In this work, three dimensional flow of a fluctuating nanofluid is examined in moving (rotating) coordinates. Carbon nanotubes (multi-wall carbon nanotubes (MWCNTs)/single-wall carbon nanotubes (SWCNTs)) are taken as nanoparticles whereas water is considered as the base fluid. Xue's model for effective thermal conductivity (carbon nanotube based composite) is utilized. Entropy generation is analyzed in the presence of both homogeneous and heterogeneous mass concentrations. The dimensionless variables are introduced to obtain the dimensionless form of the boundary layer equations along with the entropy augmentation equation. Equations are then solved using an explicit scheme based on the finite differences, and the behaviour of the entropy augmentation, Bejan number and temperature is elaborated. The effects of various dimensionless parameters such as Reynolds number, Brinkman number and radiation parameter on the entropy augmentation rate, and Bejan number are presented graphically for MWCNTs and SWCNTs. Variation in the engineering coefficients (Nusselt number, skin friction, Sherwood number) are shown with various emerging parameters for MWCNTs and SWCNTs. It is found that the entropy augmentation rate can be controlled by minimizing the action of the Brinkman and Reynolds numbers. The results also reveal that the heat transfer (rate) is bigger for SWCNTs in relation to MWCNTs.
A two-dimensional numerical study has been performed to investigate natural convection in a square cavity with curve boundaries filled with Cu–water nanofluid. Lattice Boltzmann Method (LBM) is used to simulate this problem. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. This investigation was compared with other numerical methods and was found to be in excellent agreement. Effects of nanoparticle volume fraction, Rayleigh numbers and inclination angle on flow and heat transfer are considered. The results proved that the change of inclination angle has a significant impact on the thermal and hydrodynamic flow fields. Also it can be found that maximum values of enhancement are obtained at Ra =103 and Ra =105 for γ >0° and γ <0°, respectively.
In this study natural convection heat transfer of Cu–water nanofluid in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder in the presence of horizontal magnetic field is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both circular enclosure and inner cylinder are maintained at constant temperature. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations were performed for different governing parameters such as the Hartmann number, Rayleigh number, values of the number of undulations of the inner cylinder and nanoparticle volume fraction. The results indicate that in the absence of magnetic field, enhancement ratio decreases as Rayleigh number increases while an opposite trend is observed in the presence of magnetic field. Also it is found that the average Nusselt number is an increasing function of nanoparticle volume fraction, the number of undulations and Rayleigh numbers while it is a decreasing function of Hartmann number.
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In this paper, condensing pressure drop of refrigerant-based nanofluid inside a tube is studied. Isobutene was selected as the base fluid while CuO nanoparticles were utilized to prepare nano-refrigerant. However, for the feasibility of nanoparticle dispersion into the refrigerant, Polyester oil (POE) was utilized as lubricant oil and added to the pure refrigerant by 1% mass fraction. Various values of mass flux, vapor quality, concentration of nanoparticle are investigated. Results indicate that adding nanoparticles leads to enhance frictional pressure drop. Nanoparticles caused larger pressure drop penalty at relatively lower vapor qualities which may be attributed to the existing condensation flow pattern such that annular flow is less influenced by nanoparticles compared to intermittent flow regime.
There are several methods that can be used to solve the governing equations of fluid flow and heat transfer, such as the finite difference method, the finite volume method (FVM), and the finite element method (FEM). The control volume finite element method (CVFEM) comprises interesting characteristics from both the FVM and FEM. The CVFEM combines the flexibility of the FEMs to discretize complex geometry with conservative formulation of the FVMs, in which the variables can be easily interpreted physically in terms of fluxes, forces, and sources. This chapter highlights the basic concept of CVFEM. The necessary ingredients in numerical solutions are discussed.
The electrohydrodynamic method can be one of the most promising methods among various active techniques because of its several advantages, e.g., simplified implementation using only a transformer and electrodes. Applying an electric field leads to generation of Coulomb force. Nanofluid flow in existence of an electric field has been investigated in this chapter.
Radiative nanomaterial thermal behavior within a permeable closed zone with elliptic hot source is simulated. Darcy law is selected for simulating permeable media in existence of magnetic forces. Contour plots for various buoyancy, Hartmann numbers and radiation parameter were illustrated. Carrier fluid is Al2O3-water with different shapes. Outputs prove that conduction mode augments with enhance of Ha. Nu augments with considering radiation source term.
In this paper magnetohydrodynamic free convection flow of CuO–water nanofluid in a square enclosure with a rectangular heated body is investigated numerically using Lattice Boltzmann Method (LBM) scheme. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. The influence of pertinent parameters such as Hartmann number, nanoparticle volume fraction and Rayleigh number on the flow, heat transfer and entropy generation have been examined. The results show that the heat transfer rate and Dimensionless entropy generation number increase with increase of the Rayleigh number and nanoparticle volume fraction but it decreases with increase of the Hartmann number.
The effects of CaSO<sub>4</sub> on CaCo<sub>3</sub> fouling had been studied in the batch tests at 60, 70 and 80°C. Calcium carbonate was the dominant salt and the total initial concentration of calcium was constant in all the runs. The solubility product and rate constants were determined. The results indicated that co-precipitation even in minute amount affect the thermodynamics, kinetics and the scale structure. Solubility and rate constants for the pure salt precipitation are not applicable to co-precipitation. Presence of CaSO<sub>4</sub> increased the solubility constant for the calcium carbonate in co-precipitation; the solubility product increased from 65% to 280% when CaSO<sub>4</sub> was added to the solution. The rate equation suggested by Nancollas and Reddy [1] was not applicable to the experimental data. The addition of CaSO<sub>4</sub> slowed down caCO<sub>3</sub> precipitation. The general observations indicated that the presence of CaSO<sub>4</sub> had weakened the CaCo<sub>3</sub> scale that is usually a very adherent scale.
