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The oily water from various sources in combined cycle power plants is collected in oil/water separator in which the oil separates from water due to the density difference. The idea of the presented geometry is taken from conventional oil/water separators. This paper studies the natural convection of the CuO-water nanoliquid in a rectangular cavity with fins attached to the insulated wall and porous media. Discretion of Navier-Stokes equations is done by Finite Element Method and assumptions are laminar, steady and incompressible flow. Heat transfer performance and entropy generation are investigated for distinct Rayleigh numbers (103–105), Darcy numbers (10−2–10−4), and Hartmann numbers (0, 10, 20). Different sizes of the fins are also studied to show consequences of fin size on heat transfer in cavity. This is the first time that these parameters and their impacts on Nusselt number and entropy generation are studied for a conventional oil/water separator cavity. Corollaries demonstrate that increasing Rayleigh number and Darcy number improves heat transfer performance and average Nusselt number. Nevertheless, Hartmann number has a reverse effect with average Nusselt number. Finally, a new equation for average Nusselt number is developed with regard to Rayleigh number, Hartmann number, and Darcy number.

The effect of source/sink heat location and size on Magneto-hydrodynamic mixed convection in hybrid nanofluid of Al2O3-Cu/Water within the L-shaped cavity is studied in this paper. Two uniform heat sources are put at the corners of the bottom walls of enclosure and the beginning and the end of L-shape enclosure set to be at the cold temperature. The other parts of enclosure’s walls are supposed to be insulated. The finite difference method and Boussinesq approximation is utilized to discrete the governing equations. The fundamental flow physics and thermal behavior are explored in terms of pertinent parameters such as the effects of sink/source heat generation, magnetic field and angle, Hartmann number, cavity length ratio, and hybrid volume fraction on average and surface Nusselt number, streamlines, isotherms, and entropy generation are studied. The results demonstrate that maximum amount of the sink power causes the best heat transfer performance.

Carbon nanotubes (CNTs) are inevitable due to its tremendously high thermal and electrical conductivities, strength, stiffness, and toughness characteristics. The utilization of both porous media and nanofluids with CNTs as nanoparticles can augment the thermal efficiency of typical physical systems significantly. In view of such advantages, the present study is intended to convey the influence of entropy minimization and nonlinear thermal radiation on the electromagnetic flow of nanofluids with single wall carbon nanotubes (SWCNTs) and multiwall carbon nanotubes (MWCNTs) nanoparticles suspensions past the surface of thin needle. In addition, the famous Darcy Forchheimer flow and Cattaneo-Christov heat flux models are implemented. The required numerical solution is devised pragmatically via bvp4c in MATLAB for the system of highly nonlinear ordinary differential equations. It is found that the porous matrix and local Forchheimer parameter are detrimental to the regular flow of nanofluids. Thermal fields magnify in respect of hiked porosity and temperature ratio parameters and diminish due to rise in electric and thermal relaxation parameters. Entropy minimization due to porous irreversibility is prominent for MWCNTs than SWCNTs. Bejan number upsurges due to rise in volume fraction and porosity parameter for both SWCNT-water and MWCNT-water nanofluids.

The present article candidly states the incremental impact of nonlinear thermal radiation on heat transfer enhancement due to Darcy–Forchheimer flow of spinel-type MnFe2O4-Casson/water nanofluids due to a stretched rotating disk. In present contest, the entropy generation approach is highlighted specially as a powerful tool for the analysis of the brain function, in accordance with the theological and philosophical approach of Saint Thomas Aquinas. The some of the results of the present study that strengthening of permeability and Casson parameter contribute to the diminution of radial and tangential velocity profiles and yield shrinkage of the related boundary layers. An increase in thermal radiation leading to more heat propagating into the fluid thereby improves the TBL. Fluids with non-Newtonian behavior contribute greater entropy generation rate compared to Newtonian fluids. The most significant outcome is that the entropy generation makes a real contribution to the brain function or analysis of the function of the brain.

Purpose Natural convection heat transfer analysis can be completed using entropy generation analysis. This study aims to accomplish both the natural convection heat transfer and entropy generation analyses for a hexagonal cavity loaded with Cu-H2O nanoliquid subjected to an oriented magnetic field. Design/methodology/approach Control volume-based finite element method is applied to solve the non-dimensional forms of governing equations and then, the entropy generation number is computed. Findings The results portray that both the average Nusselt and entropy generation numbers boost with increasing aspect ratio for each value of the undulation number, while both of them decrease with increasing the undulation number for each amplitude parameter. There is a maximum value for the entropy generation number at a specified value of Hartmann number. Also, there is a minimum value for the entropy generation number at a specified value of angle of the magnetic field. When the volume fraction of nanoparticles grows, the average Nusselt number increases and the entropy generation number declines. The entropy generation number attains to a maximum value at Ha = 14 for each value of aspect ratio. The average Nusselt number ascends 2.9 per cent and entropy generation number decreases 1.3 per cent for Ha = 0 when ϕ increases from 0 to 4 per cent. Originality/value A hexagonal enclosure (complex geometry), which has many industrial applications, is chosen in this study. Not only the characteristics of heat transfer are investigated but also entropy generation analysis is performed in this study. The ecological coefficient of performance for enclosures is calculated, too.

