[Show abstract][Hide abstract] ABSTRACT: The present study is a theoretical investigation of natural convective heat transfer of nanofluids, inside a vertical enclosure, in the presence of a uniform magnetic field. A modified Buongiorno's model is employed for the nanofluid, which fully accounts for the effect of nanoparticle migration. The behavior of the nanofluid is investigated for two different nanoparticles in the water-base fluid, namely alumina and titania. It was observed that the nanoparticles move from the heated walls (nanoparticles' depletion) toward the cold wall (nanoparticles' accumulation) and construct a non-uniform nanoparticle distribution. The results also indicate that for smaller nanoparticles, the nanoparticle volume fraction is more uniform and there is no abnormal variation in the heat transfer rate. Moreover, NuB is reduced in the presence of the magnetic field for alumina/water nanofluid; however, for titania/water nanofluid it is vice versa.
[Show abstract][Hide abstract] ABSTRACT: Mixed convective heat transfer of water/alumina nanofluid inside a vertical microchannel is investigated theoretically. A modified Buongiorno's model is employed for the nanofluid, which fully accounts for the effect of the nanoparticle migration. This model considers the Brownian motion and thermophoresis diffusivities as the predominant slip mechanism. Because of surface roughness in microscale channels, slip condition is considered at the walls, which appropriately represents the hydrodynamic boundary condition. The results obtained indicated that nanoparticles move from the heated walls (nanoparticle depletion) toward the core region of the channel (nanoparticle accumulation) and construct a non-uniform nanoparticle distribution. In addition, increasing the bulk mean volume fraction of nanoparticles ϕB, slip parameter λ and mixed convective parameter Ng enhances the heat transfer rate. Moreover, in contrast to λ, ϕB and Ng have a negative effect on the pressure drop of the system.
[Show abstract][Hide abstract] ABSTRACT: Force convective heat transfer of alumina/water nanofluid inside a cooled parallel-plate channel in the creeping flow regime and the presence of heat generation is investigated theoretically. A modified two-component four-equation non-homogeneous equilibrium model is employed for the alumina/water nanofluid that fully accounts for the effects of nanoparticles volume fraction distribution. To impose the temperature gradients across the channel, the upper wall is subjected to a prescribed wall heat flux while the bottom wall is kept adiabatic. Moreover, due to the nanoparticle migration in the fluid, the no-slip condition of the fluid–solid interface at the walls is abandoned in favor of a slip condition that appropriately represents the non-equilibrium region near the interface. The results indicated that nanoparticles move from the adiabatic wall (nanoparticles depletion) toward the cold wall (nanoparticles accumulation) and construct a non-uniform nanoparticle distribution. Moreover, the anomalous heat transfer rate occurs when the Brownian motion takes control of the nanoparticle migration (smaller nanoparticles).
[Show abstract][Hide abstract] ABSTRACT: In this present study, the problem of two-dimensional magnetohydrodynamic (MHD) boundary layer flow of steady, laminar flow of an incompressible, viscoelastic fluid in a parallel plate channel with slip at the boundaries is presented. The upper convected Maxwell model is implemented due to its accuracy in simulating highly elastic fluid flows at high Deborah numbers. Moreover, this paper deals with the solution of third order of nonlinear ordinary differential equations which are solved by using three analytical approximate methods, namely the Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM), and Variational Iteration Method (VIM). The comparisons of these results reveal that HAM is very effective, convenient and quite accurate for non-linear ordinary differential equation. In addition, this work demonstrates that HAM is able to solve problems with mixed (Robin) as well as other boundary conditions.
[Show abstract][Hide abstract] ABSTRACT: Unsteady two-dimensional stagnation point flow of a nanofluid over a stretching sheet is investigated numerically. In contrast to the conventional no-slip condition at the surface, Navier's slip condition has been applied. The behavior of the nanofluid was investigated for three different nanoparticles in the water-base fluid, namely copper, alumina and titania. Employing the similarity variables, the governing partial differential equations including continuity, momentum and energy have been reduced to ordinary ones and solved via Runge-Kutta-Fehlberg scheme. It was shown that a dual solution exists for negative values of the unsteadiness parameter A and, as it increases, the skin friction Cfr grows but the heat transfer rate Nur takes a decreasing trend. The results also indicated that, unlike the stretching parameter ε, increasing in the values of the slip parameter λ widen the ranges of the unsteadiness parameter A for which the solution exists. Furthermore, it was found that an increase in both ε and λ intensifies the heat transfer rate.
