In this experimental work, three types of water-based nanofluids are prepared by ultrasonic method. SiO2, TiO2 and CNT nanoparticles are used for preparing the nanofluids. Applications of these nanofluids are examined in the heating process in HVAC systems. During the experiments, total dissolved solids (TDS) of nanofluid are measured to see which nanofluid is more appropriate in heating process and makes the lower deposits and sediments. Also, heated area and nanofluid temperatures are recorded to show which nanofluid in suitable for heating from energy consumption view point. Results show that SiO2 can be more suitable from the energy consumption view point because by lower energy consumptions, it reaches to desirable temperature in the heated area.

This paper investigates numerically the problem of unsteady magnetohydrodynamic nanofluid flow and heat transfer between parallel plates due to the normal motion of the porous upper plate. The governing equations are solved via the fourth-order Runge-Kutta method. Different kind of nanoparticles is examined. The effects of kind of nanoparticle, nanofluid volume fraction, expansion ratio, Hartmann number, Reynolds number on velocity and temperature profiles are considered. Also effect of different types of nanoparticles is examined. Results indicate that velocity decreases with increase of Hartmann number due to effect of Lorentz forces. Rate of heat transfer increase with increase of nanofluid volume fraction, Hartmann number and Reynolds number but it decreases with increase of expansion ratio. Also it can be found that choosing copper as a nanoparticle leads to highest enhancement.

A novel concept of collocation method is introduced and used for the first time to obtain a simple and accurate solution for the boundary layer in unbounded domain. Similar analysis is however not available yet in the literature. The idea is to transform the equations and boundary conditions into another set of variables and also to augment an extra boundary condition. To demonstrate the effectiveness of this ideal, we apply optimal collocation method (OCM) to find the approximate solution for the boundary layer flow of a nanofluid past a porous moving semi-infinite flat plate. The influence of pertinent parameters on the flow field characteristics is studied. The obtained results have been compared with the numerical solutions from fourth order Runge–Kutta method. The solution shows that the results of the present method are in excellent agreement with those of the numerical one. It is important that we applied OCM for the problem in unbounded domain without using Pade approximants, perturbation, linearization, small parameter or auxiliary parameter. The approach used in the present work can also be extended to different nonlinear problems in unbounded domain and the conclusion is considered useful for engineering applications involving infinity domain.

In this study, a simple and high accurate series-based method called differential transformation method (DTM) is used for solving the coupled nonlinear differential equations in fluids’ mechanic problems. The concept of the DTM is briefly introduced, and its application for two different cases, natural convection of a non-Newtonian fluid between two vertical plates and Newtonian fluid flow between two horizontal plates, has been studied. DTM results are compared with those obtained by another series-based analytical technique namely homotopy perturbation method (HPM) and a numerical solution (Fourth-order Runge–Kutta) to show the accuracy of the proposed method. Results reveal that DTM is very effective and convenient and can achieve more suitable results compared to HPM in some areas of equations in engineering and science problems.

In this paper, magnetohydrodynamic flow (MHD) of a nonofluid over a stretching cylinder is investigated numerically. The Differential Quadrature Method (DQM) is applied for solving the governing equations. The influence of relevant parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed. Also, comparison with the published results is presented. The results show that the Nusselt number increases with growth in the volume fraction coefficient and Reynolds number but decreases with the magnetic parameter.

This study considers the forced convection of laminar TiO2-water nanofluid flow in a parallel plate microchannel. The small length scale associated with microchannels dictates the use of slip condition at the fluid-solid interface. The modified Buongiorno model was employed for the nanofluid to fully account for the effects of non-uniform viscosity and thermal conductivity. The partial differential equations associated with conservation laws were reduced to two-point ordinary boundary value differential equations before being numerically solved. Considering Brownian motion and thermophoresis, the effects of nanoparticle transport on concentration, velocity, and temperature profiles were analyzed for three different values of wall heat flux. To assess the efficiency of adding nanoparticles, the ratios of the pressure drop and the heat transfer coefficient of the nanofluid to that of the base fluid were studied in detail. From analyzing different heat flux ratios, one-sided heating was found to be most efficient at enhancing the heat transfer rate in the microchannel. Additionally, in the presence of the slip velocity, the increase in the value of the heat transfer coefficient for the nanofluid was smaller than that for the base fluid. (C) 2015 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

In this article, heat and mass transfer behavior of steady nanofluid flow between parallel plates in the presence of uniform magnetic field is studied. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The governing equations are solved via the Differential Transformation Method. The validity of this method was verified by comparison of previous work which is done for viscous fluid. The analysis is carried out for different parameters namely: viscosity parameter, Magnetic parameter, thermophoretic parameter and Brownian parameter. Results reveal that skin friction coefficient enhances with rise of viscosity and Magnetic parameters. Also it can be found that Nusselt number augments with an increase of viscosity parameters but it decreases with augment of Magnetic parameter, thermophoretic parameter and Brownian parameter.

