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.     

Numerical investigation of the MHD forced convection and entropy generation in a straight duct with sinusoidal walls containing water–Al2O3 nanofluid

This paper examines forced convection heat transfer and entropy generation of a nanofluid laminar flow through a horizontal channel with wavy walls in the presence of magnetic field, numerically. The Newtonian nanofluid is composed of water as base fluid and Al₂O₃ as nanoparticle which is exposed to a transverse magnetic field with uniform strength. The inlet nanofluid with higher temperature enters the cool duct and heat is exchanged along the walls of a wavy channel. The effects of the dominant parameters including Reynolds number, solid volume fraction, Hartmann number, and different states of amplitude sine waves are studied on the local and average Nusselt number, skin friction, and total entropy generation. Computations show excellent agreement of the present study with the previous literature. The computations indicate that with the increasing strength of a magnetic field, Nusselt number, skin friction, and total entropy generation are increased. It is found that increasing the solid volume fraction of nanoparticles will increase the Nusselt number and total entropy generation, but its effect on the skin friction is negligible. Also, results imply that increasing amplitude sine waves of the geometry has incremental effect on both Nusselt number and skin friction, but its effect on the total entropy generation is not so tangible.     

Cu‐Al2O3/H2O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

The resent development of research in the field of nano technology introduced hybrid nanofluids which are advanced classes of fluids with augmented thermal properties and it gives better results comparing to regular nanofluid. The aim of the present work is to study the significant effects of variable viscosity and viscous dissipation on a porous stretching sheet in the presence of hybrid nanofluid and radiative heating. In this model, two types of nanoparticles, namely copper (Cu) and alumina oxide (Al₂O₃), are suspended in the base fluid H₂O to form a hybrid nanoliquid. The novelty of this study is to introduce variable viscosity along with natural convection in the momentum equation and viscous dissipation in the energy equation. Mathematical modeling is employed in this study, whereby partial differential equations for the fluid flow are constructed and transformed to a set of ordinary differential equations, and hence resolved computationally by Runge‐Kutta‐Fehlberg method along with shooting scheme. The most important results for relevant parameters concerning the flow heat measure, surface drag, and heat transfer coefficients are thoroughly examined and presented graphically for both Cu‐Al₂O₃/water hybrid nanofluids. There is an increase in hybrid nanofluid velocity profile with mounting values of $\lambda$, and the Cu‐water nanofluid converges to the boundary more quickly than the hybrid nanofluid due to the occurrence of variable viscosity. The results concluded that the Nusselt number of the viscous fluid is lower than that of the nanofluid and hence the hybrid nanofluid (ie, heat transfer rate: normal fluid < nanofluid < hybrid nanofluid). The outcomes of present investigations are in close agreement with the viscous fluid as a particular case.     

Analytical Study on Forced Convection of Nanofluids With Viscous Dissipation in Microchannels

This article presents an analytical study on forced convection of laminar fully developed flow of incompressible, constant-property nanofluids in microchannels. Closed-form solutions for the temperature distributions in the radial direction with the incorporation of viscous dissipation are obtained under isoflux boundary condition. The effects of the governing parameters, including modified Brinkman number, thermal conductivity ratio, and nanoparticle volume fraction of the nanofluids, on the temperature distributions are investigated and analyzed for both heating and cooling processes. The heat transfer performance characterized by the Nusselt number is investigated based on the effects induced by these parameters. In the comparison between the models with and without viscous dissipation, it is found that the thermal performance of a microchannel is overrated when viscous dissipation is excluded in the analysis. It is concluded that these governing parameters are intimately interrelated in the flow and thermal analyses of nanofluids in microchannels. The interrelationship of the viscous dissipation effect and the nanoparticle volume fraction is examined in a contour deviation map of Nusselt numbers between the model with and without considering the viscous dissipation.     

Entropy Generation of Natural Convection Heat Transfer in a Square Cavity Using Al2O3–Water Nanofluid

Entropy generation of an Al₂O₃–water nanofluid due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subject to different side‐wall temperatures using a nanofluid for natural convection flow. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number between 10⁴ and 10⁷ and volume fraction between 0 and 0.05. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation, average entropy generation, and average Bejan number are determined. The results are compared for a pure fluid and a nanofluid. It is totally found that the heat transfer, and entropy generation of the nanofluid is more than the pure fluid and minimum entropy generation and Nusselt number occur in the pure fluid at any Rayleigh number. Results depict that the addition of nanoparticles to the pure fluid has more effect on the entropy generation as the Rayleigh number goes up.     