The purpose of the current study is to numerically investigate the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure. A numerical method called the control volume-based finite element method is implemented for solving the governing equations. The modified flow and thermal structures and corresponding heat transfer features are investigated. Numerical outcomes reveal very good grid independency and excellent agreement with the existing studies. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt number. Further, enhancement of Rayleigh number increases the velocity of nanofluid, while that of aspect ratio of the elliptical cylinder shows the opposite trend.

The aim of the current study is natural convection analysis conjugated with entropy generation analysis in an incinerator shaped permeable enclosure loaded with Al2O3–H2O nanofluid subjected to the magnetic field with a rectangular wavy heater block positioned on the bottom of the cavity wall. The bottom and top horizontal walls are adiabatic; the inclined and vertical walls are thought to be cooled. Firstly, the governing expressions and standard k–e turbulence model are rewritten from dimensional form to non-dimensional form using dimensionless parameters such as vorticity and stream function. In the next step, the equation of entropy generation is written in dimensionless form. Then, the system of non-dimensional governing equations is solved by the finite volume method (FVM) conjugated with a non-dimensionalization scheme using ANSYS Fluent. Fine grids (wall y+

In this article, shape effects of copper-Oxide are analyzed for heat transfer characteristics within the partially heated rhombus enclosure. Additionally, a circular barrier is that have three diverse constraints (adiabatic, cold and hot) is placed at the center of the rhombus. Water is used as a base fluid to constitute the working nanofluid (CuO-water). Heat transfer within the enclosure happens due to a differential temperature at the cavity walls. The governing partial differential equations include conservation of energy, momentum and mass which are numerically solved via CVFEM. The study concludes that heat transfer rate is ascended owing to ascendant in Rayleigh number and descended owing to ascendant in nanoparticles volume fraction. The study further discloses that the maximum heat transfer rate is ascended owing to ascendant in nanoparticles shape factor. In order to determine the stream function and isotherms, various physical domain has been selected for each emerging parameter such as nanoparticles' shape factor, Rayleigh number, and nanoparticle volume fraction. It is concluded that the heat transfer rate is maximum using Platelet shaped nanoparticles.

Homotopy analysis method (HAM) simulations for hydromagnetic stratified viscoelastic nanoliquid in frames of non-Darcian characteristics are addressed in this attempt. The nanoliquid model comprising Brownian and thermophoretic movements is taken into account for formulation and analysis. The novel aspect featuring convective conditions and stratifications is introduced. Boundary-layer idea presented by Prandtl is implemented to simplify the complex systems which are then converted to ordinary ones employing transformation procedure. Besides, a detailed discussion is elaborated for various non-dimensional variables against significant profiles.

Purpose This paper aims to study the impacts of viscous dissipation, thermal radiation and Joule heating on squeezing flow current and the heat transfer mechanism for a magnetohydrodynamic (MHD) nanofluid flow in parallel disks during a suction/blowing process. Design/methodology/approach First, the governing momentum/energy equations are transformed into a non-dimensional form and then the obtained equations are solved by modified Adomian decomposition method (ADM), known as Duan–Rach approach (DRA). Findings The effect of the radiation parameter, suction/blowing parameter, magnetic parameter, squeezing number and nanoparticles concentration on the heat transfer and flow field are investigated in the results. The results show that the fluid velocity increases with increasing suction parameter, while the temperature profile decreases with increasing suction parameter. Originality/value A complete analysis of the MHD fluid squeezed between two parallel disks by considering Joule heating, thermal radiation and adding different nanoparticles using the novel method called DRA is addressed.

Purpose The purpose of this study is to elaborate mixed convection impact in stratified nanofluid flow by convectively heated moving surface. Rheological relations of second-grade fluid are used for formulation. Magnetic field, heat absorption/generation and convective conditions are considered for modeling. Design/methodology/approach Convergent solutions are achieved using homotopy procedure. Findings The authors found opposing behavior for radiation and thermal stratification variables against thermal field. Originality/value No such analysis has yet been reported.

The critical capability of Natural circulation flow for the removing heat has been demonstrated and are widely used in the industry particularly received notable attention to improve passive safety and decrease running expenses in the latest version of nuclear reactors. Among the different type of natural circulation systems, the distinctive characteristics of single-phase natural circulation loops (NCLs), those involved even in very simplified models, are identified to be characterized by a deep complexity of chaotic behavior. In this investigation the experimental data gathered in the AKIAU-R-1P loop, a rectangular single-phase NCL through a test operation, are compared with the results of simulations obtained by one-dimensional RELAP5/Mod3.2 code and three-dimensional ANSYS FLUENT 17.1 computational fluid dynamic (CFD) code. The experimental data, including time histories of the temperature difference over the heater, was almost similar to the predicted simulation results of RELAP5 and ANSYS FLUENT. The RELAP5 code has the capability of prediction the status at low power levels (stable mode) with adequate correctness rather than CFD code whereas when the system is unstable at higher power, CFD indicates further oscillatory behavior in comparison with RELAP5 code and experimental data. The CFD code was functional in presenting the diffusive phenomena which could not be estimated by the RELAP5 one-dimensional model.