The effects of nanoparticle migration on mixed convection of titania/water nanofluid inside a vertical microchannel have been investigated numerically via Runge–Kutta–Fehlberg method. A modified two-component heterogeneous model is employed for the nanofluid in the hypothesis that the Brownian motion and the thermophoresis are the only responsible mechanisms for nanoparticle migration. Because of small dimensional structures of microchannels, a linear slip condition is considered at the boundaries, which appropriately represents the non-equilibrium region near the interface. To impose different temperature gradients, the heat flux ratio of the right to the left wall (ε) is investigated in three different situations, namely the adiabatic right wall (ε=0), unequal heat fluxes at the walls (ε<1) and equal heat fluxes (ε=1). It is revealed that the asymmetric thermal boundary condition affects the direction of nanoparticle migration and distorts the symmetry of the velocity and temperature profiles. In the rich nanoparticle concentration region, the viscosity and the local conductivity increase, which lead to a stronger conduction and a weaker convection rate. Also, it is found that splitting the total amount of heat flux on the walls unevenly, is the most efficient way to enhance the heat transfer rate in the vertical microchannels.

In this study, the problem of nanofluid flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved using Least Square Method. The concept of this method is briefly introduced, and it's application for this problem is studied. Then, the results are compared with numerical results and the validity of these methods is shown. Graphical results are presented to investigate the influence of the volume fraction of nanoparticle, non-dimensional wall dilation rate and permeation Reynolds number on the velocity, normal pressure distribution and wall shear stress. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels. The results indicate that velocity boundary layer thickness near the walls decreases with increase of Reynolds number and nanoparticle volume friction and it increases as non-dimensional wall dilation rate increases.

In this study, two phase simulation of nanofluid flow and heat transfer between parallel plates is investigated. The important effects of Brownian motion and thermophoresis have been included in the model of nanofluid. The governing equations are solved via homotopy perturbation method. According to comparison with previous works, this method has good accuracy to solve this problem. The semi analytical investigation is carried out for different governing parameters namely; the squeeze number, Hartmann number, Schmidt number and Eckert number. The results indicate that absolute skin friction coefficient decreases with increase of Hartmann number and squeeze number. Also it can be found that that Nusselt number is an increasing function of Hartmann number, Eckert number and Schmidt number but it is a decreasing function of squeeze number. (C) 2014 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

The settling behavior of solid particles is of fundamental importance in natural and artificial applications. In this paper, the unsteady motion of a vertically falling non-spherical particle in incompressible Newtonian media was investigated. The velocity and acceleration were carried out by using the differential transformation method (DTM) and a Padé approximate which are an analytical solution technique. The velocity and acceleration are shown for different values of the embedding parameters. The analytical results indicate that the velocity of the gold particle is higher than the copper and aluminum particles. Furthermore, the velocity and acceleration increases with an increase in the sphericity. Comparison of the results illustrates that the analytical method and numerical data are in a good agreement with each other.

This work presents a thermal and flow analysis of a fin shaped microchannel heat sink (MCHS) cooled by different nanofluids (Cu and Al2O3 in water) based on “saturated porous medium” and least square method then results are compared with numerical procedure. The Forchheimer–Brinkman-extended Darcy equation is used to describe the fluid flow and the two-equation model with thermal dispersion is utilized for heat transfer. The effect of nanoparticle size and volume fraction, volume flow rate, inertial force parameter and channel width investigated on total thermal resistance, friction factor and Nusselt number. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL correlation. Central composite design (CCD) is applied to obtain the desirability of the optimum value of the nanofluid flow characteristics. Results show that Cu–water nanofluid is more lucrative thermally versus Al2O3–water nanofluid. It is found that total thermal resistance, friction factor and Nusselt number are not sensitive to inertial effect while they change significantly due to other parameters such as nanoparticle size and volume fraction, volume flow rate and channel width. We obtained that Nusselt number enhancement has direct relationship with inertial force parameter and volume flow rate.

In this article, the motion of a spherical particle in a plane Couette Newtonian fluid flow is studied. The governing equations of a spherical solid particle's motion in the plane Couette fluid flow are investigated using the Differential Transformation Method (DTM) and a Padé approximant which are an analytical solution technique. For validation of the analytical solution, the governing equation is solved numerically. The horizontal and vertical velocities of spherical solid particle are shown for different fluids and values of the embedding parameters. The DTM–Padé results indicate that the horizontal and vertical velocities of spherical solid particle in water fluid are higher than the glycerin and ethylene-glycol fluids. Also the horizontal and vertical velocities increase with an increase in the particle radius. Comparison of the results (DTM and numerical) was shown that the analytical method and numerical data are in a good agreement with each other.

