Laminar nanofluid flow in microheat-sinks

In response to the ever increasing demand for smaller and lighter high-performance cooling devices, steady laminar liquid nanofluid flow in microchannels is simulated and analyzed. Considering two types of nanofluids, i.e., copper-oxide nanospheres at low volume concentrations in water or ethylene glycol, the conjugated heat transfer problem for microheat-sinks has been numerically solved. Employing new models for the effective thermal conductivity and dynamic viscosity of nanofluids, the impact of nanoparticle concentrations in these two mixture flows on the microchannel pressure gradients, temperature profiles and Nusselt numbers are computed, in light of aspect ratio, viscous dissipation, and enhanced temperature effects. Based on these results, the following can be recommended for microheat-sink performance improvements: Use of large high-Prandtl number carrier fluids, nanoparticles at high volume concentrations of about 4% with elevated thermal conductivities and dielectric constants very close to that of the carrier fluid, microchannels with high aspect ratios, and treated channel walls to avoid nanoparticle accumulation.     

Entropy generation of viscous dissipative nanofluid flow in microchannels

An analytical study on the viscous dissipation effect on entropy generation in laminar fully developed forced convection of water–alumina nanofluid in circular microchannels is reported. In the first-law analysis, closed form solutions of the temperature distributions in the radial direction for the models with and without viscous dissipation term in the energy equation are obtained. The results show that the heat transfer coefficient decreases with nanoparticle volume fraction largely in the laminar regime of nanofluid flow in microchannel when the viscous dissipation effect is taken into account. In the second-law analysis, the two models are compared by analyzing their relative deviations in entropy generation for different Reynolds number and nanoparticle volume fraction. When the viscous dissipation is taken into account, the temperature distribution is prominently affected and consequently the entropy generation ascribable to the heat transfer irreversibility is significantly increased. The increase of entropy generation induced by the increase of nanoparticle volume fraction is attributed to the increase of both the thermal conductivity and viscosity of nanofluid which causes augmentation in the heat transfer and fluid friction irreversibilities, respectively. By incorporating the viscous dissipation effect, both thermal performance and exergetic effectiveness for forced convection of nanofluid in microchannels dwindle with nanoparticle volume fraction, contrary to the widespread conjecture that nanofluids possess advantage over pure fluid associated with higher overall effectiveness from the aspects of first-law and second-law of thermodynamics.     

Forced convective heat transfer of nanofluids in microchannels

Convective heat transfer coefficient and friction factor of nanofluids in rectangular microchannels were measured. An integrated microsystem consisting of a single microchannel on one side, and two localized heaters and five polysilicon temperature sensors along the channel on the other side were fabricated. Aluminum dioxide (Al₂O₃) with diameter of 170 nm nanofluids with various particle volume fractions were used in experiments to investigate the effect of the volume fraction of the nanoparticles to the convective heat transfer and fluid flow in microchannels. The convective heat transfer coefficient of the Al₂O₃ nanofluid in laminar flow regime was measured to be increased up to 32% compared to the distilled water at a volume fraction of 1.8 volume percent without major friction loss. The Nusselt number measured increases with increasing the Reynolds number in laminar flow regime. The measured Nusselt number which turned out to be less than 0.5 was successfully correlated with Reynolds number and Prandtl number based on the thermal conductivity of nanofluids.     

Two‐phase natural convection analysis and hybrid nanoparticle migration around micromixer blades

In this paper, numerical investigations are presented for hybrid nanoparticle migration and free convection heat transfer of two kinds of nanofluids in a micromixer at the fixed propeller condition. The inner blades and outer crust of the micromixer are kept at constant hot and cold temperatures, respectively. Two kinds of hybrid nanofluids, TiO₂‐CuO water and ethylene glycol‐(MoS₂‐SiO₂), are considered. The governing equations including velocity, pressure, temperature formulation, and nanoparticle concentrations are solved by a partial differential equation solver based on the Galerkin finite element method. The results are discussed based on the governing parameters, such as nanoparticle volume fraction, thermal and solutal Rayleigh numbers. The average Nusselt number was found to increase with the increasing nanoparticle volume fractions. Also, increasing the thermal Rayleigh number enhanced heat transfer while the solutal Rayleigh number has an insignificant effect on it. More importantly, increasing the thermal Rayleigh number assisted avoiding the agglomeration of nanoparticles around the blades and ensured more uniform nanoparticle distribution.     