The objective of the present study is to peruse the natural convection in the cavity containing inclined elliptical heater under shape factor of nanoparticles and magnetic field. The control volume-based finite element method is used for solving conservation equations. Numerical results show very good grid independency and very good compromise with other works. The result shows the heat transfer grows via mounting nanofluid volume fraction. The increment of Ra number also leads the heat transfer to ascend. Heat transfer of nanofluid with three different shapes of nanoparticles is studied, and results show the platelet nanoparticle is better than the other ones. The influence of magnetic field on heat transfer is also investigated and discussed. The obtained outcomes represent that at a certain Rayleigh number, the average Nusselt number descends with the ascendant of Hartmann number. Finally, the new correlation is reported for calculating the Nu number in these geometries.

The aim of the current study is to investigate the natural convection heat transfer in a square enclosure with a wavy circular heater under magnetic field and nanoparticles. The governing equations that are expressed in dimensionless form are solved by means of control volume finite element method employing a validated FORTRAN code. The dimensionless controlling parameters of the present investigation are shape factor of nanoparticles (m), Hartmann number (Ha), Rayleigh number (Ra), and nanoparticle volume fraction (ϕ). In this study, the amplitude A and number of undulations N are fixed at a constant value of 0.2 and 8, respectively. The obtained results portray that in the presence of waves on the inner wall of the annulus, the heat transfer rate is an ascending function of Rayleigh number, nanoparticle volume fraction and less obvious function of their shape factor, while it is a descending function of the Hartmann number.

Purpose The purpose of this study is to peruse natural convection in a CuO-water nanofluid-filled complex-shaped enclosure under the influence of a uniform magnetic field by using control volume finite element method. Design/methodology/approach Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with the Koo–Kleinstreuer–Li correlation for the effective dynamic viscosity and the effective thermal conductivity have been solved numerically by control volume finite element method. Findings Effects of various pertinent parameters such as Rayleigh number, Hartmann number, volume fraction of nanofluid and shape factor of nanoparticle on the convective heat transfer characteristics are analysed. It was observed that local and average heat transfer rates increase for higher value of Rayleigh number and lower value of Hartmann number. Among various nanoparticle shapes, platelets were found to be best in terms of heat transfer performance. The amount of average Nusselt number reductions was found to be different when nanofluids with different solid particle volume fractions were considered due to thermal and electrical conductivity enhancement of fluid with nanoparticle addition. Originality/value A comprehensive study of the natural convection in a CuO-water nanofluid-filled complex-shaped enclosure under the influence of a uniform magnetic field by using control volume finite element method is addressed.

This study presents the effect of non-uniform heat source on the magneto-hydrodynamic flow of nanofluid across an expanding plate with consideration of the homogeneous-heterogeneous reactions and thermal radiation effects. A nanofluid’s dynamic viscosity and effective thermal conductivity are specified with Corcione correlation. According to this correlation, the thermal conductivity is carried out by the Brownian motion. Similarity transformations reduce the governing equations concerned with energy, momentum, and concentration of nanofluid and then numerically solved. The influences of the effective parameters, e.g., the internal heat source parameters, the volume fraction of nanofluid, the radiation parameter, the homogeneous reaction parameter, the magnetic parameter, the heterogeneous parameter and the Schmidt number are studied on the heat and flow transfer features. Further, regarding the effective parameters of the present work, the correlation for the Nusselt number has been developed. The outcomes illustrate that with the raising of the heterogeneous parameter and the homogeneous reaction parameter, the concentration profile diminishes. In addition, the outcomes point to a reverse relationship between the Nusselt number and the internal heat source parameters.

Colloidal nanoparticles suspensions (nanofluids) are the materials of consideration for thermal engineering due to their typically enhanced heat transportation characteristics in comparison to base liquid. Nanoliquids have utilizations in transportation, solar absorption, nuclear systems chilling, friction reduction and energy storage etc. Besides, magnetic nanoliquids are utilized in the cancer therapeutics via implementation of drug delivery and cancer imaging. Thus, in view of such utilizations, here modeling and simulations are presented to scrutinize the natural convective Fe 3 O 4 -water nanoliquid flow in an annulus between a triangle and a rhombus enclosures. Thermal radiation aspect is considered for formulation. CVFEM is implemented for computations of numerical outcomes. Impacts of embedding variables on the flow and heat transfer features have been perused. Furthermore a correlation for average Nusselt number is established in terms of energetic parameters. The obtained results portray that average Nusselt number rises subjected to Rayleigh number, radiation parameter and volume fraction of nanofluid while it diminishes when Hartmann number is increased.

