Search

In this work, the effect of using baffles and vortex generators on the cooling performance of a gas turbine combustion chamber is numerically investigated. The RNG k-ɛ model is utilized in order to simulate the flow turbulence. The effects of baffles and vortex generator pitch, hydraulic diameter and bypass ratio on the Nusselt number and friction coefficient at different Reynolds number are studied. The cooling performance of applying baffles and vortex generators are also evaluated and compared based on the Performance Evaluation Criterion (PEC). The numerical results are verified with available experimental data. The results show that the pitch increment results in the decrement of the Nusselt number and the wall friction coefficient due to the lower vortices generation and the turbulence kinetic energy dissipation. Also, the Nusselt number is increased by increasing both the bypass ratio and the hydraulic diameter. It is also found that vortex generators and baffles improve the cooling performance of the gas turbine combustion chamber by 18.8% and 26% respectively through decreasing the external wall temperature.

This research study aims to illustrate the dynamics of water conveying hybrid nanofluid flow over an exponentially stretchable sheet in the presence of Navier's partial slip and thermal jump conditions. The nanoparticles of Cu, TiO2 and Al2O3 are suspended into water (H2O) to prepare three forms of hybrid nanofluids. Also, the influences of Joule dissipation and thermal radiation are considered in the study. The mathematical model embodies the system of highly coupled nonlinear partial differential equations. The set of similarity equations are derived from these partial differential equations by utilizing appropriate similarity variables. Further, these similarity equations together with allied conditions are numerically solved by making use of a finite difference scheme based Lobatto IIIa-bvp4c solver in MATLAB. The significance of emerging dimensionless flow parameters on the water conveying Cu-Al2O3 hybrid nanofluid temperature and velocity are quantified by depicting various graphs. Besides, temperature and velocity profiles are compared for three different water-driven hybrid nanofluids comprising a colloidal mixture of Cu-Al2O3, TiO2-Al2O3 and Cu-TiO2 nanoparticles respectively. The local Nusselt numbers and wall velocity gradients are obtained in numerical form for various emerging physical parameters. Also, to comprehend the linking between heat transfer rate and emergent flow parameters, a statistical method is executed for the investigation of regression (quadratic) approximation on the skin friction coefficients and Nusselt numbers. Finally, the computed numerical results are compared with earlier reported paper and excellent conformity is noticed. The findings infer that the heat transport rate can be improved by the inspirations of suction and thermal radiation while viscous dissipation, magnetic field, injection and thermal slip factor are significant to reduce the heat transport rate of hybrid nanofluid

Here, continuous two-dimensional boundary layer flow of a Fe2O3 CuO/water hybrid nanofluid over a porous stretching/shrinking wedge with radiation and MHD effects has been investigated semi–analytically. The dual solutions of the problem and also its stability analysis are taken into account. Moreover, the mass-based procedure for hybrid nanofluid modeling has been used. According to this procedure, the volume fraction of first and second nanoparticles is written in terms of both nanoparticles as well as base fluid masses. The Tiwari-Das model joined with mass-based hybrid nanofluid procedure is applied to find the governing partial differential equations which are then transferred to a set of dimensionless ordinary differential equations with help of the similarity transform method. The numerical method of solution has been chosen based on a famous finite difference scheme (bvp4c) from MATLAB software. The results demonstrate that dual solutions exist for a certain domain of the wedge stretching/shrinking parameter. Also it is observed that always the first solutions have thinner boundary layer thickness than the second ones. Moreover, the critical value in which the solution is in existence increase with the enhancement of magnetic parameter and suction parameter. The magnetic parameter and the mass suction at the wedge's surface also leads to the increase in the local Nusselt number. Further, it is inferred that the second nanoparticle's mass enhancement results in the amplification of the skin friction coefficient and the local Nusselt number for the first solutions. In addition, the rise in radiation parameter tends to enhance the thermal boundary layer thickness.

Background The exploration of natural convection which is one the substantial types of convective heat transmission in various applications for instance heat exchangers and geothermal systems along with nanofluids (Nanofluids have greater thermal conductivity in comparison to the conventional fluids) engrossed all researchers’ attention. Methods This study is dedicated to the inspection of the free convection of nanofluid as well as entropy generation inside a porous cavity loaded with nano-encapsulated phase change materials (NEPCMs). The wavy bottom section of the enclosure may be subject to a constant heat flux due to the transmitted sunlight comes from a parabolic trough solar collector. The volumetric heat source/sink is comprised in the governing equation. The robust finite element method (FEM) is deployed to handle the transformed governing equations. Findings The numerical simulation of the streamlines and isotherms associated with velocity distribution for diverse factors are displayed. Further, the significant behavior of the contributing parameters on the Nusselt and Bejan numbers are represented. The results demonstrate that the various profiles of wavy bottom section could affect the heat transmission features as well as fluid flow remarkably. Furthermore, it is noteworthy that all the profiles of entropy enhance with increasing the amplitude with respect to the increasing undulation number for the existence of various Rayleigh number.