Rayleigh–Benard convection in water-based alumina nanofluid: A numerical study

Rayleigh–Benard (R-B) convection in water-based alumina (Al₂O₃) nanofluid is analyzed based on a single-component non-homogeneous volume fraction model (SCNHM) using the lattice Boltzmann method (LBM). The present model accounts for the slip mechanisms such as Brownian and thermophoresis between the nanoparticle and the base fluid. The average Nusselt number at the bottom wall for pure water is compared to the previous numerical data for natural convection in a cavity and a good agreement is obtained. The parameters considered in this study include the Rayleigh number of the nanofluid, the volume fraction of alumina nanoparticle and the aspect ratio of the cavity. For the Al₂O₃/water nanofluid, it is found that heat transfer rate decreases with an increase of the volume fraction of the nanoparticle. The results are demonstrated and explained with average Nusselt number, isotherms, streamlines, heat lines, and nanoparticle distribution. The effect of nanoparticles on the onset of instability in R-B convection is also analyzed.     

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.     

Generality of Brownian motion velocity of two phase approach in interrupted microchannel heat sink

The thermal performance of a single interrupted microchannel heat sink is analyzed. The generality of Brownian motion velocity had been investigated in the range of various Reynolds numbers of 168 to 1200 and Al₂O₃ nanofluid volume fractions of 0.01 to 0.04. Three different Brownian motion velocities represent the nanoparticle velocity had been modeled in two-phase modeling of nanofluid system. The heat transfer enhancement in this study is investigated in terms of the predicted Nusselt number. As the Reynolds number increased from 200 to 1200, augmentation in average Nusselt number is predicted from 57.64% to 57.97%. At increasing nanofluid volume fraction from 0.01 to 0.04, conduction dominated the heat transfer process results in Nusselt number increment from 3.90% to 5.13%.     

Cooling performance investigation of electronics cooling system using Al2O3–H2O nanofluid

In this study, the cooling performance of Al₂O₃–H₂O nanofluid was experimentally investigated as a much better developed alternative for the conventional coolant. For this purpose the nanofluid was passed through the custom-made copper minichannel heat sink which is normally attached with the electronic heat source. The thermal performance of the Al₂O₃–H₂O nanofluid was evaluated at different volume fraction of the nanoparticle as well as at different volume flow rate of the nanofluid. The volume fraction of the nanoparticle varied from 0.05 vol.% to 0.2 vol.% whereas the volume flow rate was increased from 0.50 L/min to 1.25 L/min. The experimental results showed that the nanofluid successfully has minimized the heat sink temperature compared to the conventional coolant. It was noticed also that the thermal entropy generation rate was reduced via using nanofluid instead of the normal water. Among the other functions of the nanofluid are to increase the frictional entropy generation rate and to drop the pressure which are insignificant compared to the normal coolant. Given the improved performance of the nanofluid, especially for high heat transportation capacity and low thermal entropy generation rate, it could be used as a better alternative coolant for the electronic cooling system instead of conventional pure water.     

Electromagnetohydrodynamic boundary layer flow in hybrid nanofluid with thermal radiation effect: Numerical simulation

Hybrid nanofluid boundary layer flow past a stretching surface with zero mass flux boundary condition is explored in this article. The main aim of this article is to analyze the electromagnetohydrodynamic role in a hybrid nanofluid containing silver and molybdenum disulfide nanoparticles. The self-similar solution is embedded to reduce the governing partial differential equation into algebraic equations and a shooting algorithm is applied to obtain the solution of the resultant boundary value problem. Variation in momentum, energy, and nanoparticle concentration is explained through graphical profiles. Nusselt number and drag force coefficients are computed for various flow parameters and their impact on the nanofluid and hybrid nanofluid is computed and presented and explained in a comparative fashion. It is observed that the velocity profile shows the opposite nature with respect to the electric field and magnetic field. For electric field parameter velocity accelerates whereas for magnetic parameter velocity diminishes. Nusselt number increases with electric field parameter and nanoparticle volume fraction.     

MHD Eyring–Powell nanofluid past over an unsteady exponentially stretching surface with entropy generation and thermal radiation

This study's primary objective is to analyze the entropy generation in an unsteady magnetohydrodynamics (MHD) Eyring–Powell nanofluid flow. A surface that stretched out exponentially induced flow. The influences of thermal radiation, thermophoresis, and Brownian motion are also taken into consideration. The mathematical formulation for the transport of mass, momentum, and heat described by a set of partial differential equation is used, which is then interpreted by embracing the homotopy analysis method and with a fourth-order precision program (bvp4c). Graphical results display the consequences of numerous parameters on velocity, temperature, concentration, and entropy generation. Moreover, escalating amounts of the magnetic parameter, thermal radiation parameter, Reynolds number, and Brinkman number improve the entropy profile of the nanofluid. The rate of heat flux and the mass flux conspicuously improves for non-Newtonian fluid as compared to Newtonian fluid.     

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.     

