by means of diagrams. Through this study, it is found that the concentration field reduces for positive values of Cr and rises for negative values of Cr whereas Sherwood number decreases when Cr increases. Increment in order of chemical reaction parameter results in increasing solutal profile. [ABSTRACT FROM AUTHOR]

This paper examines numerically by using the finite difference method the laminar steady magneto-hydrodynamic natural convection in an inclined T-shaped enclosure filled with different types of nanofluids. A uniform heat source is embedded on a part of the upper wall of the enclosure. Both left and right sidewalls of the enclosure leg are maintained at a constant cold temperature, while the other portions of the enclosure walls are considered adiabatic. A magnetic field is applied vertically downward on the bottom wall of the enclosure. Based on the numerical results, the effects of the dominant parameters such as Rayleigh number, Hartmann number, inclination angle, solid volume fraction, location and length of the heat source and enclosure aspect ratio are examined. The numerical results are obtained for Hartmann number varying as 0 ⩽ Ha ⩽ 100, inclination angle varying as 0 ⩽ Φ ⩽ 90°, Rayleigh numbers varying as 10 3 ⩽ Ra ⩽ 10 6 , aspect ratio 0.3 ⩽ AR ⩽ 0.9, heat source length 0.2 ⩽ B ⩽ 0.8, heat source location 0.2 ⩽ D ⩽ 0.5 and the solid volume fractions varying as 0 ⩽ ϕ ⩽ 0.2. Comparison with previously published numerical work is performed and a good agreement between the results is observed. It is found that the mean Nusselt number increases with the increase of Rayleigh number, inclination angle, aspect ratio, heat source location and volume fraction of nanoparticles, while, it decreases when the Hartmann number and heat source length increase. [ABSTRACT FROM AUTHOR]

Numerical results of the thermal and hydraulic characteristics of pulsating laminar flow in a three-dimensional helical microchannel heat sink (HMCHS) filled with a porous medium using Al 2 O 3 –water based nanofluid are presented in this paper. The two-phase mixture model with modified effective thermal conductivity and viscosity equations were used to solve the laminar flow governing equations. The detailed results for thermal and flow fields are reported for the effects of amplitude (1–3) and frequency (5–20 rad/s). The presence of porous media led to better thermal enhancement and significant improvement in heat transfer performance was observed for sinusoidal velocity inlet conditions as compared to steady flow conditions. In addition, the proposed model showed better accuracy in predicting nanofluid flow. [ABSTRACT FROM AUTHOR]

Numerical investigations on the thermal and hydraulic characteristics of pulsating laminar flow in a three-dimensional helical microchannel heat sink (HMCHS) model are performed using Al2O3-water-based nanofluid. The simulation is performed in the laminar regime for Reynolds number ranging from 6 to 25. The two-phase mixture model with modified effective thermal conductivity and viscosity equations is employed to solve the problem numerically. The detailed results for thermal and flow fields are reported for the effects of amplitude (1–3), frequency (5–20 rad/s), and nanoparticle concentration (1%–3%). The results indicate that the heat transfer performance improves significantly for sinusoidal velocity inlet conditions compared with steady flow conditions. [ABSTRACT FROM AUTHOR]

This study compares the prediction of two types of Computational Fluid Dynamics (CFD) models to investigate the turbulent forced convection of the Cu-water nanofluid in a tube with a constant heat flux on the tube wall. One of the CFD models is based on a single-phase (or homogeneous) model and the other is the Eulerian–Eulerian (two-fluid) two-phase model. The Reynolds number is between 10,000 and 25,000, whereas the volume fraction of the Cu particles is in the range of 0–1.5%. The results from the CFD models are compared with the results from experimental investigations in the literature. Both the single-phase and two-phase models overpredict the Nusselt number in most of the cases investigated. Unexpectedly, the two-phase model was found to be relatively less accurate than the single-phase model. The present study suggests a correction of the two-phase model in terms of selecting an appropriate effective conductivity of the solidus phase and this has resulted in a significant improvement in the predictions of the accuracy of the model. A correlation describing the effective conductivity of the solidus phase of Cu-water nanofluid as a function of the Reynolds number and particle concentrations is developed for use in the Eulerian–Eulerian two-phase model. To the best of our knowledge, such an improvement to a two-phase model has been presented for the first time. [ABSTRACT FROM AUTHOR]