Exergy efficiency, Nusselt number, friction factor, pressure drop, thermal and frictional entropy generation of water-based nanodiamond + Fe3O4 nanofluid flow in a tube and with various coiled wire inserts have been studied experimentally under turbulent and constant heat flux boundary conditions. The experiments were conducted in the Reynolds number range from 2000 to 22,000, particle concentrations of 0.05%, 0.1% and 0.2% and coiled wire inserts of different $$p/d$$ values of 3.67, 2.34 and 1.00, respectively. Results indicate that at 0.2% vol. and Reynolds number of 20,095, without coiled wire inserts, the heat transfer coefficient, Nusselt number, friction factor, pressure drop and pumping power are enhanced to 44.36%, 29.55%, 11.1%, 29.58% and 39.49% over the base fluid data. Similarly, at 0.2% vol. and Reynolds number of 20,095, with coiled wire inserts of $$p/d$$ = 1, the heat transfer coefficient, Nusselt number, friction factor, pressure drop and pumping power are further enhanced to 107.19%, 66.36%, 38.84, 64.44% and 76.54% over the base fluid data without inserts. The thermal entropy generation is decreased to 30.80% and it is further decreased to 46.34% at 0.2% vol. and Reynolds number of 20,095 with coiled wire inserts of $$p/d$$ = 1. The exergy efficiency of water is 18.95%, and it is increased to 24.06% for 0.2% vol. and it is further increased to 51.85% for 0.2% vol. and Reynolds number of 20,095 with coiled wire inserts of $$p/d$$ = 1. The study indicates that the hybrid nanofluids with coiled wire inserts are guaranteed choice for augmenting the exergy efficiency of flow through tube.

Poor thermal conductivity of phase change materials (PCMs) is the principal barrier to their widespread application. As such, numerous single or hybrid techniques have been proposed to lower the thermal resistance of PCMs. In the present paper, a hybrid approach, including the dispersing of nano-sized particles and embedding in a porous medium, was employed to augment the rate of heat transfer and melting process of the resulting nano-enhanced PCM (NePCM). Aluminum foam was used as the solid matrix, and phase-change heat transfer of a NePCM comprising n-octadecane as the phase change substance and nano-sized particles of mesoporous silica (MPSiO2) was studied. Previous experimental studies have shown that, although n-octadecane behaves as a Newtonian fluid, the mentioned NePCM behavior deviates from that of Newtonian fluids. Hence, the thermal and hydrodynamic behaviors of the non-Newtonian suspension of the NePCM in porous media were investigated numerically. Governing equations, including mass and momentum conservation for the liquid NePCM and energy equations for both solid and liquid phases, were solved using the Galerkin finite element method. The deformed mesh technique was employed to address the movement of the melting front. The finite element code was validated against several experimental and numerical works and was sufficiently accurate. Results showed that owing to the alteration of the rheological and thermophysical characteristics of the NePCM, increasing concentration of nanoparticles reduced the average Nusselt number and the normalized melt volume fraction (NMVF). It was also found that porosity played an important role in the phase-change rate. Although the steady-state condition was achieved faster in the case of lowest porosity, the maximum NMVF was achieved in the case of the highest porosity after Fourier number = 0.02.

The problem of transient Magnetohydrodynamic (MHD) combined convection within a wavy-heated rectangular cavity having two inner cylinders is investigated using the non-homogeneous nanofluid scheme. The lower wavy surface of the cavity is kept at a constant hot temperature ( T h ) while the upper flat surface is kept at a constant cold temperature ( T c ). The remaining surfaces (vertical surfaces) are maintained adiabatic. An Al 2 O 3 /water nanofluid is filled inside the cavity and a non-homogeneous approach is adopted to solve governing equations by using the Galerkin method. The effect of some parameters such as the angular rotational speed, the volume fraction of nanoparticles, Hartmann number on the flow and heat transfer characteristics are examined. The results indicate that the waving of the hot base of the cavity enhances the Nusselt number. The maximal Nusselt numbers are obtained when the number of undulations N is 2, where the Nusselt number augments by 18% when N is boosted from 0 to 2 and by 16% from 0 to and 5. Also, the outcomes reveal that the enhancement of the Nusselt number as a result of raising the rotational speed of the two cylinders from 0 to ± 500 is about 315%.

