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.     

Thermal boundary layers in magnetohydrodynamic flow over a flat plate in the presence of a transverse magnetic field

Summary A boundary layer solution for the heat transfer of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field has been studied. The heat due to viscous dissipation and stress work were also included into the energy equation. The governing nonsimilar partial differential equations are transformed into ordinary differential ones by means of difference-differential method. The temperature profiles and heat transfer coefficient are obtained for various values of the parameters entering the problem.     

Unsteady two-dimensional and axisymmetric MHD boundary-layer flows

Summary Nonsimilar solution of the unsteady laminar incompressible magneto-hydrodynamic boundary layer flow and heat transfer for an electrically conducting fluid over two-dimensional and axisymmetric bodies in the presence of an applied magnetic field has been obtained. The effects of surface mass transfer, Joule heating and viscous dissipation are included in the analysis. Numerical computation have been carried out for the flow over a circular cylinder and a sphere using an implicit finite difference scheme in combination with a quasi-linearization technique. It is observed that magnetic field and suction cause the location of vanishing skin friction to move downstream while, the effect of injection is just the opposite. The effect of magnetic field on the skin friction is more pronounced as compared to its effect on the heat transfer. On the other hand, the heat transfer is strongly affected by the viscous dissipation and the effect is more for larte times. However, heat transfer responds comparatively less to the fluctuations of the free stream than the skin friction.     

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.     

Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids

This paper examines the unsteady boundary layer magnetohydrodynamic flow and convective heat transfer of an exponentially stretching surface saturated by nanofluids in the presence of thermal radiation. The combined effect of stratifications (thermal and concentration) in the unsteady boundary layer flow past over a stretching surface embedded in a porous medium is analyzed. The system of coupled nonlinear differential equations are solved numerically by developing finite difference scheme together with the Newton’s linearization technique, which allows us to control nonlinear terms smoothly. The study shows that the thermal boundary layer thickness significantly increases with the increase of Brownian motion, thermophoresis number and magnetic field strength. The unsteadiness behavior of the flow of nanofluid has reducing effect on both momentum and thermal boundary layer thickness. The Brownian motion has controlling effect on nanoparticle migration. The entropy generation by means of Bejan number has strong impact on the applied magnetic field, dissipation of energy, thermal radiation and Biot number.     

Laminar heat transfer to power law fluids in flat gaps with various thermal wall conditions

Summary This paper deals with laminar, steady heat transfer in flat gaps formed by two wide parallel plates to power law fluids with temperature dependent rheological properties. Basic equations governing the problem to be discussed here are derived including the effects of viscous dissipation but neglecting the internal heat generation. The derived equations of motion, energy and continuity (the last in integral form) have been solved numerically by means of Dufort-Frankel scheme for various thermal wall conditions (constant and variable wall temperature as well as constant and variable wall heat flux). The results of numerical computations are presented in form of graphs illustrating the changes in temperature and velocity profiles as well as in local and mean Nusselt numbers and pressure drops with increasing distance from the inlet cross section. A special attention has been paid to the effects of viscous dissipation and temperature dependent rheological fluid properties on the changes mentioned above. The present work is intended to be an extension of the classical Graetz-Nusselt problem on non-Newtonian power law fluids with temperature dependent rheological properties flowing through a narrow gap formed by two wide parallel plates.With 8 Figures     

Effects of CuO nano powder on performance improvement and entropy production of double-pipe heat exchanger with innovative perforated turbulators

The objective of the present numerical study is to investigate the heat transfer enhancement, entropy generation, and thermal performance of turbulent nanofluids inside double-pipe heat exchangers equipped with novel perforated cylindrical turbulators. Effects of inflow velocity, CuO nanoparticles volume fraction and perforated index are evaluated on the Nusselt number, friction loss, thermal performance factor (η), and viscous irreversibilities of the double-pipe heat exchangers. The newly proposed perforated turbulators with CuO nanopowder with ϕ = 1.5% provide the thermal performance of η = 1.931, which is considerably higher than the other previous studies. The results show that raising PI reduces the turbulent kinetic energy, especially in outer regions of the cylindrical turbulator. The jet formation near the walls and the perforations is the primary physical reason for this. The viscous entropy generation is increased up to 153.0% by increasing the Re number from 6,000 to 17,000 for PI = 8% and DR = 0.7. Thermal boundary layer disruption is the primary physical reason for heat transfer enhancement.     

