Non-Newtonian fluid flow in annular pipes and entropy generation: Temperature-dependent viscosity

Non-Newtonian fluid flow in annular pipes is considered and the entropy generation due to fluid friction and heat transfer in them is formulated. A third-grade fluid is employed to account for the non-Newtonian effect, while the Reynolds model is accommodated for temperature-dependent viscosity. Closed-form solutions for velocity, temperature, and entropy fields are presented. It is found that entropy generation number increases with reducing non-Newtonian parameter, while it is the reverse for the viscosity parameter, which is more pronounced in the region close to the annular pipe inner wall.     

Entropy Generation for Flow and Heat Transfer of Sisko-Fluid Over an Exponentially Stretching Surface

In the present study, the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered. The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations. Runge-Kutta-Fehlberg method is used to solve the governing problem. The effects of magnetic field parameter M, local slip parameter λ, generalized Biot number γ, Sisko fluid material parameter A, Eckert number Ec, Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity, temperature, local entropy generation number N_G and Bejan number Be are inspected. Moreover, the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited. The current results are helpful in checking the entropy generation for Sisko-fluid. It is found that, an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity. For shear thinning fluids (n < 1), the temperature dominates and the velocity rises. Local entropy generation number is more for larger generalized Biot number, magnetic field parameter and Brinkman number. The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases. The local Nusselt number decreases as magnetic field parameter, local slip parameter and Eckert number are increase, while it increases as material parameter, generalized Biot number and Prandtl number are increase.     

Thermodynamic analysis of free convection film condensation on an elliptical cylinder

Abstract

This paper aims to perform thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical cylinder. This is the first approach to investigate how the geometric parameter‐ellipticity and surface tension affect local entropy‐generation rate during film‐wise condensation heat transfer process. The results observe that entropy generation decreases with decreasing ellipticity. It indicates that the entropy generation number is nearly unaffected by surface tension forces at small ellipticity like e ≤ 0.7, but somewhat influenced at large ellipticity for the whole perimeter. From the second law point of view, local entropy generation increases with ellipticity as local heat transfer coefficient does. Furthermore, the entropy‐generation rate due to gravity‐driven film flow friction is proportional to Brinkman group parameter. The irreversibility ratio indicates that film flow friction irreversibility starts to dominate over heat transfer irreversibility in the lower half of streamwise length for higher values of Brinkman group parameter (Br/T = 1).     

Exact-solution of entropy generation for MHD nanofluid flow induced by a stretching/shrinking sheet with transpiration: Dual solution

In this article, attempts are made to present an exact solution for the fluid flow and heat transfer and also entropy generation analysis of the steady laminar magneto-hydrodynamics (MHD) nanofluid flow induced by a stretching/shrinking sheet with transpiration. This paper is the first contribution to the study of entropy generation for the nanofluid flow via exact solution approach. The governing partial differential equations are transformed into nonlinear coupled ordinary differential equations via appropriate similarity transformations. The current exact solution illustrates very good correlation with those of the previously published studies in the especial cases. The entropy generation equation is derived as a function of the velocity and the temperature gradients. The influences of the different flow physical parameters including the nanoparticle volume fraction parameter, the magnetic parameter, the mass suction/injection parameter, the stretching/shrinking parameter, and the nanoparticle types on the fluid velocity component, the temperature distribution, the skin friction coefficient, the Nusselt number and also the averaged entropy generation number are discussed in details. This study specifies that nanoparticles in the base fluid offer a potential in increasing the convective heat transfer performance of the various liquids. The results show that the copper and the aluminum oxide nanoparticles have the largest and the lowest averaged entropy generation number, respectively, among all the nanoparticles considered.     

Entropy generation in non-Newtonian fluid flow in a slider bearing

In the present study, entropy production in flow fields due to slider bearings is formulated. The rate of entropy generation is computed for different fluid properties and geometric configurations of the slider bearing. In order to account for the non-Newtonian effect, a special type of third-grade fluid is considered. It is found that the rate of entropy generation is influenced significantly by the height of the bearing clearance and the non-Newtonian parameter of the fluid.     