An exploration of the unsteady MHD boundary layer flow over a moving vertical porous surface with nanofluids under the influence of a uniform transverse magnetic field and heat radiation absorption effects has been brought out. Two different kinds of water-based nanofluids comprising of Al2O3 and TiO2 are adopted into deliberation. The governing equations for the flow are solved by making use of the Laplace transform method, and the solutions are displayed in closed form. The velocity, temperature, concentration, the shear stress, the rate of heat and mass transportations near the surface has been described graphically for numerous values of the relevant parameters. The velocity and temperature enhances with increasing radiation absorption parameter. It is also observed that an increase of volume fraction of nanoparticles leads to the enhancement of the temperature on central line of the flow. Nusselt number might be tracked down to be elevated for alumina than titanium dioxide nanofluid. The present investigation originated applications in aerospace engineering as well as industrial many mechanisms.

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 present study encountered the impact of non-dimensional fusion temperature on the free convection of conducting nanofluid within a porous enclosure filled with nano-encapsulated phase change materials (NEPCMs). The enclosure is equipped with two parallel fins that have ability to move in both directions such as vertically as well as horizontally. In particular the particles are structured as core-shell with phase change materials. The phase change of the materials is obtained from the solid to liquid and absorbs the surrounding temperature in the hot region and releases in the cold region. The governing transformed equations are tackled by using the Finite Element Method (FEM). The numerical simulation of the isotherms, streamlines and heat transfer coefficient ratio along with velocity distribution for various parameters are presented. These are affecting a key role on the average and local Nusselt number as well as on the local Bejan number. However, the measure outcomes are; both the longitudinal and transverse velocity profiles boost up with an augmented Rayleigh number; however, the weaker flow field is generated for the increasing Hartmann 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.

Magnetic field plays an important role in numerous fields such as biological, chemical, mechanical and medical research. In clinical and medical research the magnets are extremely important to create three dimensional images of anatomical and diagnostic importance from nuclear magnetic resonance signals. In view of these applications, the purpose of present research is to the effects of thermal radiation and rotation on the unsteady MHD convective flow past an infinite vertical moving absorbent plate. The similarity transformations are employed to migrate the governing partial differential equations in a system of non-linear ordinary differential equations and elucidated computationally by making use of cubic B-splines collocation method. The consequences of physical variables on fundamental segmentations are commented through visual aids. Even if the digital estimates of frictional force, Nusselt number and Sherwood number with respect to different parameters are delivered in matrix template and exchange of views proportionally. From the results, the resultant velocity magnifies with an increasing in rotation parameter, the thermal and solutal buoyancy forces. Reversal performance is adhered with expanding in the slip parameter. An enlargement in the radiation parameter, rise in the fluid speed and temperature profiles. The concentration profiles augments with increasing in suction parameter. The rate of mass transport is influenced on strengthening in Schmidt number and slip parameter.

The impact of wall movements in different directions on mixed convection flow and thermal performance in a wavy chamber is reported. The wavy wall of the chamber is heated non-uniformly, and the upper wall is kept at a constant cold temperature, while the vertical walls of the chamber are adiabatic. Four different cases, namely Case-1, Case-2, Case-3 and Case-4, are considered on the basis of multi-directional movements of the walls of the chamber. Mathematical model of the flow physics consists of the Navier–Stokes (N-S) equations in streamfunction ( $$\psi$$ ) —vorticity ( $$\zeta$$ ) formulation including the energy transport equations which are solved by higher-order compact (HOC) scheme on curvilinear grids Pandit SK, Chattopadhyay A.(Comput Math Appl 74(6):1414–34 2017) [45]. It is found that the fluid flow and thermal performance are both influenced by the direction of moving lids and the undulations of the wavy bottom surface of the chamber. Optimum thermal performance is noticed when the wavy bottom surface of the chamber is employed with one undulation at low Richardson number (Ri). Moreover, for $$Ri=0.01$$ , Case-2, in which the upper lid is moving in left direction and the left lid is moving in upward direction, gives better heat transfer rate with maximum value of average Nusselt number for one undulation. Furthermore, it is noticed that among all the cases, the cases (Case-2 and Case-4) in which upper lid is moving in left direction produce minimum entropy generation for every undulations of the wavy surface with each of the Ri values. So, on the basis of better heat transfer rate and the minimum entropy generation, Case-2 and Case-4 may be recommended as optimum configurations.