Researchers in modern science always attempt to find new techniques to optimize the performance of energy devices through heat transfer enhancement. It comes to the knowledge that such enhancement can be done with the help of nanofluids. Therefore, the present study is aimed to investigate the role of natural convection and thermal radiation on thermo-hydrodynamics of nanofluid heat transfer in an annulus between a wavy circular cylinder and a rhombus enclosure subject to a uniform magnetic field. A new model for viscosity called magnetic field dependent (MFD) viscosity is used. Mathematical formulation of the current physical model is based on the continuity, momentum and energy equations. Numerical simulation of the reduced problem is done with the help of Control Volume based Finite Element Method (CVFEM). The impacts of controlling physical parameters, for instance, Rayleigh number, radiation parameter, Hartmann number, aspect ratio, shape factor of nanoparticles and solid volume fraction of nanoparticles on thermo-hydrodynamics of flow are studied. The quantities of physical interest are graphically presented and discussed in detail. From the present study it becomes apparent that the local heat transfer rate decreases with an increase in aspect ratio in the absence of Hartmann number. In addition, for decreasing values of aspect ratio, the space for fluid flow inside enclosure becomes wider.

A simple rectangular natural circulation loop (NCL) consists of a heater, a cooler, cold leg and hot leg. The main aim of an NCL is to reject heat from heat sources to heat sinks with the use of a mechanical pump. NCL is used in various energy systems, such as solar heaters, nuclear reactors, geothermal power production and engine and computer cooling. In this study, a simple rectangular single-phase NCL with an asymmetric heater is numerically analyzed with respect to tested experimental data. First governing equations, i.e., mass, momentum, and energy balance equations are derived. Then, these equations are written in dimensionless form with proper definitions of the dimensionless parameters. The boundary conditions of NCL are heater power and cooler temperature that are modeled by modified Grashof number and modified Stanton number, respectively. A continuous friction law is used for numerical solution of governing equations that are applicable for the laminar, transition and turbulent flow regimes. The governing equations are solved for both the steady state and transient. The equations of the transient state are solved with both linear and nonlinear methods. In most of the earlier literature, a stability map has been reported that is only applicable for laminar or turbulent flows. But in the present work, a stability map is obtained, which is valid for all the three regions (laminar, transition, and turbulent). Finally, the experimental data are compared with the numerical results.

In this work, transient movement of a vertically falling soluble spherical particle in a non-Newtonian medium is perused. It is supposed that the particle mass diminishes owing to its solubility in the fluid, and thus particle size will be diminished by a linear function. The governing nonlinear differential equation is solved analytically using Collocation Method (CM). The impacts of the effective parameters of this study are examined on the velocity and acceleration. Further, the positions of the particle are portrayed graphically at every 1 s time trend. Also, the limiting cases are gained and are found to be in good compromise with the numerical and literature results. The outcomes portray that the particle with a larger rate of diameter diminution moving with larger velocity rather than smaller diameter particle.

Purpose The purpose of this study is to investigate free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using control volume finite element method (CVFEM). Design/methodology/approach Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with Brinkman correlation for the effective dynamic viscosity and Hamilton and Crosser model for the effective thermal conductivity have been solved numerically by CVFEM. Findings The impacts of control parameters such as the Rayleigh number, Hartmann number, nanoparticles volume fraction, local triangular heater size, shape factor on streamlines and isotherms as well as local and average Nusselt numbers have been examined. The outcomes indicate that the average Nusselt number is an increasing function of the Rayleigh number, shape factor and nanoparticles volume fraction, while it is a decreasing function of the Hartmann number. Originality/value A complete study of the free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using CVFEM is addressed.

Flow and heat transfer of MHD micro-polar nanofluid in a channel with penetrable walls and considering thermal radiation impact are investigated. A similarity transformation is utilized to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The gained non-linear ordinary differential equations are solved by Duan–Rach Approach (DRA). This method allows us to detect a solution without applying numerical methods to evaluate the unspecified coefficients. The impacts of diverse active parameters such as the micro-polar parameter, the magnetic parameter, the volume fraction of nanofluid and the radiation parameter on the velocity and temperature profiles are examined. Furthermore, the value of the Nusselt number is calculated and presented through figures. Keywords: Micro-polar nanofluid, Penetrable channel, MHD, Thermal radiation, Duan-Rach Approach (DRA)

Nanofluid flow and heat transfer in a rotating system between two parallel plates in the presence of thermal radiation and heat source impacts are examined. One of the plates of the considered system is penetrable and the other one is stretchable or shrinkable. A similarity transformation is used to convert the governing momentum and energy equations into non-linear ordinary differential equations with the relevant boundary conditions. The achieved non-linear ordinary differential equations are solved by Duan-Rach Approach (DRA). This method allows us to realize a solution without applying numerical methods to evaluate the unspecified coefficients. The impacts of diverse active parameters such as the stretching/shrinking parameter, the radiation parameter, the heat source parameter, the suction/blowing parameter, the Reynolds number and the volume fraction of nanofluid on the velocity and temperature profiles are explored. Also, the correlation for the Nusselt number has been developed in terms of active parameters of the present study. The outcomes indicate that the Nusselt number is a raising function of the injection parameter, nanofluid volume fraction and the radiation parameter, while it is a decreasing function of the suction and heat source parameters. Furthermore, for injection case by soaring the shrinking parameter, the probability of occurrence of the backflow phenomenon soars.