[Show abstract][Hide abstract] ABSTRACT: Thermally fully developed mixed convection flow of nanofluids in a vertical annular pipe was investigated. Because of the non-adherence of the fluid–solid interface in the presence of nanoparticles, known as slip condition, the Navier’s slip condition was considered at the pipe walls. The Buongiorno’s model was employed for nanofluids that incorporate the effects of Brownian motion Nb and thermophoresis Nt numbers. Using the similarity variables, the governing partial differential equations were transformed into a system of ordinary ones with a constraint parameter and a solution was prepared via a reciprocal numerical algorithm. The effects of Grashof number Gr and slip parameter λ on nanoparticle volume fraction, velocity, temperature, average Nusselt number Nuavg, and pressure coefficient σ have been investigated in details. Results indicate that an increase in Gr and λ reduces the peak value of the dimensionless velocity profile in the core region of the annulus, away from the pipe walls, however, the velocity closer to the pipe walls increases. Furthermore, it was shown that nanofluids can transfer heat more efficiently in a slip condition than in a no-slip condition.
Journal of the Brazilian Society of Mechanical Sciences and Engineering 02/2014; · 0.23 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this study, entropy generation minimization (EGM) was employed to optimize fluid flow and heat transfer over a moving wedge. Governing partial differential equations including continuity, momentum and energy are reduced to ordinary ones using similarity variables and solved numerically. The novelty of this study is to consider the effects of the moving wedge parameter λ, to find the stable system via entropy generation minimization (EGM) method. The results indicated that as the slope of the wedge increases, the absolute values of the optimum moving wedge parameter λo grow as well. Moreover, it was found that the minimum value of entropy generation happens for the negative values of λo which gets smaller as Falkner–Skan power law parameter m increases.
[Show abstract][Hide abstract] ABSTRACT: In this paper, differential transform method (DTM) is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer coefficient. Using DTM, the differential equation and the related boundary conditions transformed into a recurrence set of equations and finally, the coefficients of power series are obtained based on the solution of this set of equations. DTM overcame on nonlinearity without using restrictive assumptions or linearization. Results are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem parameters. DTM results are compared with special case of the problem that has an exact closed-form solution, and an excellent accuracy is observed.
[Show abstract][Hide abstract] ABSTRACT: In this study, a simple and highly accurate semi-analytical method called the Differential Transformation Method (DTM) is used for solving the nonlinear temperature distribution equation in a longitudinal fin with temperature dependent internal heat generation and thermal conductivity. The problem is solved for two main cases. In the first case, heat generation is assumed variable by fin temperature and in the second case, both thermal conductivity and heat generation vary with temperature. Results are presented for the temperature distribution for a range of values of parameters appeared in the mathematical formulation (e.g. N, εG, and G). Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results compared to numerical methods.
[Show abstract][Hide abstract] ABSTRACT: Graphical abstract
The effects of uniform magnetic field and slip velocity at the walls on concentration of nanoparticles and heat transfer characteristics of the fluid have been investigated.
[Show abstract][Hide abstract] ABSTRACT: Magnetohydrodynamic flow in a nanofluid filled inclined enclosure is investigated numerically using the Control Volume based Finite Element Method. The cold wall of cavity is assumed to mimic a sinusoidal profile with different dimensionless amplitude, and the fluid in the enclosure is a water-based nanofluid containing Cu nanoparticles. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts and Brinkman models, respectively. Numerical simulations were performed for different governing parameters namely the Hartmann number, Rayleigh number, nanoparticle volume fraction and inclination angle of enclosure. The results show that in presence of magnetic field, velocity field retarded, and hence, convection and Nusselt number decreases. At Ra = 103, maximum value of enhancement for low Hartmann number is obtained at γ = 0°, but for higher values of Hartmann number, maximum values of E occurs at γ = 90°. Also, it can be found that for all values of Hartmann number, at Ra = 104 and 105, maximum value of E is obtained at γ = 60° and γ = 0°, respectively.
Neural Computing and Applications 01/2014; · 1.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this paper the process of solidification and melting of a phase change material is investigated in fin and tube heat exchanger. The shell side including around the tubes and spaces between fins is filled with the material R35 allocated to store energy of water, as heat transfer fluid, which flows inside the tubes. Experimental apparatus is used to investigate the effect of flow rate, inlet temperature and geometrical parameter (fin pitch) on charging and discharging processes of the phase change material. The shell side is a rectangular cube in which a continuous spiry tube creates a heat transfer surface. Results indicate that utilizing fins increases fin average temperature regardless of flow regime. While reduction in fin pitch doesn't affect this parameter sensibly for both regimes. By the increase of inlet temperature from Th = 50 °C to Th = 60 °C, melting time decreases more severally in comparison with the same rise from Th = 60 °C to Th = 70 °C.