This investigation is concerned with the boundary layer flow of viscous nanofluid over a permeable stretching wall. The fluid saturates the porous medium. Four different types of nanoparticles such as Copper (Cu), Silver (Ag), Alumina (Al2O3) and Titanium Oxide (TiO2) with water as its base fluid are considered. Resulting nonlinear system is computed for the series and numerical solutions. Comparison between series and numerical solutions showed an excellent agreement. The influence of pertinent parameters such as solid volume fraction of nanoparticles, the type of nanofluids on the flow, heat transfer, entropy generation, skin friction coefficient, Nusselt number and Bejan number are discussed. The results indicate that an increase in the Nanoparticle volume fraction decreases the momentum boundary layer thickness and entropy generation rate whereas the thermal boundary layer thickness increases. It is observed that such effects are found more noticeable in the Ag-water solution than in the other solutions.

In this study, steady and unsteady magneto-hydrodynamic (MHD) Couette flows between two parallel infinite plates have been studied through numerical Differential Quadrature Method (DQM) and analytical Differential Transformation Method (DTM), respectively. Coupled equations by taking the viscosity effect of the two phases for fixed and moving plates have been introduced. The precious contribution of the present study is introducing new, fast and efficient numerical and analytical methods in a two-phase MHD Couette fluid flow. Results are compared with those previously obtained by using Finite Difference Method (FDM). The velocity profiles of two phases are presented and a parametric study of physical parameters involved in the problem is conducted. As an outcome, when magnetic source is fixed relative to the moving plate, by increasing the Hartmann number, velocity profiles for both phases increased, but when it is fixed relative to the fluid an inverse treatment is observed. (C) 2014 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

An analytical solution of the unsteady two dimensional motion of a non-spherical particle in the plane of Couette flow was acquired using the finite parameter optimal homotopy analysis method. To achieve the best accuracy and ensure the convergence of the results, the averaged residual errors were obtained and minimized. The effects of different initial guesses and the number of convergence-control parameter (k) on the accuracy and efficiency of the problem were studied in detail. It was shown that the current method gives completely reliable results and there is no need to compare the results to those of similar numerical or experimental techniques. Furthermore, the effects of different parameters including sphericity and the proportionality constant on three different base fluids namely: water, ethylene-glycol, and glycerin were investigated. Based on the analytical results, it was shown that non-spherical particles are slower to settle rather than spherical particles and the settling velocity of the particles in the glycerin is much lower than that in the ethylene-glycol and the water base fluids.

Unsteady settling behavior of a soluble spherical particle falling in a Newtonian fluid media is investigated using a drag coefficient of the form given by Ferreira et al. (Chem. Eng. Commun. 1998). It is considered that the mass of the particle reduces due to its solubility in the fluid, and consequently diameter of the particle will be reduced by a linear function. In a current study, the equation of the motion for described variable-mass particle is introduced for the first time and is solved by Padé approximation of Differential Transformation Method (DTM-Padé) and numerical Runge–Kutta method. Also the influence of solubility parameter on velocity profile is discussed and particle's positions are depicted graphically in each 1s time step.

In this study, coupled equations of particle's motion in Couette fluid flow are solved by Multi-step Differential Transformation Method (Ms-DTM) considering the rotation and shear effects on lift force and neglecting gravity. The precious achievement of the present work is introducing a new, fast and efficient analytical technique for spherical particles in plane Couette fluid flow over the previous numerical and analytical results in the literature. Also, obtained values are compared with numerical solution and HPM–Pade which recently are done by Torabi et al. It is shown that presented method gives approximations with a high degree of accuracy and least computational effort for studying particle motion in Couette fluid flow without the need for any linearization, discretization or perturbation against the previous work. Also, the acceleration profiles of the particle are presented and positions of the particle in each 1s time step are depicted graphically in the current study.

In this paper, Cu–water nanofluid flow analysis between two parallel palates is investigated using a differential transformation method (DTM) and numerical method. The effective thermal conductivity and viscosity of nanofluids are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. For increasing the accuracy of DTM, Padé approximation is applied. Comparison between the DTM-Padé and numerical method shows that Padé with order [6,6] can be an exact and high efficiency procedure for solving these kinds of problems. The influence of the nanofluid volume fraction (φ), Eckert number (Ec), squeeze number (S) and Prandtl number (Pr) on the Nusselt number (Nu), non-dimensional temperature and velocity profiles are investigated. The results indicated for the case of squeezing flow that the Nusselt number increases with the increase of the nanoparticle volume fraction, Eckert number and squeeze number.

This paper deals with the steady two-dimensional stagnation point flow of nanofluid toward an exponentially stretching sheet with nonuniform heat generation/absorption. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of Brownian diffusion and thermophoresis simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via similarity variables and solved analytically via HAM. Effects of governing parameters such as heat generation/absorption λ , stretching parameter ε , thermophoresis , Lewis number Le, Brownian motion , and Prandtl number Pr on heat transfer and concentration rates are investigated. The obtained results indicate that in contrast with heat transfer rate, concentration rate is very sensitive to the abovementioned parameters. Also, in the case of heat generation , despite concentration rate, heat transfer rate decreases. Moreover, increasing in stretching parameter leads to a gentle rise in both heat transfer and concentration rates.