The heat transfer properties of current liquids are specifically improved by suspending nanocrystalline solid elements smaller than 100 nm in diameter. These liquids are considered as potential working fluids for applications such as car radiators, solar collectors, electronic frost systems, nuclear reactors and heat pipes. Due to such uses, here we formulate CuO–H2O nanofluids in a two-dimensional circular geometry with a rhombus-shaped barrier maintaining the constant temperature of two adjacent high walls. The streamlines and isotherms have been plotted using the control volume finite element method and applying the KKL model for nanofluid simulation. The results were calculated for different concentrations of nanoparticles, Hartmann number and Rayleigh number. It was found that in a large number of volume fraction and Hartmann number, the isotherms near the outer margin are more prominent while the low-volume-concentration isotherms are concentrated near the adiabatic wall of the obstacle. It was also found that there is a temperature gradient in the radial direction at a higher volume fraction and Hartmann number (Ha). The temperature gradient was limited to adiabatic walls of the obstruction in lower volume fraction and Ha. Two similar shapes but differently directed eddies are formed for any value of Ra in streamlines. |Ψmax|nf increases with an increase in the values of Ra from 103 to 105.

This study provides numerical analysis of the free convection of copper–water-based nanofluid filling a triangular cavity with semicircular bottom wall. The cavity sidewalls are maintained at cold temperature, while the semicircular wall is maintained at hot temperature. The other wall segments are thermally insulated. To control the energy transport within the cavity, a uniform magnetic field is applied horizontally. The physical domain is discretized according to the control volume finite element method which has been used to solve the governing equations. The physical and geometrical aspects of the current problem are investigated by inspecting the impacts of Rayleigh number, Hartman number, aspect ratio and the volume fraction of the Cu nanoparticles. Decreasing the radius of the hot semicircle enlarges the average Nusselt number at the absence of the magnetic field. When the magnetic field is applied, this effect is conversed within Ra ≤ 104. This conversed impact does not hold up when Ra is raised to 105. The numerical results are correlated in a sophisticated correlation of the average Nusselt number with other parameters.

In this work, magneto-hydrodynamic natural convection of a nanofluid in a wavy cavity considering Brownian motion is studied numerically using the control volume finite element method. The effective viscosity and thermal conductivity of the nanofluid are defined by the correlation in which the impact of Brownian motion on the thermal conductivity is considered. The considered wavy cavity is heated from the left side and it cooled from the right side. Also, the top and bottom walls of the considered wavy cavity are assumed adiabatic. The impacts of various controlling parameters such as the Rayleigh number, wavy contraction ratio, Hartmann number and undulation number are examined on the contour maps of the streamlines and the isotherms. Further, the average and local Nusselt numbers are calculated and presented graphically and discussed. The findings narrate that the strength of the convective flow has a direct relationship with the Rayleigh number and also it has a reverse relationship with the wavy contraction ratio.

The present article has been groomed to explore the boundary-driven magnetized flow of cross nanoliquid over thin needle subject to auto catalysis chemical reactions. In addition to it, the effect of entropy optimization model is incorporated and transportation of heat under non-uniform heat source/sink, Cattaneo-Christov heat flux (rectified Fourier) viewpoint (CCHF), and non-linear thermal radiation is also taken into account. Furthermore, the Brownian and thermophoresis aspects of nanoliquid are invoked. The dimensionless governing equations are solved by apposite shooting scheme. The outcomes of the present study via demonstrated graphs and numerical benchmarks seem to indicate that controlled Sakiadis and Blausius flow pattern of cross nanofluids is attained due to incremented magnetic field strength. Temperature ratio parameter contributes the upgradation of thermal boundary layer thickness and homogenous reaction rate leads to the diminution of nanoparticles concentration. The relative values of needle velocity and the velocity of cross nanofluid are most important factor for the regulation of viscous drag force and rate of heat transportation. Augmented Weissenberg parameter and Reynolds number are the prime factor for the uplift of the flow field and the related layer thickness. Furthermore, the existence of CCHF could result in augmentation in Nusselt.

In this paper, MHD nanofluid flow, heat and mass transfer between non-parallel walls is investigated. Brownian diffusion and thermophoresis effects which are two momentous slip mechanisms in nanofluids have been considered in the nanofluid model. Also, Joule heating effect is taken into account. The governing radial momentum, energy and mass equations are solved by Duan–Rach Approach (DRA). This method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The effects of active parameters such as the Reynolds number, the opening angle parameter, the Schmidt number, thermophoretic parameter and Brownian parameter are investigated on the velocity, temperature and concentration. Also, the value of the Nusselt number is calculated and presented through figures. The results indicate that the temperature and concentration profiles and Nusselt number increase with the increasing Schmidt number. In addition, the limiting cases are gained and found to be in an excellent agreement with the previous works.