Nonsimilar laminar incompressible boundary layers with vectored mass transfer

The effect of vectored mass transfer on the flow and heat transfer of the steady laminar incompressible nonsimilar boundary layer with viscous dissipation for two-dimensional and axisymmetric porous bodies with pressure gradient has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The skin friction is strongly influenced by the vectored mass transfer, and the heat transfer both by the vectored mass transfer and dissipation parameter. It is observed that the vectored suction tends to delay the separation whereas the effect of the vectored injection is just the reverse. Our results agree with those of the local nonsimilarity, difference-differential and asymptotic methods but not with those of the local similarity method.     

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.     

Thermomechanical behaviour of metals in cyclic loading

Temperature variation induced by repeated mechanical cyclic loading on AISI 1045 mild steel was studied.The experimental results of cyclic loading at low stress levels elucidate the coupling phenomena of thermal/mechanical behaviour which causes cooling and/or heating corresponding to the stressed state. The governing factors are thermoelastic effect and viscous dissipation. The thermoelastic effect causes the specimen temperature to go down and/or up which corresponds to the loading and/or unloading in cycling, where the viscous dissipation effect causes heat to generate inside the sample which steadily heats the specimen. As a result, a trend of increasing specimen mean temperature with periodical local fluctuation on temperature history can be observed. The heating rate, due to viscous dissipation, is increased with increasing strain rate. Cyclic loading at high stress levels results in large amounts of heat generation where thermoplasticity predominates. An abrupt temperature rise in the first few cycles, followed by a slow-down in later cycling, is to be seen. The phenomena and results were discussed. In addition, the effect of heat transfer between the specimen and its surroundings should be considered for both cases if the time is sufficiently long or the temperature gradient evolved is of significance.     

Analysis of slip flow heat transfer between two unsymmetrically heated parallel plates with viscous dissipation

This paper presents an analytical investigation to study the heat transfer and fluid flow characteristics in the slip flow region for hydrodynamically and thermally fully developed flow between parallel plates. Both upper and lower plates are subjected to asymmetric heat flux boundary conditions. The effect of first order velocity slip, temperature jump, asymmetric heat flux ratio and viscous dissipation on the heat transfer performance is analyzed. Closed form expressions are obtained for the temperature distribution and Nusselt number. Present predictions are verified for the cases that neglect the viscous heating and microscale effects. The effect of asymmetric heat flux ratio with and without viscous dissipation on Nusselt number for both macroscale and microscale is highlighted. The heat transfer characteristics are found to depend on various modeling parameters, namely, modified Brinkman number, Knudsen number and heat flux ratio.     

Heat transfer in micropolar boundary layer flow over a flat plate

Boundary layer solutions are presented to study the steady state heat transfer from a semi-infinite flat plate to a micropolar fluid. The boundary conditions of isothermal wall, constant surface heat flux and insulated wall with viscous dissipation effects have been treated in this paper. Numerical results for the temperature distribution and the missing wall values of the thermal functions have been given. The range of Prandtl numbers investigated was from 10 to 1000 while the dimensionless grouping of the material properties was allowed to vary over a wide range.     

The study of entropy generation during flow boiling in a micro-fin tube

Increasing in the heat transfer rate in flow boiling is a common and key issue for engineers. Generally, the heat transfer coefficient augmentation methods are divided into two main categories (active and passive methods). In passive methods the increase in heat transfer rate causes the increase in pressure drop. In order to evaluate the contribution of heat transfer and pressure drop mechanisms, the entropy generation analysis is used. In this paper, the entropy generation in micro-fin tube is investigated under flow boiling condition. The effect of different geometrical parameters and flow conditions is discussed on pressure drop contribution and heat transfer one in entropy generation, irreversibility distribution ratio (IDR) and Bejan number (Be). The frictional pressure drop and heat transfer coefficient in the micro-fin tube and the helically coiled one are compared as two enhancements passive heat transfer methods with the smooth straight tube in the literatures. Therefore, by introducing entropy generation number (N_s), the favorable geometry between the micro-fin tube and the helically coiled one with respect to the smooth straight tube is recognizable at equivalent boundary conditions.     