Numerical investigation of non‐Newtonian nanofluid mixed convection in a two‐opposite direction lid‐driven cavity with variable properties

The mixed convection fluid flow in a square cavity filled with AL₂O₃‐water non‐Newtonian nanofluid is numerically analyzed. The left and right vertical boundaries of the enclosure have been kept in the constant temperature. Remaining walls of the cavity have been considered to have adiabatic boundary condition. Two different cases have been considered. In the first case, left and right side walls have been moved vertically with constant speed V_b in opposite directions. In the second case, the directions of their motions have been reversed. The transport equations, written in terms of the primitive variables for the non‐Newtonian nanofluid, have been solved numerically using the finite volume method. The shear stresses were calculated using the Ostwald‐de Waele model for the shear‐thinning nanofluid. The model introduced by Patel et al was used to obtain the thermal conductivity of the nanofluid. The variation of the fluid flow with respect to the Richardson number and volume fraction of the nanoparticles was investigated through a parametric study. Even though increasing the volume fraction of nanoparticles leads to heat transfer enhancement, for the second case of this study, for Ri = 1, the average Nusselt number initially drops sharply by increasing the volume fraction of nanoparticles, then remains constant.     

Study of flow field,heat transfer,and entropy generation of nanofluid turbulent natural convection in an enclosure utilizing the computational fluid dynamics‐artificial neural network hybrid method

In this study, the turbulent natural convection of Ag‐water nanofluid in a tall, inclined enclosure has been investigated. The main objective of this study is finding the optimized angle of the enclosure with operational boundary condition in cooling from ceiling utilizing the computational fluid dynamics‐artificial neural network (CFD‐ANN) hybrid method, which has not been noticed in previous studies. To achieve this, we proposed two approaches. First, the simulations have been done with a deviation angle of 0 to 90° by using water and Ag‐water nanofluid. And second, a new prediction approach is proposed based on radial basis function artificial neural networks (RBF‐ANN) to predict the mean Nusselt number and entropy generation with the variation of Rayleigh numbers, deviation angles, and volume fractions as inputs. The results from the first approach indicate that the Rayleigh number has a considerable function in the determination of optimized angle. The results from the second approach, which used the first approach simulation results as training data set, could predict the mean Nusselt number and entropy generation with 1.4577e^?022 and 1.552e^?015 mean square error, respectively. Moreover, a new set of data for Rayleigh numbers, deviation angles, and volume fractions were used to test the performance of the prediction model, which shows promising and superior prospects for RBF‐ANN.     

Al2O3–Water nanofluid heat transfer and entropy generation in a ribbed channel with wavy wall in the presence of magnetic field

In this article, a parametric study is conducted to evaluate heat transfer enhancement in a ribbed channel containing Al₂O₃–Water nanofluid with wavy wall. The physical domain is under the influence of the magnetic field that creates a negative force against the working fluid to move. Nanofluid with higher temperature enters the cool ribbed duct and heat is exchanged along the walls of channel. The effects of the dominant parameters including number of the blocks, solid volume fractions of nanofluid, Hartmann number, Reynolds number, and different states of amplitude sine waves are numerically tested on the local and average Nusselt number, skin friction, and total entropy generation. Excellent agreement between present study and previous literature is observed. It is found that, an augmentation in magnetic field will result in higher values of both local and average Nusselt number accompanying with bigger values of skin friction and entropy generation. Computations illustrate that, increasing the solid volume fraction of the Al₂O₃ nanoparticles will raise the Nusselt number and total entropy generation rate but its effect on the skin friction is negligible. Also, numerical results imply that increasing amplitude sine waves of the geometry has incremental effect on the Nusselt number and skin friction but its effect on the total entropy generation rate is not so clear. Moreover, by adding number of the used blocks in the presence of magnetic field, the local Nusselt number experiences more jumps but it does not increase the average Nusselt number, necessarily. In addition, using more blocks increases skin friction but it has a reverse effect on the total entropy generation rate.     

Bioconvective electromagnetic nanofluid transport from a wedge geometry: Simulation of smart electro‐conductive bio‐nanopolymer processing

A mathematical model is presented for steady, two‐dimensional, stagnation‐point flow, heat, mass, and micro‐organism transfer in a viscous, incompressible, bioconvective, electromagnetic nanofluid along a wedge with Stefan blowing effects, hydrodynamic slip, and multiple convective boundary conditions. Gyrotactic micro‐organisms are present in the nanofluid and bioconvection arises, characterized by micro‐organisms swimming under a competing torque. Similarity transformations are used to render the system of governing partial differential equations into a system of coupled similarity equations. The transformed equations are solved numerically with the BVP5C method. The impact of emerging parameters on dimensionless velocity, temperature, magnetic induction function, nanoparticle volume fraction, and density of motile micro‐organisms is studied graphically. Furthermore, the responses of the local skin friction, local Nusselt number, local Sherwood number, and the wall gradient of density of motile micro‐organism number to variation in these parameters are elaborated. Validation of solutions with previous studies based on special cases of the general model is included. The simulations are relevant to the processing of biological, electro‐conductive nanomaterials and industrial hygienic coating systems exploiting combined electromagnetics, nanosystems, and microscopic, bio‐propulsion mechanisms.     

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.     

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