In this paper, flow and heat transfer of MHD Go-water nanofluid between two parallel flat plates in the presence of thermal radiation are studied. One of plates is externally heated and cooled by coolant injection through the other plate, which also expands or contracts with time. A similarity transformation is used to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The obtained non-linear ordinary differential equations are solved by Duan–Rach Approach (DRA). This method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The impacts of various parameters such as the Reynolds number, the expansion ratio, the magnetic parameter, the power law index, the solid volume fraction and the radiation parameter are investigated on the velocity and temperature. Furthermore, the value of the Nusselt number is calculated and presented through figures. The results indicate that the temperature profile and the Nusselt number have a direct relationship with the solid volume fraction and have an inverse relationship with the radiation parameter. In addition, the limiting cases are gained and found to be in an excellent agreement with the previous works.

In this paper, the nanofluid flow and heat transfer between non-parallel stretching walls with Brownian motion effect is investigated. The governing radial momentum and energy equations are solved by Duan–Rach Approach (DRA). This method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The effective viscosity and thermal conductivity of nanofluid are calculated via KKL (Koo–Kleinstreuer–Li) correlation in which influence of Brownian motion on the thermal conductivity is considered. The effects of various parameters such as the stretching/shrinking parameter, the radiation parameter, Reynolds number, the opening angle and the heat source parameter are investigated on the velocity and temperature. Also, the value of the Nusselt number is calculated and presented through figures. The results show that the fluid velocity, temperature profile and Nusselt number increase with the increasing of stretching parameter. The results also reveal that the temperature profile increases with the increasing of the heat source parameter and it decreases with the rising of radiation parameter for both divergent and convergent channel. In addition, the results were compared with the previous works and found proposed method has high accuracy to solve this nonlinear problem.

In this work, magnetic nanofluid natural convection in the porous enclosure considering Brownian motion is studied numerically using Control Volume Finite Element Method (CVFEM). The effective viscosity and thermal conductivity of nanofluid are specified by Corcione correlation in which the impact of Brownian motion on the thermal conductivity is considered. The considered porous enclosure is heated from the inner circular side and it cooled from the outer circular side while two other walls are insulated. The impacts of various controlling parameters such as the Rayleigh number, Hartmann number, Darcy number and angle of magnetic field parameter are examined on the streamlines and isotherms. In addition, the average and local Nusselt numbers are obtained and presented via figures. The results state that the intensity of the convective flow has a direct relationship with the Rayleigh number and Darcy number while it has a reverse relationship with the Hartmann number and inclination angle of the magnetic field. Keywords: Magnetic nanofluid, Porous enclosure, Natural convection, Brownian motion, CVFEM

One of the important problems in the field of heat transfer is the investigation of natural convection heat transfer in cavities. The next step is the study of entropy generation. The object of the present work is the investigation of the entropy generation in a semi-annulus porous cavity filled with Cu-water nanofluid in the presence of a magnetic field. The outer and inner semi-circular walls are kept at constant temperatures whereas the two other walls are insulated. Firstly, the governing equations (i.e. continuity, momentum and energy equations) are numerically solved by the Control Volume based Finite Element Method (CVFEM) and then the entropy generation number is calculated. The effects of the Rayleigh number, Darcy number, Hartmann number, angle of magnetic field, the nanoparticle volume fraction, the particle shape and the angle of turn for the enclosure, number and amplitude of undulation in the wavy wall on the entropy generation number are investigated. Also, a new criterion for the evaluation of cavity thermal performance is defined that is called ECOP. The results were compared with those of the literature and good agreement was observed. The results show that the Nusselt number and entropy generation number increase as the Rayleigh number and the nanoparticle volume fraction increase. Also, the entropy generation number decreases with increasing the Hartmann number whereas it increases as the Darcy number increases.

Researchers have a wide-ranging tradition in endeavoring to rise the thermophysical aspects of convection heat transferors for illustration, transformer oil and water. Technological advancements in recent years permit the dispersal of elements having ranges between 10 and 100 nm in such liquids. Recent researches regarding nanoliquids have been elaborated to exhibit anomalously higher convection heat transportation. Keeping such implications in mind, we formulated CuO-H2O nanoliquid flow with wavy circular cylinder as heater subjected to magnetohydrodynamics. The well-known Darcy model featuring porous medium along with KKL (Koo–Kleinstreuer–Li) model is considered simultaneously for analysis. Heat transportation is reported considering radiation effect. The impact of shape factor of nanoparticles is also considered. Simulations are presented employing the novel control volume finite element method. The influences of notable parameters like Darcy number, Rayleigh and Hartmann numbers, radiation parameter, amplitude of undulations, nanofluid volume fraction and shape factor of nanoparticles have been investigated on flow and heat transfer features. Moreover, a novel correlation regarding average Nusselt number has been developed subject to analysis’s active parameters. Our outcomes report that lower values of amplitude of undulations provide the uppermost estimations of average Nusselt number.