International Communications in Heat and Mass Transfer 01/2014; · 2.21 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this study MHD effect on natural convection heat transfer in an enclosure filled with nanofluid is investigated. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The Navier Stokes equations in their vorticity-stream function form are used to simulate the flow pattern, isotherms and concentration. The governing equations are solved via Control Volume based Finite Element Method. The inner and outer circular walls are maintained at constant temperatures while two other walls are thermally insulated. The heat transfer between cold and hot regions of the enclosure cannot be well understood by using isotherm patterns so heatline visualization technique is used to find the direction and intensity of heat transfer in a domain. Effect of Hartmann number (Ha = 0, 30, 60 and 100), buoyancy ratio number (Nr = 0.1–4) and Lewis number (Le = 2, 4, 6 and 8) on streamline, isotherm, isoconcentration and heatline are examined. Also a correlation for Nusselt number corresponding to active parameters is presented. The results indicate that Nusselt number is an increasing function of buoyancy ratio number but it is a decreasing function of Lewis number and Hartmann number. Also it can be concluded that as buoyancy ratio number increases the effects of other active parameters are more pronounced.
[Show abstract][Hide abstract] ABSTRACT: The current study is a theoretical investigation of magnetohydrodynamic (MHD) flow and mixed convective heat transfer of Al2O3–water nanofluid inside a vertical microtube. A two-phase mixture model is used for nanofluid in the hypothesis that Brownian motion and thermophoretic diffusivities are the only significant slip mechanisms between solid and liquid phases. Because of the non-adherence of the fluid–solid interface due to the microscopic roughness in microtubes, the Navier׳s slip boundary condition is considered at the surfaces. Assuming a fully developed flow and heat transfer, the basic partial differential equations including continuity, momentum, and energy equations are reduced to two-point ordinary boundary value differential equations with endpoint singularities and solved numerically. The results indicate that for smaller nanoparticles, the nanoparticle volume fraction is more uniform and there is no abnormal variations in the heat transfer rate and pressure drop. Also, the heat transfer rate is enhanced in the presence of the magnetic field especially for the smaller nanoparticles. Moreover, as the magnetic field strength (Ha) intensifies, the peak of the velocity profile near the walls is increased; however, the peak of the velocity profile at the core region is decreased.
Journal of Magnetism and Magnetic Materials 01/2014; 369:132–141. · 1.83 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Unsteady motion of a rigid spherical particle in a quiescent shear-thinning power-law fluid was investigated analytically. The accurate series solution was found by coupling the homotopy-perturbation method (HPM) and the variational iteration method (VIM). The results were compared with those obtained from VIM and the established finite difference scheme. It was shown that both methods (VIM and HPM–VIM) gave accurate results; however, the amount of calculations required for HPM–VIM was significantly reduced. In addition to improved efficiency, it was revealed that HPM–VIM leads to completely reliable and precise results. The terminal settling velocity—that is the velocity at which the net forces on a falling particle eliminate—for three different spherical particles (made of plastic, glass and steel) and three flow behavior index n, in two sets of power-law non-Newtonian fluids was investigated, based on the series solution. Analytical results obtained indicated that the time of reaching the terminal velocity in a falling procedure is significantly declined with growing the particle size. Further, with approaching flow behavior to Newtonian behavior from shear-thinning properties of flow (n → 1), the transient time to achieving the terminal settling velocity is decreased.
Journal of Molecular Liquids 01/2014; · 1.68 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The present study is a theoretical investigation of the laminar flow and convective heat transfer of water/alumina nanofluid inside a parallel-plate channel in the presence of a uniform magnetic field. A modified two-component, four-equation, nonhomogeneous equilibrium model was employed for the alumina/water nanofluid, which fully accounted for the effect of the nanoparticle volume fraction distribution. The no-slip condition of the fluid–solid interface is abandoned in favor of a slip condition which appropriately represents the non-equilibrium region near the interface at micro/nano channels. The results obtained indicated that nanoparticles move from the heated walls (nanoparticles depletion) toward the core region of the channel (nanoparticles accumulation) and construct a non-uniform nanoparticles distribution. Moreover, in the presence of the magnetic field, the near wall velocity gradients increase, enhancing the slip velocity and thus the heat transfer rate and pressure drop increase.
Journal of Magnetism and Magnetic Materials 01/2014; 362:172–179. · 1.83 Impact Factor