Laminar forced convection heat transfer of water–Cu nanofluids in a microchannel was studied utilizing the lattice Boltzmann method (LBM). The entering flow was at a lower temperature compared to the microchannel walls. Simulations were performed for nanoparticle volume fractions of 0.00 to 0.04 and slip coefficient from 0.005 to 0.02. The model predictions were found to be in good agreement with earlier studies. The effects of wall slip velocity and temperature jump of the nanofluid were studied for the first time by using lattice Boltzmann method. Streamlines, isotherms, longitudinal variations of Nusselt number, slip velocity and temperature jump as well as velocity and temperature profiles for different cross sections were presented. The results indicate that LBM can be used to simulate forced convection for the nanofluid micro flows. Moreover, the effect of the temperature jump on the heat transfer rate is significant. Also, the results showed that decreasing the values of slip coefficient enhances the convective heat transfer coefficient and consequently the Nusselt number (Nu) but increases the wall slip velocity and temperature jump values.
Forced convection of non-Newtonian nanofluid, aqueous solution of carboxymethyl cellulose (CMC)–Aluminum oxide through a microtube is studied numerically. The length and diameter of tube are mm and mm, respectively which means the length is long enough compared to the diameter. The effects of different values of nanoparticles volume fraction, slip coefficient and Reynolds number are investigated on the slip velocity and temperature jump boundary conditions. Moreover the suitable validations are presented to confirm the achieved results accuracy. The results are shown as the dimensionless velocity and temperature profiles; however the profiles of local and averaged Nusselt number are also provided. It is seen that more volume fraction and slip coefficient correspond to higher Nusselt number especially at larger amounts of Re.
This article presents a numerical study of natural convection cooling of a heat source embedded on the bottom wall of an enclosure filled with nanofluids. The top and vertical walls of the enclosure are maintained at a relatively low temperature. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The results indicate that adding nanoparticles into pure water improves its cooling performance especially at low Rayleigh numbers. The type of nanoparticles and the length and location of the heat source proved to significantly affect the heat source maximum temperature.
Classical Nusselt’s condensate falling film theory is extended in this paper to the case when the base fluid is added ingredients of some frequently used popular nanoparticles. The resulting mixture, i.e, nanofluids, is analytically investigated either when the nanoparticles are uniformly distributed across the condensate boundary layer which is the most used model (single phase) in the literature, or when the concentration of nanoparticles through the film is allowed to vary from the wall to the outer edge of the condensate film in the light of modified Buongiorno’s nanofluid model (multi-phase) incorporating mechanisms of the Brownian and thermophoretic diffusion. In both theoretical cases, momentum and energy equations are solved analytically to deduce the flow and heat transport phenomena. As a result, the influences of employed nanofluids on the flow and heat of the condensate film are determined exactly. When the concentration of nanoparticles is assumed constant both models are shown to coincide. Otherwise, effects of nanofluids as compared to the regular fluid on the velocity profiles, the mass flow rate, the thickness of the condensate film and the Nusselt number are easy to conceive from both single and multi-phase models. In particular, the theoretical treatment in both models enables us to understand the heat transfer enhancement feature of the nanofluids models. When the diffusion parameter is increased in the multi-phase model, more enhancement in the rate of heat transfer is observed. In agreement with the experimental evidences, the water-based nanofluid with nanoparticles is the best heat transferring mixture.
This work is focused on the numerical modeling of steady laminar mixed convection flow in a lid-driven inclined square enclosure filled with water–Al O nanofluid. The left and right walls of the enclosure are kept insulated while the bottom and top walls are maintained at constant temperatures with the top surface being the hot wall and moving at a constant speed. The developed equations are given in terms of the stream function–vorticity formulation and are non-dimensionalized and then solved numerically subject to appropriate boundary conditions by a second-order accurate finite-volume method. Comparisons with previously published work are performed and found to be in good agreement. A parametric study is conducted and a set of graphical results is presented and discussed to illustrate the effects of the presence of nanoparticles and enclosure inclination angle on the flow and heat transfer characteristics. It is found that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.