Numerical study on transient local entropy generation in pulsating turbulent flow through an externally heated pipe

This study presents an investigation of transient local entropy generation rate in pulsating turbulent flow through an externally heated pipe. The flow inlet to the pipe pulsates at a constant period and amplitude, only the velocity oscillates. The simulations are extended to include different pulsating flow cases (sinusoidal flow, step flow, and saw-down flow) and for varying periods. The flow and temperature fields are computed numerically with the help of the Fluent computational fluid dynamics (CFD) code, and a computer program developed by us by using the results of the calculations performed for the flow and temperature fields. In all investigated cases, the irreversibility due to the heat transfer dominates. With the increase of flow period, the highest levels of the total entropy generation rates increase logarithmically in the case of sinusoidal and saw-down flow cases whereas they are almost constant and the highest total local entropy is also generated in the step case flow. The Merit number oscillates periodically in the pulsating flow cases along the flow time. The results of this study indicate that flow pulsation has an adverse effect on the ratio of the useful energy transfer rate to the irreversibility rate.     

Magnetorheological rotational flow with viscous dissipation

Effects of a magnetic field and fluid nonlinearity are investigated for the rotational flow of the Carreau-type fluid while viscous dissipation is taken into account. The governing motion and energy balance equations are coupled, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow-gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, and the Deborah number on the stability of the flow were investigated. The introduction of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slow down the fluid motion. It, however, increases the fluid temperature. Moreover, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and increases with increasing Brinkman number.     

MHD boundary-layer flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream

Summary The MHD flow and heat transfer of a non-Newtonian power-law fluid over a continuously moving surface with a parallel free stream have been investigated. The partial differential equations governing the non-similar flow have been solved numerically using an implicit finite-difference scheme. The skin friction and heat-transfer coefficients increase with the magnetic parameter, and they are more for the pseudoplastic fluid than for the dilatant fluid. The heat-transfer coefficient increases significantly with the Prandtl number. The gradient of the velocity at the surface is negative when the wall velocity is greater than the free stream velocity, and it is positive when the wall velocity is less than the free stream velocity.     

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.     

Second Law Analysis and Optimization of Elliptical Pin Fin Heat Sinks Using Firefly Algorithm

One of the most significant considerations in the design of a heat sink is thermal management due to increasing thermal flux and miniature in size. These heat sinks utilize plate or pin fins depending upon the required heat dissipation rate. They are designed to optimize overall performance. Elliptical pin fin heat sinks enhance heat transfer rates and reduce the pumping power. In this study, the Firefly Algorithm is implemented to optimize heat sinks with elliptical pin-fins. The pin-fins are arranged in an inline fashion. The natureinspired metaheuristic algorithm performs powerfully and efficiently in solving numerical global optimization problems. Based on mass, energy, and entropy balance, three models are developed for thermal resistance, hydraulic resistance, and entropy generation rate in the heat sink. The major axis is used as the characteristic length, and the maximum velocity is used as the reference velocity. The entropy generation rate comprises the combined effect of thermal resistance and pressure drop. The total EGR is minimized by utilizing the firefly algorithm. The optimization model utilizes analytical/empirical correlations for the heat transfer coefficients and friction factors. It is shown that both thermal resistance and pressure drop can be simultaneously optimized using this algorithm. It is demonstrated that the performance of FFA is much better than PPA.     

Numerical study on heat transfer and entropy generation of developing laminar nanofluid flow in helical tube using two-phase mixture model

Nanofluids and helical tubes are among the best methods for heat transfer enhancement. In the present study, laminar, developing nanofluid flow in helical tube at constant wall temperature is investigated. The numerical simulation of Al₂O₃-water nanofluid with temperature dependent properties is performed using the two-phase mixture model by control volume method in order to study convective heat transfer and entropy generation. The numerical results is compared with three test cases including nanofluid forced convection in straight tube, velocity profile in curved tube and Nusselt number in helical tubes that good agreement for all cases is observed. Heat transfer coefficient in developing region inside a straight tube using mixture model shows a better prediction compared to the homogenous model. The effect of Reynolds number and nanoparticle volume fraction on flow and temperature fields, local and overall heat transfer coefficient, local entropy generation due to viscous dissipation and heat transfer, and the Bejan number is discussed in detail and compared with the base fluid. The results show that the nanofluid and the base fluid have almost the same axial velocity profile, but their temperature profile has significant difference in developing and fully developed region. Entropy generation ratio by nanofluid to the base fluid in each axial location along the coil length showed that the entropy generation is reduced by using nanofluid in at most length of the helical tube. Also, better heat transfer enhancement and entropy generation reduction can be achieved at low Reynolds number.     

