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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.

The principal goal of the present investigation is to inspect the flow characteristics of an electrically conducting hybrid nanofluid containing copper and graphene nanoparticles past a linearly stretched sheet with velocity slip condition at the interface. Since, the non-Newtonian fluid models result in a better understanding of the flow and heat transfer attributes of the nanofluids, therefore, non-Newtonian Maxwell nanofluid has been chosen as the base fluid in our study with an unsteady magnetic field applied at a certain angle to the direction of the flow. Consideration of thermal radiation along with heat absorption under the mutual influence of viscous and Joule dissipations is one of the key features of this research investigation. With the help of similarity transformations, the governing flow equations have been converted into a system of coupled non-dimensional differential equations. After that, Shooting method along with Runge–Kutta–Fehlberg numerical technique is employed to find the solutions for velocity and temperature of the hybrid nanofluid. The obtained numerical results are well demonstrated with a number of graphs and tables. Apart from this numerical technique, a statistical method is implemented of multiple quadratic regression estimation analysis on the various graphs of skin friction coefficient and wall temperature gradient to establish the connection among physical entities and heat transfer rate. The applications of this investigation in solar energy, ventilation, heating as well as refrigeration , medical science, defence sector etc. Some noteworthy findings include that Maxwell parameter, velocity slip and porosity have a tendency to reduce the hybrid nanofluid velocity whereas graphene Maxwell hybrid nanofluid’s temperature is getting enhanced for rising the values of magnetic field’s inclination angle, radiation, unsteadiness parameters, Biot number and viscous dissipation whereas a reverse trend is visible for heat absorption parameter. Furthermore, the permeability of the porous medium has a more significant impact on changing the nanofluid velocity than that of magnetic parameter whereas the rate of heat transfer is high sensitive for thermal radiation than that of viscous dissipation. As per authors’ knowledge there is no such attempt where the mutual effects of hybrid Maxwell nanofluid (graphene and copper), porous media and viscous dissipation have been considered.

In this investigation, a comprehensive and accurate numerical analysis of the local thermal non-equilibrium effects on the natural convection characteristics in a horizontal elliptical porous annulus saturated with nanofluid has been carried out using finite volume technique. The internal surface is isothermally heated while the external one is fixed at uniform lower temperature. The nanofluid phase and the solid phase of the porous structure are hors local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy-Brinkman Forchheimer model were solved computationally by the finite volume technique using the standard SIMPLER algorithm. The results have been examined for various porous medium properties under the LTNE condition. The standard 0.05 significance level was used to identify the local thermal equilibrium within the system. According to the obtained results, the higher the Darcy number and the smaller the non-dimensional heat transfer coefficient for the solid/nanofluid interface, the modified thermal conductivity ratio and the media’s porosity, the higher are the LTNE effects. In addition, the spatial distribution contours of the LTNE sources within the porous annulus were schematized.

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.

This paper is basically devoted to carry out an investigation regarding the unsteady flow of dissipative and heat absorbing hydromagnetic graphene Maxwell nanofluid over a linearly stretched sheet taking momentum and thermal slip conditions into account. Ethylene glycol is selected as a base fluid while graphene particles are considered as nanoparticles. The highly nonlinear mathematical model of the problem is converted into a set of nonlinear coupled differential equations by means of fitting similarity variables. Further, Runge-Kutta Fehlberg algorithms along with the shooting scheme are instigated to analyse the numerical solution. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters have been demonstrated via numerous graphs whereas Nusselt number and skin friction coefficients are illustrated in numeric data form and are reported in different tables. In addition, a statistical method is implemented for multiple quadratic regression estimation analysis on the numerical figures of wall velocity gradient and local Nusselt number to establish the connection among heat transfer rate and physical parameters. Our numerical findings reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. The regression analysis confers that Nusselt number is more prone to heat absorption parameter as compared to Eckert number. Finally, the numerical findings are compared with those of earlier published articles under restricted conditions to validate the numerical solution. The comparison of numerical findings shows an excellent conformity among the results.