The present examination is considered to discuss the steady, two-dimensional flow of heat and mass transfer of nanofluid flow along with the variable suction under the influence of heat source/sink alongside the viscous dissipation. Because of the stretchable surface, flow is generated. Spectral relaxation technique is used to acquire the numerical solution for the altered nonlinear group of differential equations. Thereafter, outcomes which were obtained from the above numerical technique are validated by comparing with the available outcomes in the existing literature and also with MATLAB inbuilt solver bvp4c. All the acquired results from the above numerical system are shown through graphs and tables to discuss different resulting parameters related to the present analysis. The range of the physical parameters is taken as $$- \;0.1 \le f_{w} \le 0.5, \;0.1 \le Nt \le 0.7, \;0.1 \le Nb \le 0.7, \;0 \le Ec \le 1.2, \; - 0.5 \le Q \le 0.5, 1 \le Pr \le 10,\; 1 \le Le \le 5.$$ The main findings are as follows: For the effect of suction parameter, the profiles of velocity, temperature and mass friction are decreased, and the coefficient of skin friction and Nusselt number is declined for the impact of thermophoresis parameter.

We have explored theoretically the Hall and ion slip impacts on an unsteady laminar MHD convective rotating flow of heat generating or absorbing second grade fluid over a semi-infinite vertical moving permeable surface. The non-dimensional equations for the governing flow are solved to the most excellent possible investigative solution using perturbation methodology. The effects of parameters on velocity, temperature and concentration are demonstrated graphically and described in detail. For engineering curiosity, the shear stresses, Nusselt number and Sherwood number are obtained analytically, represented computationally in a tabular format as well as explained with respect to foremost parameters. It is concluded that, the resultant velocity is increased with an increasing in Hall and ion slip parameters throughout fluid region. The thermal and solutal buoyancy forces contribute to the resultant velocity ever-increasing to high. The temperature distribution is trim downs through an increasing in heat source parameter. The concentration is reduced with an increase in the chemical reaction parameter in the entire fluid region. Rotation parameter is to diminish the skin friction, whereas it is augmented through an increase of the Hall and ion slip effects. The rate of mass transfer is increased with increasing chemical reaction parameter.

This article explains the effect of magnetite nanofluid taking into account water as the base fluid, over a rotating disk in the presence of external magnetic field. The governing boundary layer equations of laminar and incompressible flow over rotating disk have been formulated under the simultaneous influence of thermophoresis and Brownian motion. Additionally, influence of chemical reaction between species, prompted by Arrhenius activation energy is considered into the model. The Von Karman’s transformations of the Navier-Stokes equations are used to obtain the non-dimensional forms of the governing equations, and then fourth order finite difference scheme is used to find the numerical solutions using Noumerov’s discretization. This technique has strong impact on the accuracy of finite difference scheme. The physical descriptions of fluid velocity, temperature, concentration profiles and quantities of practical interest such as skin friction coefficient, Nusselt number and Sherwood number are presented with the help of graphs. One of the significant findings of this analysis include that an intensification in the thermophoresis parameter causes a downfall in the rate of heat transfer at the surface of the disk whereas another significant outcomes of the present investigation is that there is a downfall in the behaviours of the species concentration with the strengthening of Arrhenius activation energy. The fluid flow due to rotating disks has application in mechanisms of thermal transformations for nuclear propulsion devices.

Mixed convection has been one of the most interesting subjects of study in the area of heat transfer for many years. The entropy generation due to MHD mixed convection heat transfer in L-shaped enclosure being filled with Cu-water nanofluid and having an internal heating generation is explored in this investigation by the finite volume technique. Lid-motion is presented by both right and top parts of walls to induce forced convection and the cavity is under an inclined uniform magnetic field along the positive horizontal direction. The statistics concentrated specifically on the impacts of several key parameters like as the aspect ratio of the enclosure, Hartmann number, nanoparticle volume fraction, and heat source length/location on the heat transfer inside the L-shaped enclosure. Outcomes have been manifested in terms of isotherm lines, streamlines, local and average Nusselt numbers. The obtained results show that addition of nanoparticles into pure fluid leads to increase of heat transfer. The maximum value of local Nusselt pertaining to the heat source occurs when L = 0.1. Impacts of heat source size and location, internal heat generation absorption, angle of magnetic field on heat transfer and entropy generation are completely analyzed and discussed. The best configuration and values of important parameters are also presented using thermal performance criteria.