A computational study of viscous dissipation and entropy generation in unsteady pipe flow

Numerical simulations of transient entropy generation in a reservoir-pipe-valve system are presented. The flow transient is initiated through sudden closure of the downstream valve. An unsteady two-dimensional water hammer model is adopted. Time integration is performed using the classical fourth-order Runge?CKutta method while the spatial terms are discretized using central difference expressions. Entropy generation is shown to depend on a non-dimensional parameter representing the ratio of the viscous diffusion time scale to the pipe period. For small values of the non-dimensional parameter, entropy generation is rapidly attenuated from its steady-state value to zero while for large values, entropy generation persists for a much longer time. Moreover, for large values of the non-dimensional parameter, excessive entropy generation rates are realized during the transient which are several orders of magnitude higher than the steady-state rate. Such a behavior is attributed to elevated transient shear stress values in the near wall region which result in excessive viscous dissipation and hence higher entropy generation rates. Finally, it is shown that during the transient, the location of maximum entropy generation is no longer restricted to the pipe wall.     

Investigation of entropy generation in a helically coiled tube in flow boiling condition under a constant heat flux

There are many methods to augment the heat transfer rate in flow boiling in industrial applications. The helically coiled tubes are one of the best geometries to enhance the heat transfer rate. The entropy generation analysis is an appropriate tool to evaluate the contribution of heat transfer and pressure drop mechanisms. In the present paper, the entropy generation in the helically coiled tube under flow boiling is studied. The optimum tube and coil diameters under specified conditions are found. The effect of different flow conditions such as mass velocity, inlet vapor quality, saturation temperature, and heat flux on contributions of pressure drop and heat transfer in entropy generation is discussed. The Bejan number (Be) and irreversibility distribution ratio (IDR) at different saturation temperatures versus mass velocity are plotted. The comparison between entropy generation and contributions of pressure drop and heat transfer for the helically coiled tube and the straight one is presented. The entropy generation number (N_s) for different flow conditions is plotted. The entropy generation analysis shows that there is a favorable region to use the helically coiled tube with respect to the straight one.     

Thermal boundary layers over a shrinking sheet: an analytical solution

In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word.     

Unsteady MHD forced flow due to a point sink

Summary An analysis is performed to study the unsteady laminar incompressible boundary-layer flow of an electrically conducting fluid in a cone due to a point sink with an applied magnetic field. The unsteadiness in the flow is considered for two types of motion, viz. the motion arising due to the free stream velocity varying continuously with time and the transient motion occurring due to an impulsive change either in the strength of the point sink or in the wall temperature. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The magnetic field increases the skin friction but reduces heat transfer. The heat transfer and temperature field are strongly influenced by the viscous dissipation and Prandtl number. The velocity field is more affected at the early stage of the transient motion, caused by an impulsive change in the strength of the point sink, as compared to the temperature field. When the transient motion is caused by a sudden change in the wall temperature, both skin friction and heat transfer take more time to reach a new steady state. The transient nature of the flow and heat transfer is active for a short time in the case of suction and for a long time in the case of injection. The viscous dissipation prolongs the transient behavior of the flow.     

载冷气泡直接接触式对流换热过程熵产分析

研究了载冷气泡和制冰溶液的直接接触换热过程,建立了对流换热微分方程,得到了努塞尔数和雷诺数、普朗特数的传热关联式,通过实验数据验证了模型的准确性。利用传热关联式,针对换热过程的熵产作了分析,在以气泡直径作为换热特征尺寸下,换热过程中熵产数随着雷诺数的变化存在最小值。研究为直接接触式对流换热过程的优化提供了理论基础。     

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.     

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).