This work is focused on the numerical modeling of steady laminar mixed convection flow in single and double-lid square cavities filled with a water–Al O nanofluid. Two viscosity models are used to approximate nanofluid viscosity, namely, the Brinkman model and the Pak and Cho correlation. The developed equations are given in terms of the stream function–vorticity formulation and are non-dimensionalized and then solved numerically by a second-order accurate finite-volume method. Comparisons with previously published work are performed and found to be in good agreement. A parametric study is conducted and a selective set of graphical results is presented and discussed to illustrate the effects of the presence of nanoparticles and the Richardson number on the flow and heat transfer characteristics in both cavity configurations and to compare the predictions obtained by the two different nanofluid models. It is found that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by increasing the nanoparticle volume fractions at moderate and large Richardson numbers using both nanofluid models for both single- and double-lid cavity configurations. However, for small Richardson number, the Pak and Cho model predicts that the presence of nanoparticle causes reductions in the average Nusselt number in the single-lid cavity configuration.
Natural convection of a nanofluid in a square cavity filled with a porous matrix is numerically investigated using a meshless technique. The Darcy–Brinkman and the energy transport equations are used to describe the nanofluid flow and the heat transfer process in the porous medium as these are generated by heating one of the cavity walls. The role of the nanofluid properties in the cooling performance of the medium and in the relevant heat process is thoroughly investigated. Numerical results are obtained for the stream function, the temperature profile, and the Nusselt number over a wide range of dimensionless quantities (Rayleigh number between 10 and 10 , Darcy number between 10 and 10 ). The effect of the porous medium in the cooling efficiency of the nanofluidic system is also discussed. Alternative expressions are suggested for the estimation of the effective conductivity and the thermal expansion coefficient of the nanofluid and their effects on the heat transfer problem are investigated. Excellent agreement with experimental data and trends as well as with previously published numerical results for less complicated systems was found.
Recently, an analytical solution was derived for the governing equations of condensate laminar film from stationary vapors on curved vertical walls of convex/concave shape (Soliman et al., 2014). The present research paper develops a theory covering the impacts of different nanofluids and derives further closed-form solutions concerning the hydrodynamic and thermal transport through the condensate film over curved walls when the single phase and two-phase models of nanofluids are taken into account. From both approaches, exact expressions are obtained for the velocity and temperature fields as well as the shear stress, thickness and Nusselt number of the film influenced by the presence of nanoparticles of frequently used nanofluids in the literature. It is found that heat transfer is enhanced, even more in the two-phase model case in the presence of nanoparticles. The concentration of nanoparticles favors the best rate of heat transfer among the considered nanofluids.
The paper investigates the energy conservation properties of two well-known projection-based particle methods, namely, MPS and ISPH methods. The enhancing effects of a set of refined schemes including Higher order Source term (HS), Higher order Laplacian (HL), Error Compensating Source (ECS), Dynamic Stabilizer (DS) and pressure Gradient Correction (GC) are shown through the simulations of a standing wave, oscillating drop and impacts of two fluid patches. The results highlight the superiority of corrected Taylor series consistent pressure gradient models for projection-based particle methods in providing accurate results with the best energy conservation as well as accurate reproductions of physical dissipations in fluid impact problems.
The present paper is a theoretical investigation on effects of nanoparticle migration and asymmetric heating on forced convective heat transfer of alumina/water nanofluid in microchannels in presence of a uniform magnetic field. Walls are subjected to different heat fluxes; for top wall and for bottom wall, and because of non-adherence of the fluid–solid interface due to the microscopic roughness in microchannels, Navier’s slip boundary condition is considered at the surfaces. A two-component heterogeneous mixture model is used for nanofluid with the hypothesis that Brownian motion and thermophoretic diffusivities are the only significant slip mechanisms between solid and liquid phases. Assuming a fully developed flow and heat transfer, the basic partial differential equations including continuity, momentum, and energy equations have been reduced to two-point ordinary boundary value differential equations and solved numerically. It is revealed that nanoparticles eject themselves from heated walls, construct a depleted region, and accumulate in the core region, but more likely to accumulate near the wall with lower heat flux. Also, the non-uniform distribution of nanoparticles causes velocities to move toward the wall with a higher heat flux and enhances heat transfer rate there. In addition, inclusion of nanoparticles in a very strong magnetic field and slip velocity at the walls has a negative effect on performance.