A three-dimensional helical microchannel heat sink (HMCHS) model is developed to investigate the heat transfer characteristics using Al2O3–water-based nanofluid. The two-phase mixture model with modified effective thermal conductivity and viscosity equations is employed for solving the problem numerically. The model developed is validated by comparing the results of Nusselt number with available experimental and numerical data for a wide range of Reynolds number. The detailed results of the thermal field are reported for the effects of helix radius (0.15–0.30 mm), pitch (0.5–2.0 mm), number of turns (7–10), and aspect ratio (1.5–3.0). The analysis presents a unique fundamental insight into the complex secondary flow pattern in the channel due to curvature effects. [ABSTRACT FROM PUBLISHER]

The present study analyzed convective heat transfer and fluid flow characteristics of nanofluid in a two-dimensional square cavity under different combinations of thermophysical models of nanofluids. The right vertical wall temperature is varying linearly with height and the left wall is maintained at low temperature whereas the horizontal walls are adiabatic. Finite volume method is used to solve the governing equations. Two models are considered to calculate the effective thermal conductivity of the nanofluid and four models are considered to calculate the effective viscosity of the nanofluid. Numerical solutions are carried out for different combinations of effective viscosity and effective thermal conductivity models with different volume fractions of nanoparticles and Rayleigh numbers. It is found that the heat transfer rate increases for Models M1 and M3 on increasing the volume fraction of the nanofluid, whereas heat transfer rate decreases for Model M4 on increasing the volume fraction of the nanoparticle. The difference among the effective dynamic viscosity models of nanofluid plays an important role here such that the average Nusselt number demonstrates an increasing or decreasing trend with the concentration of nanoparticle. [ABSTRACT FROM AUTHOR]

A numerical study is performed to investigate the effects of amplitude and phase deviation of sinusoidal temperature distribution on the convective flow and heat transfer of nanofluids in a square cavity. The horizontal walls of the cavity are adiabatic. The governing equations are solved by the finite volume method with the SIMPLE algorithm. The results are discussed for different combinations of phase deviation, amplitude ratio, volume fraction of nanoparticles, and Rayleigh numbers. It is observed that the heat transfer rate is increased when increasing the amplitude ratio and volume fraction of nanoparticles. The heat transfer rate behaves nonlinearly with the Rayleigh number and the phase deviation, attaining the maximum at 3π/4. [ABSTRACT FROM AUTHOR]

This study compares the predictions of five types of computational fluid dynamics (CFD) models, including two single-phase models (i.e. Newtonian and non-Newtonian) and three two-phase models (Eulerian–Eulerian, mixture and Eulerian–Lagrangian), to investigate turbulent forced convection of Cu–water nanofluid in a tube with a constant heat flux on the tube wall. The Reynolds (Re) number of the flow is taken between 10,000 and 25,000, while the volume fraction of Cu particles used is in the range of 0% to 2%. The results from the CFD models are compared with results of experimental investigations from literature. According to the results of this study, the non-Newtonian single-phase model, in general, does not show a good agreement with Xuan and Li's correlation in the prediction of the Nu number. The Eulerian–Eulerian model gives inaccurate results except for φ = 0.5%. The mixture model gives a maximum error of 15%. The Newtonian single-phase model and Eulerian–Lagrangian model, overall, are the recommended models. This work can be used as a reference for selecting an appropriate model for future investigation. The study also gives a proper insight into the important factors such as the Brownian motion, fluid behavior parameters and effective nanoparticle conductivity which should be considered or changed by each model. [ABSTRACT FROM AUTHOR]

Highlights: [•] Nu increases with solid volume fraction. [•] Nano fluid affects boundary layer. [•] Nu increases with Re. [ABSTRACT FROM AUTHOR]

Highlights: [•] Convection very strong when Ra is high and Ha =0. [•] Isotherms smooth when Ra is low and Ha is high. [•] Maximum stream function increases by adding nano-particle. [•] Flow circulation decreases when magnetic orientation angle increases. [•] Nusselt number ratio increases when Ra increases. [ABSTRACT FROM AUTHOR]