Natural convection heat transfer of copper–water nanofluid in a porous gap between hot internal rectangular cylinder and cold external circular cylinder under the effect of inclined uniform magnetic field has been investigated. Domain of interest is a porous sector, where horizontal and vertical adiabatic borders are the external circular cylinder radii. Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the Brinkman-extended Darcy model for the porous medium, single-phase nanofluid model with Brinkman correlation for the nanofluid viscosity and Hamilton and Crosser model for the nanofluid thermal conductivity have been solved numerically by the control volume finite element method. Effects of the Rayleigh number, Hartmann number, Darcy number, magnetic field inclination angle, nanoparticles volume fraction, nanoparticles shape factor, nanoparticles material, nanofluid thermal conductivity and dynamic viscosity models and nanofluid electrical conductivity correlation on streamlines, isotherms, local and average Nusselt numbers have been studied. Obtained results have shown the heat transfer enhancement with the Rayleigh number, Darcy number, nanoparticles volume fraction and nanoparticles shape factor, while the heat transfer rate reduces with the Hartmann number and magnetic field inclination angle. At the same time, the average Nusselt number increases at about 16% when nanoparticles volume fraction rises from 0 till 4% for Ra = 105 , Ha = 25, while for Ha = 0 one can find the heat transfer rate augmentation at about 9% for the same conditions. In the case of different nanofluid thermal conductivity and dynamic viscosity models, it has been found that KKL model reflects the heat transfer rate reduction with nanoparticles volume fraction, while for the Hamilton–Crosser–Brinkman model, the heat transfer rate increases. Comparison between the Maxwell correlation for the nanofluid electrical conductivity and the base fluid electrical conductivity illustrates an intensification of the convective heat transfer rate for high values of the Rayleigh number (Ra C 104) in the case of Maxwell correlation for the nanofluid electrical conductivity. At the same time, the effect of the nanoparticles volume fraction becomes more significant when nanofluid electrical conductivity is a function of nanoparticles volume fraction.

A boundary layer analysis of three dimensional electromagnetic flows of single and multi walls carbon nanotubes over the surface of a thin needle is addressed. Both single wall (SWCNTs) and multi wall (MWCNTs) are considered as nanoparticles whereas water is considered as base liquid. The energy equation is modeled by using non-linear thermal radiation because it has a major impact on the solar energy absorption capacity of nanofluid. Because of such solar energy utilization at greater scale, global warming/pollution levels can be controlled. Homogeneous-heterogeneous reactions are taken into consideration as they find their applications in catalysis, biochemical systems, combustion, batteries, corrosion phenomenon and electrolytic cells. Xue model describing the augmentation of thermal conductivity of carbon nanotubes is invoked. Entropy generation model is adopted because its minimization prevents the loss of available energy which in turn boosts the efficiency of thermal systems. Nonlinear differential equations representing flow expressions are numerically solved by shooting technique. The outcome of the present study is that velocity field lines are grown due to strengthening of electric field parameter in the flow of SWCNT-water and MWCNT-water nanofluids. Brinkman number uplifts the entropy generation.

In this paper, buoyancy flow and heat transfer of MHD nanofluid over a stretching sheet in the presence of thermal radiation and considering Brownian motion is studied. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo-Kleinstreuer-Li) correlation in which influence of Brownian motion on the effective thermal conductivity is considered. The effects of various parameters such as the buoyancy parameter, the magnetic parameter, the volume fraction of nanofluid and the radiation parameter are investigated on the velocity and temperature. Furthermore, the values of the Nusselt number and the skin friction coefficient are calculated and presented through figures. The results show that the fluid velocity and temperature distribution decreases with the increasing of radiation parameter.

In this paper, the unsteady squeezing flow and heat transfer of MHD nanofluid between the infinite parallel plates with thermal radiation effect is investigated. A similarity transformation is used to convert the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. These non-linear ordinary differential equations are solved analytically by Duan–Rach Approach ( DRA ). This method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. This method modifies the standard Adomian Decomposition Method ( ADM ) by evaluating the inverse operators at the boundary conditions directly. The effects of various parameters such as the squeeze number, the magnetic parameter, the volume fraction of nanofluid, the Eckert number and the radiation parameter are investigated on the velocity and temperature. Also, the values of skin friction coefficient and the Nusselt number are calculated and presented through figures. The results show that the temperature profile and Nusselt number increase with the increase of radiation parameter. Furthermore, the limiting cases are obtained and are found to be in good agreement with the previously published results.

In this paper, heat transfer of a steady, viscous incompressible water based MHD nanofluid flow from a source or sink between two stretchable or shrinkable walls with thermal radiation effect is investigated. A similarity transformation is used to convert the governing radial momentum and energy equations into nonlinear ordinary differential equations with the appropriate boundary conditions. These nonlinear ordinary differential equations are solved analytically by Duan–Rach Approach (DRA). This method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. This method modifies the standard Adomian Decomposition Method (ADM) by evaluating the inverse operators at the boundary conditions directly. The approximate analytical investigation is carried out for different values of the embedding parameters, namely: stretching/shrinking parameter, radiation parameter, Reynolds number, Hartmann number, opening angle and solid volume fraction. The results show that the fluid velocity and temperature distribution increase with the increasing of stretching parameter. The results were also compared with numerical solution in order to verify the accuracy of the proposed method. It has been seen that the current results in comparison with the numerical ones are in excellent agreement.