In the present work, natural convection heat transfer in a differentially heated cavity is considered, in which, source–sink pairs are located on vertical walls with a constant temperature while other wall parts of the enclosure are insulated. The effects of different arrangements, sizes, and number of heat source–sink pairs on the flow and thermal fields are investigated by using the Lattice Boltzmann Method to solve the flow and thermal field equations. In this paper, streamlines, isotherms, the average Nusselt number, and the entropy generation are presented to get a better insight into the nature of the problem. Results of this study showed that the arrangement of the heat source–sink pairs could strongly affect the flow and thermal fields in the cavity due to the formation of the vortices. It was also found that the highest amount of heat transfer with the lowest entropy generation was achieved by splitting the discrete heat source–sink pairs into the smaller segments and putting them alternately on one sidewall.

This study aims to unfold the significance of numerous physical parameters such as magnetic field, heat absorption, thermal radiation, viscous and Joule dissipations, etc. on the flow of graphene Maxwell nanofluid over a linearly stretched sheet with considerations of momentum and thermal slip conditions. The prevailing mathematical equations are reformed into extremely nonlinear coupled ordinary differential equations (ODE) utilizing similarity variables and then the equations are solved numerically by the scheme of Runge-Kutta Fehlberg method along with the shooting technique. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters are shown via numerous graphs whereas numerical values of skin friction coefficients and Nusselt numbers are illustrated and reported in different tables. In addition, statistical approach is followed for the multiple regression estimation analysis on the numerical findings of wall velocity gradient and local Nusselt number and are reported in tabular form to demonstrate the relationship among the heat transfer rate and physical parameters. Our results reveal that the graphene Maxwell nanofluid velocity gets reduced owing to enhancement in magnetic field, angle of inclination of magnetic field, porosity and unsteadiness parameters whereas behavior of nanofluid velocity is reversed due to Maxwell parameter. Further, it is noticed that the heat transfer rate of nanofluid is augmented owing to heat absorption, radiation and thermal slip parameters while it is reduced due to increase in viscous dissipation and unsteadiness parameters. The numerical results of the paper are validated by making comparisons with the earlier published paper under the restricted conditions and we found an excellent agreement with those results. A careful review of research papers reported in literature reveals that none of the authors has attempted this problem earlier although the thoughts and methodology explained in this paper can be anticipated to lead to enormously prolific connections across disciplines.

The nano encapsulated phase change materials are of the great energy storage potential in various engineering applications. Since they are new nanomaterials, new models for understanding their thermal behavior and capability are essential. This work aims to investigate the unsteady thermal behavior of Nano-Encapsulated Phase Change Material (NEPCM) suspensions in a cylindrical cavity. The particles contain a Phase Change Material (PCM) core, which can absorb/release a substantial amount of thermal energy upon phase change. The phase change particles are well dispersed in a liquid fluid and freely move along with the fluid. The flow, heat transfer, and the particle phase change were modeled using partial differential equations. A non-dimensional approach was employed to generalize the study. The unsteady charging and discharging behavior of the NEPCM suspension are investigated for the volume fraction of the NEPCM particles, fusion temperature of nanoparticles, Stefan number, and the Rayleigh number. Numerical results show that an increment in the Stefan number, i.e., Ste, can significantly reduce the Nusselt number, i.e., Nua, at the charging mode of the system. However, the dependency of the Nua at the discharging mode on the Ste is negligible. Also, it was found that the effect of the fusion temperature of the particle’s core (θf) on heat transfer depends on the working mode of the system. In the charging mode, using a higher value of θf decreases the heat transfer rate. Reversibly, a higher value of θf inhibits the Nua during discharging state. Furthermore, the results show that for Ra = 106, Ste = 0.2, and θf = 0.1, a rise of ϕ from 0 to 0.05 leads in about 1.73 and 1.55 times of improvement in the value of Nua for the cases of the melting and solidification of the core of NEPCM particles.