Semianalytical solution of axisymmetric flows of Cu‐ and Ag‐water nanofluids between two rotating disks

Present study analyses the axisymmetric flows of copper‐ and silver‐water nanofluids between two rotating disks in the presence of Hartmann number, porous medium, and drag coefficient. Effect of thermal radiation enriches the study as well. In addition to that, the coupling parameter and the Eckert number appear because of the inclusion of viscous dissipation in energy equation. The well‐posed transformations are used to transform the governing equation into ordinary and semianalytical procedure, that is, Adomain Decomposition method is used to solved these coupled ODEs. The surface and contour plots for the velocity profiles of both Cu‐ and Ag‐water nanofluids for the effect of physical parameters such as solid volume fraction, drag coefficient, and Reynolds number are obtained and presented in graphs. Also, the behavior of other pertinent parameters characterizes the flow phenomena on the nanofluid velocity and temperature are presented through graphs. The numerical computation of skin friction and Nusselt number are obtained and presented through tables. For the validity, the present results show a good agreement with earlier studies. The major findings of this study are as follows: an increase in solid volume fraction, a resistive force like drag opposes the velocity of the nanofluid, whereas Eckert number enhances the fluid temperature significantly.     

Entropy generation in an unsteady Eyring‐Powell hybrid nanofluid flow over a permeable surface: A Lie group analysis

In thermal processes, the choice of the thermofluid plays an essential role in minimizing entropy generation and thereby improving thermal efficiency. In this study, entropy generation in a viscous hybrid nanofluid described by the Eyring‐Powell model is investigated. The model accounts for the effect of the nanoparticle volume fraction and viscous dissipation on an Eyring‐Powell Cu‐Al₂O₃/ethylene glycol nanofluid. A similarity solution to the time‐dependent model is found using the Lie group symmetry technique. The bivariate spectral quasi‐linearization method is used for the solution of the self‐similar transport equations. We analyze the effects of the nanoparticle volume fraction, suction/injection, and viscous dissipation on the fluid properties. The skin friction and Nusselt number are determined. A comparison between the Nusselt number of a regular nanofluid and a hybrid nanofluid shows that the hybrid nanofluid has better thermal characteristics compared with the regular nanofluid. The findings show that a decrease in the nanoparticle volume fraction and Eckert number minimizes entropy generation in the system.     

Heat transfer enhancement for combined convection flow of nanofluids in a vertical rectangular duct considering radiation effects

In this paper, combined convective heat transfer and nanofluids flow characteristics in a vertical rectangular duct are numerically investigated. This investigation covers Rayleigh numbers in the range of 2 × 10⁶ ≤ Ra ≤ 2 × 10⁷ and Reynolds numbers in the range of 200 ≤ Re ≤ 1000. Pure water and five different types of nanofluids such as Ag, Au, CuO, diamond, and SiO₂ with a volume fraction range of 0.5% ≤ φ ≤ 3% are used. The three‐dimensional steady, laminar flow, and heat transfer governing equations are solved using finite volume method (FVM). The effects of Rayleigh number, Reynolds number, nanofluids type, nanoparticle volume fraction of nano‐ fluids, and effect of radiation on the thermal and flow fields are examined. It is found that the heat transfer is enhanced using nanofluids by 47% when compared with water. The Nusselt number increases as the Reynolds number and Rayleigh number increase and aspect ratio decreases. A SiO₂ nanofluid has the highest Nusselt number and highest wall shear stress while the Au nanofluid has the lowest Nusselt number and lowest wall shear stress. The results also revealed that the wall shear stress increases as Reynolds number increases, aspect ratio decreases, and nanoparticle volume fraction increases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20354     