This paper presents a linear stability analysis for the onset of natural convection in a horizontal nanofluid layer. The employed model incorporates the effects of Brownian motion and thermophoresis. Both monotonic and oscillatory convection for free–free, rigid–rigid, and rigid–free boundaries are investigated. The oscillatory instability is possible when nanoparticles concentrate near the bottom of the layer, so that the density gradient caused by such a bottom-heavy nanoparticle distribution competes with the density variation caused by heating from the bottom. It is established that the instability is almost purely a phenomenon due to buoyancy coupled with the conservation of nanoparticles. It is independent of the contributions of Brownian motion and thermophoresis to the thermal energy equation. Rather, the Brownian motion and thermophoresis enter to produce their effects directly into the equation expressing the conservation of nanoparticles so that the temperature and the particle density are coupled in a particular way, and that results in the thermal and concentration buoyancy effects being coupled in the same way.
Laminar forced convection flow of nanofluids in a wide rectangular micro-channel has been numerically studied. The present study investigated the flow and heat transfer characteristics of Aluminium oxide (Al O ), silver (Ag) and hybrid (Al O +Ag) nanofluids in a micro-channel. The conduction phenomena of the solid region show a significant effect on the heat transfer characteristics of nanofluid. Hence, the channel is considered with finite thickness on its bottom to accommodate heat source or electronic component and a uniform heat flux is applied to the three sides of the solid region. A two-dimensional conjugate heat transfer homogeneous phase model has been developed and results are reported for different Reynolds numbers. The governing equations are solved by Simplified Marker and Cell (SMAC) algorithm on non-staggered grid using finite volume method. The effects of Reynolds number, pure nanoparticles volume concentration, hybrid nanoparticles mixture volume concentrations and nanoparticles size on the flow and heat transfer characteristics are reported. The results show that the average convective heat transfer coefficient increases with increase in nanoparticles volume concentration and Reynolds number. The nanofluids obtained by dispersing nanoparticles such as Al O , Ag and hybrid (Al O +Ag) in the base fluid shows a significant enhancement of average convective heat transfer coefficient in comparison with pure water. It is also observed that 3 vol.% hybrid nanofluid (0.6 vol.% Al O +2.4 vol.% Ag) shows higher average convective heat transfer coefficient than that of pure water, pure oxide (Al O ) and pure metallic (Ag) nanofluids. The study presents that hybrid nanofluids are the new class of working fluids with less volume concentration of metallic (Ag) nanoparticles. Moreover, use of hybrid nanofluids at high volume concentration reduces the cost of the working fluid and enhances the heat transfer characteristics in comparison with that of metallic nanofluids. The interface temperature between solid and fluid regions are reported for different nanofluids. The size of the nanoparticle shows significant effect on heat transfer characteristics. The present results are matching with the numerical and experimental results available in the literature.
The traditional laminar plane wall jet is studied when the medium is filled with nanoparticles of Ag, Cu, CuO, Al O and TiO . It is aimed to understand the effects of several nanofluids on the heat and flow behaviors of the wall jet. Momentum and thermal integral flux relations are obtained initially. Later on, some important shape factors are defined designing the momentum boundary layer, shear layer as well as the thermal boundary layer when the wall is subjected to either adiabatic or isothermal wall constraints. By means of these parameters, the flow field is shown to be decelerated and as a consequence the shear stress on the wall is enhanced. Without solving the energy equation, the thermal layer shape factor enables one to fully seize the cooling effect of considered nanofluids for both adiabatic and isothermal wall cases. As a result, the heat transfer rate is found to be greatly enhanced by the presence of nanoparticles. Same conclusions are reached by two different popular nanofluid models made use in the recent nanofluid researches.