The present work aims to examine the thermal efficacy of half-sinusoidal nonuniform heating at different spatial frequencies for a porous natural convection system using Cu–Al2O3/water hybrid nanofluid and magnetic field. The system is presented utilizing a classical square enclosure heated nonuniformly at the bottom wall, and the sidewalls are allowed to exchange heat with the surroundings. The Brinkman–Forchheimer–Darcy model is adopted catering other additional terms for buoyant force and magnetic field. The governing equations are transformed into nondimensional forms and then solved numerically using a finite volume-based computing code. The importance and fundamental flow physics are explored in terms of the pertinent parameters such as the amplitude (I) and spatial frequency (f) of half-sinusoidal heating, Darcy–Rayleigh number (Ram), volume fraction of hybrid nanoparticles ( $$ \phi $$ ), and Hartmann number (Ha). The flow structure and heat transfer characteristics are analyzed and presented utilizing heatlines, streamlines and isotherms and average Nusselt number. The results show that the use of half-sinusoidal nonuniform heating along with hybrid nanofluid can be a viable method for enhancement and control of the overall thermal performance. The study indicates that half-sinusoidal heating could be a promising technique for better heat transfer even in the presence of flow dampening effects like porous media and magnetic fields.

Modeling and computations are performed to study the ND-Co3O4/EG hybrid nanoliquid mixed convective flow past a vertical porous cylinder. The flow analysis and formulation are given accounting for slip effects and homogeneous-heterogeneous reaction impacts. The governing complex equations formed with prescribed boundary conditions are simplified into self-similar equations through the use of suitable transformations. The numerical solutions of the drag coefficient, Nusselt number, liquid velocity, liquid temperature, and the liquid concentration are explored through graphs with the setting of pertaining parameter values. From the results, it is noticed that an ND-Co3O4/EG nanofluid plays a more impressive role in the process of energy transfer than a Co3O4/EG nanofluid. Further, it is found that the heterogeneous reaction parameter decreases the concentration whereas multiple slips enhance the temperature.

The problem of steady-state laminar two-dimensional rarefied gaseous flow by natural convection heat transmission in a partly heated square two-sided wavy cavity with an internal heat generation is numerically studied employing the finite volume procedure. The Boussinesq approximation is adopted to account for buoyancy effects. A favorable comparison for validation purposes with previously published work is obtained. The study is performed with distinct values of the external Rayleigh number (104 ≤ RaE ≤ 106), Knudsen number (0.01 ≤ Kn ≤ 0.1), inclination angle (ϕ = 0°, 30°, 60°, and 90°), three non-dimensional heater lengths (L/H = 0.175, 0.35, and 0.52), while the Prandtl number (Pr) is fixed at 0.7. The outcomes of this research yield that the average Nusselt number (Nuavg) relies inversely on Kn and directly on RaE. Moreover, it is revealed that increasing L/H value decreases Nuavg values at the lower partially heated cavity wall. Additionally, the study reveals that as the heat generation term (Qgen) increases, the Nuavg increases as well. Finally, a correlation between Nuavg and the parameters inspected in this research is suggested.

The current problem is performed to analyze the heatline visualization of the mixed convection mechanism and heat transfer in a double lid-driven square cavity having a heated wavy bottom surface. The moving vertical surfaces are under adiabatic conditions, and the top surface is at a cold temperature. The finite element method is employed to determine the dimensionless governing equations controlled by specific boundary conditions. The implications of the Reynolds number ( $$10 \le {\mathrm{Re}} \le 500$$ ), the directions of the constant moving wall ( $$\lambda _{\mathrm{l}}= \pm 1, \lambda _{\mathrm{r}}= \pm 1$$ ), Richardson number ( $$0.01 \le {\mathrm{Ri}} \le 100$$ ), Prandtl number ( $$0.015 \le \Pr \le 10$$ ) and the number of oscillations ( $$1 \le {\mathrm{N}} \le 4$$ ) are visualized by the streamlines, isotherms and the heatlines. The same direction of lid-driven cases leads to two primary circulation cells. The Richardson number increases as it imposes the increment of the vertical temperature gradient. At a high Prandtl number, the convection mode of heat transfer is fully established, and heat conduction occurs at a low Prandtl number. Moreover, the number of oscillations has the most significant direct impact on the streamlines and the temperature distributions compared to the flat surface. Higher Reynolds and Prandtl numbers result in an increment in the local and average Nusselt numbers. The result shows that one oscillation of the wavy surface with a low Richardson number yields to have an optimum heat transfer in the cavity.