Heat transfer enhancement with laminar pulsating nanofluid flow in a wavy channel

In this study, the heat transfer characteristics of Al₂O₃–water based nanofluids in a wavy mini-channel under pulsating inlet flow conditions are investigated numerically. The simulations are performed for nanofluid volume fractions, pulsating frequency and amplitude while the other parameters are kept constant by using control volume based cfd solver. The flow is both thermally and hydrodynamically developing while the channel walls are kept at a constant temperature. Results indicate that there is a good potential in promoting the thermal performance enhancement by using the nanoparticles under pulsating flow. Pulsation in nanofluids is a new idea for enhancement of heat transfer. Furthermore, the pulsating flow has an advantage to prevent sedimentation of nanoparticles in the base fluid. Results show that the heat transfer performance increases significantly with increase in nanoparticle volume fraction and with the amplitude of pulsation while the pulsation frequencies have a slight effect. In the pulsating flow conditions the combined effect of pulsation and nanoparticles is favorable for the increasing Nusselt number when compared to the steady flow case. The obtained results are given as dimensionless parameters.     

Forced convection heat and mass transfer flow of a nanofluid through a porous channel with a first order chemical reaction on the wall

This study is devoted to investigate the fully developed forced convection heat and mass transfer in a horizontal porous channel filled with a nanofluid. It is assumed that the walls of the channel are subject to a constant heat flux. It is also assumed that the first order catalytic reaction takes place on the walls and that the viscous dissipation term in the energy equation is taken into account. Brinkman model is used for the flow in the porous media and “clear fluid compatible” viscous dissipation model is considered. Thermal effect is taken also into account in the concentration equation. Closed form analytical solutions are presented for the governing dimensionless momentum, energy and concentration equations. The effects of nanoparticle volume fraction, Darcy, Brinkman, Damkohler and Soret numbers are investigated on the Nusselt number, velocity, temperature and concentration distributions.     

Convective heat transfer of Titania nanofluids of different base fluids in cylindrical annulus with discrete heat source

In the current work, the hydrodynamic and thermal characteristics of Titania nanofluids filling a cylindrical annulus are numerically investigated. Ethylene glycol, engine oil, and water are used as base fluids. The Maxwell model for convective heat transfer in nanofluids is followed to account for the effects of nanoparticle volume fraction distribution on the continuity, momentum, and energy equations, in which a developed computer code is used. The latter is based upon the finite volume method coupled with the SIMPLER algorithm. Numerical results for the heat transfer are presented in the form of streamlines and isotherm profiles for a different value of Rayleigh number, base fluid, and nanoparticle volume fraction. The effects of these parameters on the local Nusselt number are analyzed.     

Effect of thermal radiation on magnetohydrodynamic three‐dimensional motion of a nanofluid past a shrinking surface under the influence of a heat source

An analytical technique known as the homotopy analysis method is used to acquire solutions for magnetohydrodynamic 3‐D motion of a viscous nanofluid over a saturated porous medium with a heat source and thermal radiation. The governing nonlinear partial differential equations are changed to ordinary differential equations employing appropriate transformations. Validation of the present result is done with the help of error analysis for flow and temperature. The influences of pertinent parameters on momentum, energy, and Nusselt number are studied and discussed. The major findings are: the velocity of the nanofluid is affected by the nanoparticle volume fraction and the thickness of the thermal boundary layer becomes thinner and thinner subject to sink, whereas the effect is revered in case of the source.     

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.     

Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid

In this study, natural convection in a concentric annulus between a cold outer square and heated inner circular cylinders in presence of static radial magnetic field is investigated numerically using the lattice Boltzmann method. The inner and outer cylinders are maintained at constant uniform temperatures and it is assumed that all walls are insulating the magnetic field. The numerical investigation is carried out for different governing parameters namely; the Hartmann number, nanoparticles volume fraction and Rayleigh number. The effective thermal conductivity and viscosity of nanofluids are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. Also, the multi-distribution-function (MDF) model is used for simulating the effect of uniform magnetic field. The results reveal that the average Nusselt number is an increasing function of nanoparticle volume fraction as well as the Rayleigh number, while it is a decreasing function of the Hartmann number.     