This article deals with the numerical simulation to examine the significant effects of MHD flow and nanoparticle migration inside a permeable space including two temperature model. For more physical situation, thermal radiation influence is considered. Viable transformation is assumed to alter the governing set of PDEs into dimensionless form. CVFEM was adopted to model this article. Impacts of radiation parameter, Rayleigh number (103 < Ra < 104), nanofluid–solid interface factor (10 < Nhs <1000), Hartmann number (0 < Ha < 20) and nanoparticles’ shape (3 < m < 5.7) on nanofluid behavior were demonstrated. Outcomes depict that stronger convection can be obtained with augmenting in shape factor. Average Nusselt number increases as enhancing the buoyancy and radiation effect whereas decreases as enhancing nanofluid–solid interface factor and Hartmann number. Comparison of the numerical outputs achieved by means of CVFEM with published data was also deliberated. It is evident that the applied approach is very accurate to investigate solution of the discussed problem.
Magnetohydrodynamic and ferrohydrodynamic are investigated in this chapter. The existence of a magnetic field has a noticeable effect on heat transfer reduction under natural convection and mixed convection, but in many engineering applications such as magnetic sensors, magnetic storage media, and cooling systems of electronic devices, increasing heat transfer from solid surfaces is a goal. Therefore, the effect of the magnetic field on nanofluid flow and heat transfer has been considered via several examples. There are two models for simulating nanofluid flow and heat transfer: single phase and two phase. In the single-phase model, nanoparticles are in thermal equilibrium, and there are not any slip velocities between the nanoparticles and fluid molecules; thus, they have a uniform mixture of nanoparticles. In the two-phase model, the nanoparticles cannot accompany the fluid molecules because of some slip mechanisms such as Brownian motion and thermophoresis, so the volume fraction of the nanofluid may not be uniform anymore, and there would be a variable concentration of nanoparticles in a mixture. Finally, the governing equations for natural convection and mixed convection of nanofluids are presented considering a magnetic field.
In this article, the effect of magnetic field on the Nanofluid flow inside a sinusoidal two-tube heat exchanger is investigated numerically. This study focuses on the influence of variable magnetic field in the heat transfer of heat exchanger while mixture is single phase. In this heat exchanger, the inner tube is sinusoidal and the outer tube is considered smooth. The magnetic field is established orthogonal to sinusoidal tube. The basis fluid is water with 4vol.% Nano particles (Fe3O4). In our study, Ferrofluid flows in the internal tube (sinusoidal tube) as hot fluid and air flows counter currently as cold fluid in external tube. The finite volume method with the SIMPLEC algorithm is used for handling the pressure⿿velocity coupling. The numerical results present validated data with experimentally measured data and show good agreement with measurement. The influence of the variation of different parameters like geometric shape, intensity of magnetic field non-dimensional number and Reynolds number, on heat transfer is investigated. According to obtained results, sinusoidal formation of the internal tube significantly increases the Nusselt number inside a two-tube heat exchanger. Also, magnetic field enhances diffusion of the cold boundary layer to the central parts of the inner tube for various geometric shape coefficients. Our findings show that the diffusion also elevates as the intensity of the magnetic field is increased. So, Nusselt number and heat transfer increase and this augmentation intensifies in high Reynolds number.
In this research, the effects of non-uniform magnetic field on the heat transfer of ferrofluid inside a T-junction are investigated. The finite volume method with the SIMPLEC algorithm is applied to simulate the effects of non-uniform magnetic field on the thermal and friction factor of ferrofluid. The ferrofluid inside T-junction is assumed single phase and laminar and constant heat flux is applied on the wall while three wires are chosen as a source of non-uniform magnetic field. This study focused on main effects of magnetic field on the flow feature and temperature distribution in the vicinity of magnetic source. Comprehensive parametric studies are performed to investigate the influence of various factors such as intensity of magnetic field and Reynolds number on the heat transfer. Obtained results show that average heat transfer of ferrofluid rises more than 64% when magnetic field is applied. In addition, the local heat transfer increases more than 200% in vicinity of the first magnetic field.
Effect of typical and perforated conical ring turbulators on hydrothermal behavior of air to water double pipe heat exchanger is investigated. Two arrays (Direct conical ring (DCR) array and Reverse conical ring (RCR) array) are considered. Experimental analysis is examined for different values of open area ratio (0–0.0833), Reynolds number (6000–12,000), conical angle (0°–30°) and pitch ratio (1.83–5.83). Correlations for friction factor, Nusselt number and thermal performance factor are presented. To reach the optimal design, Non Sorting Genetic Algorithm II is applied. Pareto front of optimized solution is presented. Also the finite volume method (commercial code) is utilized for numerical section in order to show physical phenomena. Results indicate that friction factor reduces with augment of open area ratio, pitch ratio and Reynolds number. Nusselt number reduces with increase of open area ratio and pitch ratio while it augments with enhance of Reynolds number. Also it can be concluded that thermal performance rises with augment of conical angle for direct conical ring array.
In this investigation, the simulation of nanoparticle convective motion in permeable space has been presented numerically in the presence of the Lorentz effect. The working fluid is a H2O-based nanofluid. The non-Darcy model was utilized to employ porous terms in momentum equations. A radiation effect has been reported for various shapes of nanoparticles. The impact of shape factor, radiation parameter, magnetic force, shape of the nanoparticles and Rayleigh number on nanofluid conduct was demonstrated. The CVFEM (control-volume finite-element method) approach was utilized. The radiative flow is considered and the impact of physical parameters on nanofluid performance was demonstrated. The results prove that higher values of shape factor lead to stronger convection. By adding Lorentz forces, conduction becomes more practical.