In this work, the thermal behavior of a turbulent forced-convection flow of air in a rectangular cross section channel with attached W-shaped obstacles is investigated. The continuity, momentum and energy equations employed to control the heat and velocity in the computational domain. The turbulence model of k-ε is employed to simulate the turbulence effects. The finite volume method with SIMPLE algorithm is employed as the solution method. The results are reported temperature, local and average Nusselt numbers, and mean velocity contours. The subject is relevant and important for industrial applications.

The steady flow of a nanofluid (mixture of titanium dioxide and water) in a rectangular channel under the influence of an inclined magnetic field is studied. The channel contains an upstream hot splitter plate in alignment with the upper and lower plates of the channel. It may be said that two incoming channel flows merge to form a single channel flow. This setup may apply to the heating chamber in which titanium dioxide can be used to enhance the thermal transfer rate. It is observed that the position of the splitter plate (that may act as an electric heater) affects the velocity and temperature of the fluid. Therefore, in order to ensure these facts, the examination of the flow behavior and the temperature distributions in the channel if the splitter is placed at different positions in the upstream have been probed. In addition, the effect of nanoparticles on the convection process has been probed. The streamlines are almost similar for a clear fluid as well as for a nanofluid (for low values of solid volume fraction of nanoparticles (i.e. $$\varphi < 0.05$$ )) for all values of the Reynolds number. However, the rise in the temperature is noted for the nanofluid if the concentration of nanoparticles is increased. The increase in the Reynolds number also supports the enhancement of the Nusselt number and, hence, the thermal transfer rate of the nanofluid. The Nusselt number is dominant in the vicinity of the trailing edge of the splitter because the trailing edge exhibits as a stagnation point. In addition, the maximum Nusselt number for nanofluid at moderate Reynolds number (e.g., Re = 100) is enhanced to 0.3% with respect to the clear fluid. Moreover, obtained results for this particular case are compared with the existing literature, and the results compare well.

In this paper, we have investigated the Hall and ion slip effects on the unsteady magnetohydrodynamic (MHD) free convective rotating flow over an exponentially accelerated inclined plate entrenched in a saturated porous medium with the effect of angle of inclination, variable temperature and concentration. The flow induced by the presence of heat source/sink and destructive reaction. The Laplace transform technique has been used to solve the governing equations. The effects of the non-dimensional parameters on the governing flow velocity, temperature and concentration are examined with graphical profiles. Also for engineering interest the shear stress, Nusselt number and Sherwood number are obtained analytically and discussed computationally with reference to foremost flow parameters. It is reported that the presence of magnetic field prevents the flow reversal. Angle of inclination sustains a retarding effect on velocity distribution. The present study has an immediate application in understanding the drag experienced at the heated and inclined surfaces in a seepage flow.

The present work is a computational investigation of a periodically fully developed nanofluid transport through a wavy module. The governing equations for this investigation are formulated along with the appropriate boundary conditions and then solved using the finite volume method. Comparisons with previously reported results show excellent agreement. The simulations are carried out using five wavy amplitudes for a range of Reynolds number from 102 to 103. It is found that increasing the amplitude and increasing the nanoparticle volume fraction achieve enhancement of the heat transfer at the cost of increased pumping power. Correlations for the friction factor and the Nusselt number as functions of the amplitude and the Reynolds number are provided.

In the current study, magnetohydrodynamics mixed convective flow of Ag–MgO/water hybrid nanofluid in a triangular shaped partitioned cavity involving a porous layer is numerically investigated by using the finite element method. In the numerical simulation, various effects of pertinent parameters such as Richardson number (between 0.01 and 100), Hartmann number (between 0 and 60), magnetic field inclination angle (between 0 and 90), Darcy number (between $$10^{-4}$$ and $$5 \times 10^{-2}$$ ), location of the vertex of triangular porous region (between 0.2 and 0.8 H) and hybrid nanoparticle solid volume fraction ( $$\phi _1$$ between 0 and 0.01, $$\phi _2$$ between 0 and 0.01) on the fluid flow and convective heat transfer features are examined. It was observed that a large vortex is established below the main vortex near the upper wall for the lowest value Ri number. At the highest magnetic field strength, multi-recirculation flow pattern is seen in the right bottom corner. The average heat transfer enhances with higher values of permeability of the porous medium, magnetic field inclination angle, distance of the porous layer vertex from the hot wall and solid nanoparticle volume fraction of each particles in the hybrid nanofluid. The impact is reverse for higher values of Richardson number and Hartmann number. In the current work, significant changes in the average Nusselt number are obtained by varying the location of the porous medium. The triangular shaped porous compound can be used as an excellent tool for convective heat transfer control.