Computational Analysis of the Effect of Nano Particle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption

The present study is concerned with the physical behavior of the combined effect of nano particle material motion and heat generation/absorption due to the effect of different parameters involved in prescribed flow model. The formulation of the flow model is based on basic universal equations of conservation of momentum, energy and mass. The prescribed flow model is converted to non-dimensional form by using suitable scaling. The obtained transformed equations are solved numerically by using finite difference scheme. For the analysis of above said behavior the computed numerical data for fluid velocity, temperature profile, and mass concentration for several constraints that is mixed convection parameter λ_t, modified mixed convection parameter λ_c, Prandtl number Pr, heat generation/absorption parameter δ, Schmidt number Sc, thermophoresis parameter N_t, and thermophoretic coefficient k are sketched in graphical form. Numerical results for skin friction, heat transfer rate and the mass transfer rate are tabulated for various emerging physical parameters. It is reported that in enhancement in heat, generation boosts up the fluid temperature at some positions of the surface of the sphere. As heat absorption parameter is decreased temperature field increases at position X = π/4 on the other hand, no alteration at other considered circumferential positions is noticed.     

Heat transfer in the flow of a viscoelastic fluid over a stretching sheet

Summary The problem of heat transfer in the viscoelastic fluid flow over a stretching sheet is examined. The important physical quantities such as the skin-friction coefficient and the heat transfer coefficient, are determined. It is found that the heat transfer coefficient decreases with the non-Newtonian parameter.     

Effects of curvature ratio on forced convection and entropy generation of nanofluid in helical coil using two-phase approach

Applying nanofluid and helical coils are two effective methods for thermal performance enhancement. Combination of these techniques could improve the energy efficiency of thermal equipment dramatically. In this study, a numerical analysis of nanofluid flowing in helical coil with constant wall temperature boundary condition was performed to evaluate nanofluid superiority over the base fluid. Forced convective heat transfer and entropy generation of aqueous Al₂O₃ nanofluid with temperature dependent properties were investigated. Eulerian two-phase mixture model was employed for nanofluid modeling and governing mass, momentum, energy, and volume fraction equations were solved using finite volume method. Simulations covered a range of nanoparticle volume fraction of 1–3%, Reynolds number from 200 to 2000, and curvature ratio of 0.05–0.2. In order to evaluate the heat transfer performance, a parameter referred as thermo-hydrodynamic performance index was applied. Also, entropy generation analysis was performed to examine the efficiency of the helical coil and nanofluid. The results demonstrate that performance index enhances by decreasing the Reynolds number and the increasing nanoparticle concentration. The best thermo-hydrodynamic performance can be obtained at low Reynolds number, high nanoparticle volume fraction, and large curvature ratio. Increasing curvature ratio decreases the ratio of local entropy generation by nanofluid to the base fluid. So, utilization of water based Al₂O₃ nanofluid in higher curvature ratio is more efficient from irreversibility point of view.     

Natural convection flow of a non-Newtonian fluid between two vertical flat plates

Summary The natural convection of a homogeneous incompressible fluid of grade three is investigated between two infinite parallel vertical plates. The effect of the non-Newtonian nature of fluid on the skin friction and heat transfer are studied.With 2 Figures     

Experimental study on pressure drop and heat transfer in pipelines for brine based ice slurry. Part I: Operational parameters correlations

Ice slurry flow through horizontal pipes is studied experimentally in order to find out its heat transfer and isothermal friction properties. Using 9% NaCl brine as the carrier fluid, different flow conditions are discussed with a view to analyse each involved variable. In this Part I, experimental data are directly correlated and easy-to-use expressions for the Darcy friction factor and the Nusselt number were obtained as functions of non-dimensional parameters expressing flow and geometrical properties. The most remarkable conclusion obtained is a clear influence of the ice particle–pipe diameter ratio in the pressure drop parameters, not previously taken into account, which must be confirmed in heat transfer process. The thermal and hydraulic performance of ice slurry flowing through corrugated pipes is also analysed showing, with regard to smooth pipe, the same behaviour in pressure drop and opposite behaviour in heat transfer.     