Purpose This study aims to focus on a thermo-fluid flow in a partially driven cavity (PDC) using Cu-water nanoliquid, magnetic field and porous substance. The cooling and sliding motion are applied on the upper half of the vertical walls and the bottom wall is heated. Thermal characteristics are explored to understand magnetohydrodynamic convection in a nanoliquid filled porous system from a fundamental viewpoint. The governing parameters involved to cater to the moving speed of the sidewalls and partial translation direction are the relative strength of thermal buoyancy, porous substance permeability, magnetic field intensity, nanoparticle suspension and orientation of the cavity. Design/methodology/approach The coupled transport equations of the problem are solved using an in-house developed finite volume-based computing code. The staggered nonuniform grids along the x and y directions are used. The SIMPLE algorithm technique is considered for the iterative solution of the discretized equations with the convergence check of the continuity mass defect below 10–10. Findings The present study unveils that the heat transfer enhances at higher Ri with the increasing value of Re, irrespective of the presence of a porous substance or magnetic field or the concentration of nanofluid. Apart from different flow controlling parameters, the wall motions have a significant contribution to the formation of flow vortices and corresponding heat transfer. Orientation of the cavity significantly alters the transport process within the cavity. The upward wall velocity for both the sidewalls could be a better choice to enhance the high heat transfer (approximately 88.39% at Richardson and Reynolds numbers, respectively, 0.1 and 200). Research limitations/implications Considering other multi-physical scenarios like porous layers, conducting block, microorganisms and the present investigation could be further extended to analyze a problem of complex flow physics. Practical implications In this study, the concept of partially driven wall motion has been adopted under the Cu-water nanoliquid, magnetic field, porous substance and oblique enclosure. All the involved flow-controlling parameters have been experimented with under a wide parametric range and associated thermo-flow physics are analyzed in detail. This outcome of this study can be very significant for designing as well as controlling thermal devices. Originality/value The convective process in a partially driven cavity (PDC) with the porous medium has not been investigated in detail considering the multi-physical scenarios. Thus, the present effort is motivated to explore the thermal convection in such an oblique enclosure. The enclosure is heated at its bottom and has partially moving-wall cold walls. It consists of various multi-physical conditions like porous structure, magnetic field, Cu–H2O nanoliquid, etc. The system performance is addressed under different significant variables such as Richardson number, Reynolds number, Darcy number, Hartmann number, nanoliquid concentration and orientation of cavity.

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.

The article deals with 2D unsteady nanofluid flow past a vertical wedge along with nonlinear mixed convection. Brownian diffusion and thermophoresis effects are considered to model nanofluid flow. ...

This paper examines the capability of hybrid lattice Boltzmann method to simulate developed turbulent buoyancy-driven flows in closed rectangular cavities. The two-relaxation time mesoscopic lattice Boltzmann method is used as a fluid dynamics solver, whereas the thermal behavior is described in terms of the macroscopic energy equation. Numerical simulation is performed for air-filled square and tall cavities in a range of the Rayleigh number $$10^{9} \le Ra \le 10^{11}$$ . An in-house numerical code is developed in this study and successfully validated against up-to-date numerical and experimental data of other researches. It is found that the proposed hybrid approach accurately predicts the location of thermal plumes at the isothermal walls despite an insignificant error in the heat transfer rate with the $$Ra \ge 3 \cdot 10^{10}$$ .

This problem considers the instabilities, which can occur when a horizontal sparsely filled nanofluid porous layer is saturated with a binary mixture with fast chemical reaction. The upper and lower plates are heated isothermally. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The energy equation includes cross and regular diffusion conditions. In conjunction with the Brownian motion, the nanoparticle fraction becomes stratified; hence the viscosity and the conductivity are stratified. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation, in the vertical direction, of conductivity and viscosity. The oscillatory and stationary convection are evaluated analytically. The reaction rate is supposed to be greater than the diffusion rate. We find that both a stationary instability and an oscillatory instability can occur as the first bifurcation, depending on the sign and the value of the heat of reaction. The execution of the porous parameter, Prandtl number, Soret parameter, Dufour parameter, Lewis number, solutal Rayleigh number, chemical reaction and the modified diffusivity ratio parameters is implemented pictorially. It is found that the presence of nanoparticles the critical Rayleigh number is increased and helps to stabilize the system. The presence of chemical reaction parameter destabilizes the system. The results of previously-published work are also obtained as special cases of the general solution.

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%.