Viscous dissipation effects on thermal transport characteristics of combined pressure and electroosmotically driven flow in microchannels

This study investigates the influence of viscous dissipation on thermal transport characteristics of the fully developed combined pressure and electroosmotically driven flow in parallel plate microchannels subject to uniform wall heat flux. Closed form expressions are obtained for the transverse distributions of electrical potential, velocity and temperature and also for Nusselt number. From the results it is realized that the Brinkman number has a significant effect on Nusselt number. Generally speaking, to increase Brinkman number is to decrease Nusselt number. Although the magnitude of Joule heating can affect Brinkman number dependency of Nusselt number, however the general trend remains unchanged. Depending on the value of flow parameters, a singularity may occur in Nusselt number values even in the absence of viscous heating, especially at great values of dimensionless Joule heating term. For a given value of Brinkman number, as dimensionless Debye–Huckel parameter increases, the effect of viscous heating increases. In this condition, as dimensionless Debye–Huckel parameter goes to infinity, the Nusselt number approaches zero, regardless of the magnitude of Joule heating. Furthermore, it is realized that the effect of Brinkman number on Nusselt number for pressure opposed flow is more notable than purely electroosmotic flow, while the opposite is true for pressure assisted flow.     

Entropy generation on unsteady stagnation-point Casson nanofluid flow past a stretching sheet in a porous medium under the influence of an inclined magnetic field with homogeneous and heterogeneous reactions

This study explores the entropy generation analysis on unsteady nonlinear radiative ethylene glycol-based Casson nanofluid flow near stagnation point towards a stretching sheet through a porous medium. Analysis has been accomplished in the presence of an inclined magnetic field, heat generation, homogeneous–heterogeneous reactions, and viscous dissipation with velocity slip and convective boundary conditions. The nondimensional governing equations are solved by the shooting technique with the help of the RK45 method. We have experimented with copper and silver nanoparticles and a comparative analysis has been highlighted for both copper and silver nanofluids. Numerical outcomes are executed by the MATLAB built-in bvp4c function. The consequences of the experiment for various pertinent flow parameters are portrayed by graphs and tables for both the Ag- and Cu-Casson nanofluids. Results reveal that the enhancement of nanoparticles volume fraction accelerates temperature but it slows down concentration and velocity distributions. Higher values of the Eckert number boost velocity and temperature but reduce skin friction coefficient and Nusselt number. Enhancement of the Brinkman number boosts up entropy generation but it slows down Bejan's number. The results of the model can be applied in the movement of biological fluids, separation of biomolecules, glass manufacturing, paper production, food processing, crude oil purification, polymer drag reduction, and cooling atomic reactors.     

Thermal radiation and magnetic field effects on squeezing motion analysis for Cu–kerosene and Cu–water nanofluids

This article examines the squeezing motion of Cu–kerosene and Cu–water nanofluids with thermal radiation and magnetic field between two parallel sheets. By appropriate transformation, the governing nonlinear partial differential equations are converted into ordinary differential equations and then solved numerically by the Runge–Kutta technique. The motion characteristics have been examined with graphs by relevant parameters. It is observed that fluid temperature reduces if squeezing parameter, thermal radiation, and Hartmann number increases, but fluid temperature improves if nanoparticle volume fraction, Eckert number, and Prandtl number increases and it is observed that liquid momentum improves if the squeezing parameter increases, but fluid velocity reduces if nanoparticle volume fraction and Hartmann number increases.     