A numerical investigation of entropy generation due to MHD-free convective of Cu–water nanofluid in a porous I-shaped cavity is reported. The cavity is under Darcy law with inclined uniform magnetic field. The cavity is cooled from the top and a part of bottom wall subjected to uniform heat flux, while the other parts of walls of the cavity are adiabatic. Mathematical pattern formulated employing the single-phase nanofluid approach in governing equations the problem has been solved by finite difference technique. Prime efforts have been concentrated on the impacts of the pertinent parameters on the fluid flow and heat transfer inside the cavity. Numerical data have been plotted in the form of streamlines, isotherms, and average Nusselt numbers. The results show that the Nu number decreases via increasing the Ha number. It increases when the Ra number is increased. The maximum and minimum values of Nusselt occur at B = 0.2 and B = 0.8, respectively. Exerting an angle for magnetic flux leads to the improvement in thermal performance for all amount of B. The effects of Ha, nanofluid volume fraction, heat source size, location and angle of magnetic field on heat transfer, entropy generation, and thermal performance are completely studied and discussed.

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.

This paper investigates the natural convection inside a partially layered porous cavity with a heated wavy solid wall; the geometry is encountered in compact heat exchangers. Alumina nanoparticles are included in the water to enhance the heat exchange process. The incidental entropy generation is also studied to evaluate the thermodynamic irreversibility. The nanofluid flow is taken as laminar and incompressible while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The Darcy number (Da), porosity of the porous layer ( $$\varepsilon$$ ), number of undulations (N), and the nanoparticles volume fraction ( $$\phi$$ ) are varied to assess the heat transfer and the incidental entropy generation. It is found that the waviness of the solid wall augments the average Nusselt number and minimizes the generation of entropy. The results show for some circumstances that the Nusselt number is augmented by 43.8% when N is raised from 0 (flat solid wall) to 4. It is also found that the porosity of the porous layer is a more crucial parameter than its permeability, where a 37.4% enhancement in the Nusselt number is achieved when the porosity is raised from 0.2 to 0.8.

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+

Purpose The purpose of this paper is to carry out a hydrodynamic and thermal analysis of turbulent forced-convection flows of pure water, pure ethylene glycol and water-ethylene glycol mixture, as base fluids dispersed by Al2O3 nano-sized solid particles, through a constant temperature-surfaced rectangular cross-section channel with detached and attached obstacles, using a computational fluid dynamics (CFD) technique. Effects of various base fluids and different Al2O3 nano-sized solid particle solid volume fractions with Reynolds numbers ranging from 5,000 to 50,000 were analyzed. The contour plots of dynamic pressure, stream-function, velocity-magnitude, axial velocity, transverse velocity, turbulent intensity, turbulent kinetic energy, turbulent viscosity and temperature fields, the axial velocity profiles, the local and average Nusselt numbers, as well as the local and average coefficients of skin friction, were obtained and investigated numerically. Design/methodology/approach The fluid flow and temperature fields were simulated using the Commercial CFD Software FLUENT. The same package included a preprocessor GAMBIT which was used to create the mesh needed for the solver. The RANS equations, along with the standard k-epsilon turbulence model and the energy equation were used to control the channel flow model. All the equations were discretized by the finite volume method using a two-dimensional formulation, using the semi-implicit method for pressure-linked equations pressure-velocity coupling algorithm. With regard to the flow characteristics, the interpolation QUICK scheme was applied, and a second-order upwind scheme was used for the pressure terms. The under-relaxation was changed between the values 0.3 and 1.0 to control the update of the computed variables at each iteration. Moreover, various grid systems were tested to analyze the effect of the grid size on the numerical solution. Then, the solutions are said to be converging when the normalized residuals are smaller than 10-12 and 10-9 for the energy equation and the other variables, respectively. The equations were iterated by the solver till it reached the needed residuals or when it stabilized at a fixed value. Findings The result analysis showed that the pure ethylene glycol with Al2O3 nanoparticles showed a significant heat transfer enhancement, in terms of local and average Nusselt numbers, compared with other pure or mixed fluid-based nanofluids, with low-pressure losses in terms of local and average skin friction coefficients. Originality/value The present research ended up at interesting results which constitute a valuable contribution to the improvement of the knowledge basis of professional work through research related to turbulent flow forced-convection within channels supplied with obstacles, and especially inside heat exchangers and solar flat plate collectors.