The principal aim of this study is to explore the impact of relaxation-retardation viscous dissipation, nonlinear convection, variable chemical reaction, and nonlinear thermal radiation on the three-dimensional rotating flow of an Oldroyd-B nanofluid over an exponentially extended surface. The Buongiorno model that takes into account the Brownian movement and thermophoresis responsible for nanoparticle motion. Exponentially varying temperature and concentration associated with convective heat transfer coefficients are assumed in the boundary conditions. The system of dimensionless ODEs is solved by the spectral quasi-linearization method. The results of the analysis show, among other results that the relaxation time parameter opposes the momentum transport while assisting heat transportation. The retardation time parameter acts to support momentum growth while reducing and resists heat transport. The present study focused on the investigation the effect of relaxation and retardation viscous dissipation on rotating flow of a non-Newtonian fluid (Oldroyd B fluid) past an exponential stretching sheet.

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.

Exploiting the impact of Lorentz force and convective heating boundary on second-grade nanofluid flow alongside a Riga pattern is the main objective of the present work. Modelling of the present work is done through Grinberg term and a Lorentz force applied parallel to the wall of a Riga plate. The nanoparticles fraction on the solid surface of Riga pattern maintained a strong retardation because of zero mass flux. Theories of Cattaneo–Christov heat flux and generalized Fick’s relations are employed by following the modern aspects of heat and mass transportations. In the current study, additional features of thermal radiation are also included in the energy equation in terms of linear expressions. In order to make the analysis more worthy, effect of chemical reaction is also included. By applying the suitable variables, constituted problem is converted into dimensionless form. Solution of the problem with desired accuracy is obtained by utilizing popular method called Runge–Kutta–Fehlberg. The graphical representations are used to illustrate the flow controlling parameters involved by their attractive physical consequences. Velocity distribution is observed for the increase with the second-grade parameter. Further, an improved nanoparticles temperature distribution is observed with the increase in radiation parameter and Biot number. Additionally, the distribution of the concentration of nanoparticles increases with increase in values of the thermophoretic parameter. Based on the scientific calculations obtained, it is established that the reported results may play a useful role in production processes and in the improvement of energy and thermal resources.

The present study analyzes the forced convective boundary layer flow of viscous incompressible time-established fluid. The base fluid containing water-based nanoparticles and gyrotactic microbes. The flat surface is considered with leading-edge accretion (or) ablation. Characteristics of flow are explored by the impacts of thermal radiation and constructive/destructive chemical reaction. The present flow problem is formed with the partial differential equations, and transformed nonlinear boundary value problems are solved mathematically by the finite difference with the collocation method. There is a good correlation between present work and previous work. Results of selected parameters on velocity, temperature, nanoparticles volume fraction, and microbe density function are discovered. Skin friction, heat transport, mass transfer, and microbes transfer rates are tabular. Efforts of the current work rise in progressive microflow devices to bio-modified nanomaterial dispensation.

The current study explores the consequences of thermo-diffusion, chemical reaction, Hall and ion-slip impacts on unsteady heat and mass transport of free convective hydro-magnetic micro-polar liqui...

Drag and lift forces are very important in engineering applications and, therefore, many research projects have been conducted to control these forces. In this paper, the effects of an upstream porous plate on the hydrodynamic forces over a square cylinder are investigated using lattice Boltzmann method. The main idea is to separate the obstacle from the upstream flow by adding such a porous plate, since the magnitudes of the drag and lift forces have a direct relationship with the phenomena of vortices shedding from the obstacle. In order to have a better insight into the problem, streamlines, vorticity contours and lift and drag coefficients are presented for different case studies. Results proved that the porous plate can reduce the drag and lift coefficients. Furthermore, increasing the height and the gap spacing (i.e., the surface-to-surface distance between the porous plate and the obstacle) could significantly affect the flow field characteristics and the forces acting on the obstacle.

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.

In this numerical contribution, hybrid nanofluid flow behavior, thermal characteristics, and entropy generation analysis through a porous enclosure containing three circular cylinders with magnetic field effects were investigated using finite element approach. The cylinders are arranged in horizontal arrangement in the middle of cavity height, and the active hot central cylinder can move along the vertical central axis while other cold cylinders are considered fixed. The cylinders are enclosed by an adiabatic wavy cavity loaded with Cu-Al2O3-water. The results are discussed for the scrutinized parameters e.g., Rayleigh number (Ra), Darcy number (Da), Hartmann number (Ha), relative position of the hot cylinder (δ), and concentration in volume of nanoparticles (ϕ). It was inferred that the thermal-natural convective flow and overall heat transmission were reinforced by boosting Ra and Da, and lowering Ha. Changing the relative position of the hot cylinder has a remarkable effect on nanoliquid flow patterns, convective heat transfer and entropy generation characteristics.