Natural convection boundary layer flow over a truncated cone in a porous medium saturated by a nanofluid

This work studies the natural convection boundary layer flow over a truncated cone embedded in a porous medium saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A suitable coordinate transformation is performed, and the obtained nonsimilar equations are solved by the cubic spline collocation method. The effect of the Brownian motion parameter and thermophoresis parameter on the temperature, nanoparticle volume fraction and velocity profiles are discussed. The effects of the thermophoresis parameter, Brownian parameter, Lewis number, and buoyancy ratio on the local Nusselt number have been studied. Results show that an increase in the thermophoresis parameter or the Brownian parameter tends to decrease the local Nusselt number. Moreover, the local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased.     

Thermal slip and radiative heat transfer effects on electro‐osmotic magnetonanoliquid peristaltic propulsion through a microchannel

A mathematical study is described to examine the concurrent influence of thermal radiation and thermal wall slip on the dissipative magnetohydrodynamic electro‐osmotic peristaltic propulsion of a viscous nanoliquid in an asymmetric microchannel under the action of an axial electric field and transverse magnetic field. Convective boundary conditions are incorporated in the model and the case of forced convection is studied, that is, thermal and species (nanoparticle volume fraction) buoyancy forces neglected. The heat source and sink effects are also included and the diffusion flux approximation is employed for radiative heat transfer. The transport model comprises the continuity, momentum, energy, nanoparticle volume fraction, and electric potential equations with appropriate boundary conditions. These are simplified by negating the inertial forces and invoking the Debye–Hückel linearization. The resulting governing equations are reduced into a system of nondimensional simultaneous ordinary differential equations, which are solved analytically. Numerical evaluation is conducted with symbolic software (MATLAB). The impact of different control parameters (Hartmann number, electro‐osmosis parameter, slip parameter, Helmholtz–Smoluchowski velocity, Biot numbers, Brinkman number, thermal radiation, and Prandtl number) on the heat, mass, and momentum characteristics (velocity, temperature, Nusselt number, etc) are presented graphically. Increasing Brinkman number is found to elevate temperature magnitudes. For positive Helmholtz–Smoluchowski velocity (reverse axial electrical field) temperature is strongly reduced, whereas for negative Helmholtz–Smoluchowski velocity (aligned axial electrical field), it is significantly elevated. With increasing thermal slip, nanoparticle volume fraction is also increased. Heat source elevates temperatures, whereas heat sink depresses them, across the microchannel span. Conversely, heat sink elevates nanoparticle volume fraction, whereas heat source decreases it. Increasing Hartmann (magnetic) parameter and Prandtl number enhance the nanoparticle volume fraction. Furthermore, with increasing radiation parameter, the Nusselt number is reduced at the extremities of the microchannel, whereas it is elevated at intermediate distances. The results reported provide a good insight into biomimetic energy systems exploiting electromagnetics and nanotechnology, and, furthermore, they furnish a useful benchmark for experimental and more advanced computational multiphysics simulations.     

Heat transfer augmentation in concentric elliptic annular by ethylene glycol based nanofluids

In this article, laminar mixed convective heat transfer at different nanofluids flow in an elliptic annulus with constant heat flux boundary condition has been numerically investigated. The three dimensional governing equations (continuity, momentum and energy) are solved using the finite volume method (FVM). The investigation covers Reynolds number and nanoparticle volume fraction in the ranges of 200–1000 and 0–4% respectively. In the present work, four different types of nanofluids are examined in which Al₂O₃, CuO, SiO₂ and ZnO are suspended in the base fluid of ethylene glycol (EG) with different nanoparticle sizes 20, 40, 60 and 80 nm. The results show that SiO₂-EG nanofluid has the highest Nusselt number, followed by Al₂O₃-EG, ZnO-EG, CuO-EG, and lastly pure ethylene glycol. The Nusselt number increased as the nanoparticle volume fraction and Reynolds number increased; however, it decreased as the nanoparticle diameter increased. It is found that the glycerine-SiO₂ shows the best heat transfer enhancement compared with other tested base fluids. Comparisons of the present results with those available in the literature are presented and discussed.     

Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field

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.