The present work deals with the development and application of a 2D Smoothed Particle Hydrodynamics (SPH) model to simulate a broad range of open-channel flows. Although in the last decades the SPH modelling has been widely used to simulate free-surface flows, few applications have been performed for free-surface channels. For this reason, an appropriate algorithm is developed to enforce different upstream and downstream flow conditions and simulate uniform, non-uniform and unsteady flows. First, the proposed algorithm is validated for a viscous laminar flow in open channel characterized by Reynolds numbers of order . The second test case deals with a hydraulic jump for which different upstream and downstream conditions are needed. Varying the Froude number, several types of jumps are investigated with specific focus on the velocity field, pressure forces, water depths and location of the jump. Comparisons between numerical results, theory and experimental data are provided. Finally, the interaction between a flash flood generated by an unsteady inflow condition and a bridge is shown as an example of an engineering application.
A potential flow model is derived for a large flap-type oscillating wave energy converter in the open ocean. Application of Green’s integral theorem in the fluid domain yields a hypersingular integral equation for the jump in potential across the flap. The solution is found via a series expansion in terms of the Chebyshev polynomials of the second kind and even order. Several relationships are then derived between the hydrodynamic parameters of the system. Comparison is made between the behaviour of the converter in the open ocean and in a channel. The degree of accuracy of wave tank experiments aiming at reproducing the performance of the device in the open ocean is quantified. A parametric analysis of the system is then undertaken. In particular, it is shown that increasing the flap width has the beneficial effect of broadening the bandwidth of the capture factor curve. This phenomenon can be exploited in random seas to achieve high levels of efficiency.
In this study, the sources of uncertainty of hot-wire anemometry (HWA) and oil-film interferometry (OFI) measurements are assessed. Both statistical and classical methods are used for the forward and inverse problems, so that the contributions to the overall uncertainty of the measured quantities can be evaluated. The correlations between the parameters are taken into account through the Bayesian inference with error-in-variable (EiV) model. In the forward problem, very small differences were found when using Monte Carlo (MC), Polynomial Chaos Expansion (PCE) and linear perturbation methods. In flow velocity measurements with HWA, the results indicate that the estimated uncertainty is lower when the correlations among parameters are considered, than when they are not taken into account. Moreover, global sensitivity analyses with Sobol indices showed that the HWA measurements are most sensitive to the wire voltage, and in the case of OFI the most sensitive factor is the calculation of fringe velocity. The relative errors in wall-shear stress, friction velocity and viscous length are , and , respectively. Note that these values are lower than the ones reported in other wall-bounded turbulence studies. Note that in most studies of wall-bounded turbulence the correlations among parameters are not considered, and the uncertainties from the various parameters are directly added when determining the overall uncertainty of the measured quantity. In the present analysis we account for these correlations, which may lead to a lower overall uncertainty estimate due to error cancellation Furthermore, our results also indicate that the crucial aspect when obtaining accurate inner-scaled velocity measurements is the wind-tunnel flow quality, which is more critical than the accuracy in wall-shear stress measurements.
In this study MHD flow in a lid driven nanofluid filled square cavity with a flexible side wall is numerically investigated. The top wall of the cavity is colder than the bottom wall and it moves in the direction with constant speed. Other walls of the cavity are insulated. The finite element formulation is utilized to solve the governing equations. The Arbitrary-Lagrangian-Eulerian method is used to describe the fluid motion with the flexible wall of the cavity in the fluid–structure interaction model. The influence of the Young’s modulus of the flexible wall on the flow and heat transfer characteristics are numerically investigated for the following parameters: ( ), with a Richardson number of ( ), a Hartmann number of ( ) and a volume fraction of the solid particles given by ( ). The effect of Brownian motion on the effective thermal conductivity of the nanofluid is taken into account. Averaged heat transfer decreases with increasing Hartmann number and decreasing Richardson numbers. As the Young’s modulus of the flexible wall decreases, the averaged heat transfer increases and 66.5% of the heat transfer enhancement is obtained for compared with . An averaged heat transfer enhancement of 33.87% is obtained for a solid volume fraction of 4% compared to the base fluid for the fluid–structure model coupled with the magnetic field.