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 current study is concerned with the investigation of the combined effects of thermophoretic motion and thermal radiation on steady, viscous, incompressible and two-dimensional mixed convection flow of optically dense grey fluid. The governing equations are made dimensionless by using suitable dimensionless variables and further are transformed into a convenient form for a numerical algorithm. The transformed flow model is integrated by using an efficient finite difference methd. Effects of the assorted parameters involved in the flow model such as Prandtl number, mixed convection parameter, modified mixed convection parameter, Schmidt number, radiation parameter, thermophoresis parameter and thermophoretic coefficient on velocity field, temperature distribution, and mass concentration are demonstrated graphically. The numerical results of skin friction, the heat transfer rate and the mass transfer rate under the effect of pertinent parameters are displayed in tabular form.

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.

An analysis into the transient natural convective flow of a nanofluid in a vertical tube is made. The governing equations of momentum, heat transfer and nanoparticle volume fraction are deduced, and the influence of the thermophoresis parameter and Brownian motion is incorporated. By direct integration and variation of the parameter, analytical solutions are obtained for flow formation and heat/mass transfer at steady-state. On the other hand, due to the complexity of same problem at transient state, a numerical solution is used to solve the discretized equations of motion using the implicit finite difference technique. The influence of the thermophoresis parameter and Brownian motion is noted and well discussed. For accuracy check, a numerical comparison is made between the steady state and transient state solution at large time; this comparison gives an excellent agreement. The role of various principal parameters on velocity profile, temperature, concentration of nanoparticles, Sherwood and Nusselt numbers are presented graphically and well discussed. It is noted that the buoyancy ratio decreases the fluid velocity significantly.

In the current investigative paper, the impact of Hall current on an unsteady magnetohydrodynamic liberated convection revolving flow of a nanofluid restricted with a uniform absorbent medium over an oscillatory moving vertical smooth plate with convective as well as diffusive frontier conditions has been reviewed. The non-dimensionalized governing differential equations by the appropriate frontier conditions are resolved by the perturbations technique. The impacts of the physical constants on the flow as well as the heat transfer features are displayed graphically and analyzed for Cu as well as Al2O3nanoparticles. For the engineering industry, the skin friction coefficient, local Nusselt number, along with the Sherwood’s number are examined numerically in detail.

The applications of fluid flow with Newtonian heating effect include conjugate heat conveyance around fins, petroleum industry, and heat exchangers designing. Motivated from these applications, an attempt has been made to analyze the stream of viscous nanomaterial subjected to a curved stretching sheet. Also, heat and mass transport mechanism due to a chemical reaction, Brownian and thermophoresis motion are discussed. The equations of the mathematical model are formulated by considering the Newtonian heating and Stefan blowing conditions at the boundary. These modelled equations are then changed to a system of nonlinear equation involving ordinary derivatives of a function by means of suitable similarity transformations. Further, shooting technique with Runge-Kutta-Fehlberg-45 process is utilized to solve the reduced equations. Outcomes disclose that, the gain in Stefan blowing parameter escalates the liquid velocity. The intensification in chemical reaction rate parameter deteriorates the concentration gradient. The rise in Schmidt number and thermophoresis parameter drops the mass transfer rate. The increased values of Newtonian heating parameter with respect to thermophoresis parameter decays the heat transport rate.

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 passive feature of natural convection encourages continuous investigation on this field. This research work studies the natural convection inside a cavity of wavy vertical surfaces, including a...

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.

This paper theoretically clarifies the impact of pertinent parameters, including viscous dissipation on the flow of Carreau fluid through a permeable arched elongating sheet. Flow describing equations are metamorphosed as ODEs and executed using the combination of shooting and Runge-Kutta strategies. Consequences are elucidated using tables and graphs. We discovered that (a) an appreciable decline in the concentration against temperature difference and reaction rate parameters (b) curvature parameter and porosity parameters registered opposite behaviour to each other on velocity profile (c) there is a reduction in the heat transfer rate with larger Eckert number and curvature parameters (d) Biot number ameliorates the temperature and local Nusselt number (e) Schmidt number and activation energy parameters are showing different behaviours on local Sherwood number. And also, magnetic field and porosity parameters minimize the velocity and surface drag force and Biot number ameliorates the temperature. Further, present results are validated with the earlier outcomes and perceived an acceptable agreement.