In this article, the simultaneous convection–radiation heat transfer through a moving fin with heat generation is studied. The heat transfer coefficient, thermal conductivity and heat generation are variable and supposed to be temperature dependent. The heat transfer in fin with longitudinal rectangular profile was carried out by using the Differential Transformation Method (DTM). The results indicated that the fin tip temperature increases with an increase in the heat generation gradient and a decrease in the Peclet number and the radiation–conduction parameter. Also, the optimal temperature distribution for a longitudinal rectangular fin is accomplished at stationary fin with heat generation-without radiation case. Furthermore, the limiting cases are obtained and found to be in good agreement with the numerical results.

Heat transfer, free convective flow and entropy generation of water, Al2O3-water, and nano encapsulated phase change material (NEPCM) diluted in water as NEPCM-water suspension in a hot enclosure is studied. The enclosure is a square porous cavity which heated from below, and the remained walls are thermally insulated. The cavity is cooled by four cooling channels with three different configurations (CONF 1–3). By considering internally heat generation, the impacts of the magnetic field (Ha = 0 and 100), Darcy number (Da=0.001 and 100) and laminar Rayleigh number (Ra=104, 105, and 106) at an equal concentration of nanoparticle and NEPCM ( ϕ = 2 % ) are evaluated by finite volume method (FVM) using ANSYS Fluent. The dimensionless form of the governing equations and entropy generation are used to tune the primitive parameters of the CFD code. The validation test and grid verification check are performed to guarantee the accuracy of the results. The results show that the average Nusselt number decreases from CONF1 to CONF3. The buoyancy effect amplified in higher Rayleigh number and porous medium while the magnetic field controls the buoyancy-driven flow. In addition, at low Rayleigh number, the cavity that contains the NEPCM-water suspension is desirable due to its heat transfer capability and low irreversibility.

The object of this study is entropy generation analysis in the concentric annuli of a gas insulation transmission line enclosure (GIL) loaded with air and SF6-N2 mixture gas. The inner and outer cylinders of the cavity are hot and cold, respectively. Because of symmetric conditions the ½ cylinder is considered for modeling. The standard k–ɛ turbulence model, the equation of entropy generation, and the conservation equations are transformed from dimensional form to non-dimensional form utilizing the definition of dimensionless parameters, stream function, and vorticity. Then dimensionless governing equations are solved by a finite volume method (FVM) using an innovative ANSYS Fluent non-dimensionalization scheme. Inflated layers applied to the fine grids to improve the simulation capability for turbulent modeling. The effects of the Rayleigh number at Ra = 2.5 × 106, 1.7 × 109, 2.1 × 109, 4.2 × 109 and 5.7 × 109 are investigated. The results demonstrate that the Nusselt number grows as the Rayleigh number grows and entropy generation number and the Bejan number decreases as the Rayleigh number increases. The GILs have a proper morphology in geometry that reducing the high irreversibility in higher Rayleigh numbers conditions.

A novel shape of cavity filled by Fe3O4-water nanofluids and porous media associated with natural convection under a constant inclined magnetic field has been studied. A novel model for viscosity named magnetic field dependent (MFD) viscosity is applied. The effects of Darcy, Hartmann and Rayleigh numbers, inclination angle and the cavity aspect ratio on heat and flow fields characteristics have been examined. The results represent that more the heat transfer rate has been constrained with any increment in the Hartmann number and therefore, the magnetic field can be utilized as an excellent controller of the heat transfer. Further, it is inferred that more values of the aspect ratio give always a greater average Nusselt number, at a given Ra.

Background and objective The swimming mechanism of self-propelling organisms has been imitated by biomedical engineers to design the mechanical micro bots. The interaction of these swimmers with surrounding environment is another important aspect. The present swimming problem integrates Taylor sheet model with couple stress fluid model. The thin passage containing micro-swimmers and mucus is approximated as a rigid (passive) two-dimensional channel. The spermatozoa forms a pack quite similar as a complex wavy sheet. Methods Swimming problem with couple stress cervical liquid (at low Reynolds number) leads to a linear sixth order differential equation. The boundary value problem (BVP) is solved analytically with two unknowns i.e. speed of complex wavy sheet and flow rate of couple stress mucus. After utilizing this solution into equilibrium conditions these unknowns can be computed via Newton-Raphson algorithm. Furthermore, the pairs of numerically calculated organism speed and flow rate are utilized in the expression of power dissipation. Results This work describes that the speed of micro-swimmers can be enhanced by suitable rheology of the surrounding liquid. The usage of couple stress fluid as compared to Newtonian fluid enhances the energy dissipation and reduces the flow rate. On the other hand complex wavy surface also aids the organisms to swim faster.

In this work, the role of various configurations of wavy circular heater and nanoparticles on convective heat transfer inside an enclosure having a wavy circular heater is explored. Various configurations of the inner wavy heater are considered. Numerical solutions of dimensionless governing equations are obtained via a hybrid method called Control Volume Finite Element Method (CVFEM). The influence of active parameters e.g. undulation number, wavy contraction ratio and so on is perused on convective heat transfer. According to the outcomes, it was found that the configuration of the wavy heater plays a crucial role in controlling the convective flow characteristic and the heat transfer rate within the enclosure. Hence, the present study can be a useful source for the manufactures of heated elements.