Effect of an inclined partition with constant thermal conductivity on natural convection and entropy generation of a nanofluid under magnetic field inside an inclined enclosure: Applicable for electronic cooling

Free convection heat transfer of Al₂O₃/water nanofluid in an inclined closed enclosure is investigated numerically considering radiation effects. A horizontal and constant magnetic field is applied to the chamber. The chamber also has an angle with the horizontal axis. A partition with constant thermal conductivity is positioned on the horizontal diameter of the enclosure and divides the fluid inside it into two parts. Parts of the left and lower walls of the chamber are kept at high temperature, and the right wall is kept at low temperature. The rest of the walls are also insulated. In the present work, in addition of investigation of the heat transfer rate (HTR), total entropy generation (TEG) and Bejan number (Be) are also evaluated. The results show that as the Hartmann number intensifies from 0 to 40, heat transfer and entropy generation decrease by 35% and 46%, respectively. An intensification of the Rayleigh number results in an intensification of the HTR by 39% and the entropy generation by 90%. The Bejan number decreases by augmenting the Rayleigh number and intensifies with the Hartmann number. The addition of radiation heat transfer results in an intensification of the entropy generation and a reduction in the Bejan number. The enclosure angle changes have different effects on the vortices formed at the top and bottom of the partition. As the hot wall length intensifies from 0.1 to 0.9, the Nusselt number and entropy generation become 3.77 and 2.8 times, respectively.     

Hydromagnetic stagnation point flow by a perturbation technique

An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generating/absorbing fluid at the stagnation point of an isothermal two-dimensional porous body immersed in a fluid saturated porous medium. The results are obtained by solving the coupled non-linear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique [A. Aziz, T.Y. Na, Perturbation Methods in Heat Transfer, Springer-Verlag, Berlin, 1984 (pp. 1–184), R. Kenneth Cramer, Shih-I Pai, Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill Book Company, New York, 1973 (pp. 164–171).]. These results are presented to illustrate the influence of the Hartmann number, Prandtl number, and dimensionless heat generation/absorption coefficient and suction injection parameter. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various parameters. These effects of the different parameters on the velocity and temperature as well as the skin friction and wall heat transfer are presented graphically.     

Effects of tangential and radial velocity on fluid flow and heat transfer for flow through a pipe with twisted tape insert—laminar flow

The present study reports the numerical analysis of fluid flow and heat transfer in a pipe with full length twisted tape insert. The investigation is carried out for five different twist ratios of 4, 5, 6, 8 and 10 at 100 ≤ Re ≤ 1000. The velocity field in terms of streamwise, tangential and radial velocity and temperature field are studied as a function of Reynolds number and twist ratio. The variation of friction factor and Nusselt number with Reynolds number for different twist ratios is also presented. The heat transfer enhancement due to insertion of twisted tape mainly comes from the tangential and radial components of velocities, which are regarded as secondary fluid motion. It is evident from the results that with increase in Reynolds number the axial convection increases. However, with the decrease in the twist ratio, the tangential and radial convection increases, leading to increased heat transfer. The secondary flow affects the thermal boundary layer inside the tube and increases the cross-flow mixing, which increases the heat transfer. The correlations for prediction of friction factor and Nusselt number based on the numerical data are also proposed.     

Boundary element method for natural convection in non-Newtonian fluid saturated square porous cavity

The main purpose of this work is to present the use of the Boundary Element Method (BEM) in the analysis of the natural convection in the square porous cavity saturated by the non-Newtonian fluid. The results of hydrodynamic and heat transfer evaluations are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated. The flow in the porous medium is modelled using the modified Brinkman extended Darcy model taking into account the non-Darcy viscous effects. The governing equations are transformed by the velocity–vorticity variables formulation enabling the computation scheme to be partitioned into kinematic and kinetic parts. To analyse the effects of the available non-Newtonian viscosity and to evaluate the presented approach, the power law model for shear thinning fluids (n<1), for shear thickening fluids (n>1) and in the limit for the Newtonian fluids (n=1) is considered. Numerical model is tested also for the Carreau model adequate for many non-Newtonian fluids. Solutions for the flow and temperature fields and Nusselt numbers are obtained in terms of a modified Rayleigh number Ra^*, Darcy number Da, and the non-Newtonian model parameters. The agreement between the results obtained with finite difference method is very good indicating that BEM can be efficiently used for solving transport phenomena in saturated porous medium.