Present assessment is considered to analysis flow as well as heat characteristics of steady, thermal slip flow of three-dimensional Casson fluid embedded in a porous medium with internal heat generation. Geometry of the present analysis is linearly stretched surface. Later, all the PDEs corresponding to the study are altered to set of nonlinear equations ODEs by means of appropriate similarity transformations. An efficient numerical scheme of spectral relaxation method (SRM) is applied to solve the nonlinear ordinary system. Variations of Nusselt number, temperature, velocity, and local skin friction coefficient with fluid parameters exhibited by graphs and tables. Spectral relaxation method gives an exact convergence to the nonlinear boundary value problems compare with general methods. In this study, to improve the precision and accuracy of the SRM successive over-relaxation (SOR) strategy is utilized. Proposed method as well as outcomes is checked with the comparison. A sensible connection is acquired between the current outcomes and accessible outcomes in writing. Some of the observations are skin friction coefficient raises and velocities decreases by the magnetic field strength. Skin friction and Local Nusselt number at the surface is more pronounced for non-Newtonian case than that of Newtonian case.

A hydromagnetic transverse flow of an Oldroyd-B-type liquid with a heat flux of the Cattaneo–Christov model with variable thickness has been analyzed. Consider additional impacts of thermal conductivity as well as heat generation. Governing equations were transmitted into a set of nonlinear ordinary differential equations using similarity conversion, and then, numerical solution was evaluated using the procedure Runge–Kutta–Fehlberg. The physical response related to velocity and temperature is investigated computationally. The outcomes also show that the momentum boundary-layer thickness increases the values of magnetic field strength, but the reverse trend is observed for the thermal boundary layer. Impacts of retardation and relaxation time effects are quite the opposite of the temperature field. The obtained computations are useful in transport phenomena which are involving hydromagnetic rheological fluids.

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.

In this examination, a mathematical model is developed for Darcy free convection with reference to an isothermal vertical cone along with fixed apex half angle, pointing downward in a nanofluid-saturated porous medium. The aim of this methodology is to offer another sort of primary fluid containing nanoparticles and gyrotactic microorganism’s consistence of permeable medium, chemical reaction alongside convective boundary circumstance. The model presents design rules for improvement of imperative fabrication of fertilizer and polymer substance. The present model includes the gyrotactic microorganisms alongside nanoparticles, and cone is dependent on concentration of nanoparticles as well as density of motile microorganisms. Two important impacts Brownian motion as well as thermophoresis are also included in the present model for nanofluids. Reduced system of nonlinear differential equations is derived from governing partial differential of the present flow by using usual transformations along with Oberbeck–Boussinesq approximation. After that, this reduced system is solved numerically with the use of fifth-order Runge–Kutta method in conjunction with the shooting technique. Relevant outcomes are exhibited graphically and talked about quantitatively as for variety in the flow controlling parameters related to the present analysis. Mainly, the observations are bioconvection parameters will in general improve the concentration of the rescaled density of microorganisms and nanoparticles volume fraction and dimensionless motile microorganisms reduce with strong chemical reactions.

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.

Heat and flow pattern of a vertical free jet impinging on a hot disk were numerically investigated. A cylinder with various thicknesses and materials exposed simultaneously to uniform heat flux on one side and a free impinging jet on the other side is simulated by ANSYS Fluent 19.3. For simulations, the thermal boundary condition on the hot surface might differ due to the nature of the heat flow. The Volume of Fluid (VOF) approach is used to model the free jet heat transfer and fluid dynamics with the presence of air, while only the energy equation is solved in the cylinder. Heatline equation is solved to reveal the heat flow direction and effects of different geometry conditions. The maximum heat flux of 2.5 MW/m2 was obtained at the edge of stagnation region for hot target made of copper, while the value was 1.5 MW/m2 when the material was combined with stainless steel. However, the general thermal and hydrodynamic features of the jet flow were not influenced. It means that hot object condition may only affect the balance between heat flux and temperature, and the ideal uniform heat flux on the impinging wall may not be achieved in any experimental conditions.

An attempt is made to improve the overall performances of channel heat exchangers. The techniques of baffles and nanofluids are combined to enhance the dynamic and thermal behaviors within the chan...