Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

Influence of the Inclination Angle on Mixed Convection and Heat Transfer in a“T”Shaped Double Enclosure

The effect of the tilt angle on mixed convection and related heat transfer in a“T”shaped double enclosure with four heated obstacles on the bottom surface is numerically investigated.The considered obstacles are constantly kept at a relatively high(fixed)temperature,while the cavity’s upper wall is cooled.The finite volume approach is used to solve the mass,momentum,and energy equations with the SIMPLEC algorithm being exploited to deal with the pressure-velocity coupling.Emphasis is put on the influence of the tilt angle on the solution symmetry,flow structure,and heat exchange through the walls.The following parameters and related ranges are considered:Rayleigh number 104≤Ra≤5.105,tilt angle 0°≤φ≤90°,Reynolds number 100≤Re≤1000,Prandtl number Pr=0.72,block height B=0.5,opening width C=0.15,and distance between blocks D=0.5.The results reveal different branches of solutions on varying Re andφ.They also show that the symmetry of the solution regarding the P_(2)axis is retained for all cases with no tilt and for values of Re between 100 and 1000.

Modeling of Mixed Convection in a Lid Driven Wavy Enclosure with Two Square Blocks Placed at Different Positions

The purpose of this paper is to investigate the simulation of mixed convection in a lid-driven wavy enclosure with blocks positioned at various positions. This study also examined the impact of the longitudinal position of the heated block on heat transfer enhancement. The Galerkin weighted residual finite element method is employed to computationally solve the governing equations of Navier-Stokes, thermal energy, and mass conservation. The enclosure consists of two square heated blocks strategically placed at different heights—firstly, one set is closer to the bottom surface;secondly, one set is nearer to the middle area and finally, one set is closer to the upper undulating surface of the enclosure. The wavy top wall’s thermal insulation, along with active heating of the bottom wall and blocks, generates a dynamic convective atmosphere. In addition, the left wall ascends as the right wall falls, causing the flow formed by the lid. The study investigates the impact of the Richardson number on many factors, such as streamlines, isotherms, dimensionless temperature, velocity profiles, and average Nusselt numbers. These impacts are depicted through graphical illustrations. In all instances, two counter-rotating eddies were generated within the cage. Higher rotating speed consistently leads to improved performance, irrespective of other characteristics. Furthermore, an ideal amalgamation of the regulating factors would lead to increased heat transmission.

Numerical Simulations of Hydromagnetic Mixed Convection Flow of Nanofluids inside a Triangular Cavity on the Basis of a Two-Component Nonhomogeneous Mathematical Model

Nanofluids have enjoyed a widespread use in many technological applications due to their peculiar properties.Numerical simulations are presented about the unsteady behavior of mixed convection of Fe_(3)O_(4)-water,Fe_(3)O_(4)-kerosene,Fe_(3)O_(4)-ethylene glycol,and Fe_(3)O_(4)-engine oil nanofluids inside a lid-driven triangular cavity.In particular,a two-component non-homogeneous nanofluid model is used.The bottom wall of the enclosure is insulated,whereas the inclined wall is kept a constant(cold)temperature and various temperature laws are assumed for the vertical wall,namely:
θ=1(Case 1),θ=Yð1YÞ(Case 2),andθ=sinð2-YÞ(Case 3).A tilted magnetic field of uniform strength is also present in the fluid domain.From a numerical point of view,the problem is addressed using the Galerkin weighted residual finite element method.The role played by different parameters is assessed,discussed critically and interpreted from a physical standpoint.We find that a higher aspect ratio can produce an increase in the average Nusselt number.Moreover,the Fe_(3)O_(4)-EO and Fe_(3)O_(4)-H2O nanofluids provide the highest and smallest rate of heat transfer,respectively,for all the considered(three variants of)thermal boundary conditions.

Mixed Convection in a Two-Sided Lid-Driven Square Cavity Filled with Different Types of Nanoparticles:A Comparative Study Assuming Nanoparticles with Different Shapes

Steady,laminar mixed convection inside a lid-driven square cavity filled with nanofluid is investigated numerically.We consider the case where the right and left walls are moving downwards and upwards respectively and maintained at different temperatures while the other two horizontal ones are kept adiabatic and impermeable.The set of nonlinear coupled governing mass,momentum,and energy equations are solved using an extensively validated and a highly accurate finite difference method of fourth-order.Comparisons with previously conducted investigations on special configurations are performed and show an excellent agreement.Meanwhile,attention is focused on the heat transfer enhancement when different nano-particles:Cu,Ag,Al2O3,TiO2 and Fe3O4 are incorporated separately in different base fluids such as:Water,Ethylene-glycol,Methanol and Kerosene oil.In this framework,the numerical results related to several mixtures are presented and concern flow pattern and heat transfer curves for various values of Richardson number[Ri=0.1,1 and 10].It turns out that the choice of the efficient binary mixture for an optimal heat transfer depends not only on the thermophysical properties of the nanofluids but also on the range of the Richardson number.Special attention is devoted to shedding light on the effect of the shape of the nanoparticles on the heat transfer in the case of Water-Ag nanofluid.It is concluded that the spherical shape is more suitable for a better heat transfer enhancement in comparison to the cylindrical ones.

Mixed convection boundary layer flow near stagnation-point on vertical surface with slip

This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.

Mixed convection stagnation-point flow on vertical stretching sheet with external magnetic field

The problem of steady laminar magnetohydrodynamic （MHD） mixed con- vection stagnation-point flow of an incompressible viscous fluid over a vertical stretch- ing sheet is studied. The effect of an externally magnetic field is taken into account. The transformed boundary layer equations are solved numerically by using an implicit finite-difference scheme. Numerical results are obtained for various values of the mixed convection parameter, Hartmann number, and Prandtl number. The effects of an exter- nally magnetic field on the skin friction coefficient, local Nusselt number, velocity, and temperature profiles for both A 〉 1 and A ~ 1, where A is the velocity ratio parameter, are presented graphically and discussed in detail. Both assisting and opposing flows are considered, and it is found that dual solutions exist for the opposing flow.

Mixed convection boundary layer flow past vertical flat plate in nanofluid: case of prescribed wall heat flux

An analysis is carried out to investigate the steady mixed convection bound- ary layer flow of a water based nanofluid past a vertical semi-infinite flat plate. Using an appropriate similarity transformation, the governing partial differential equations are transformed into the coupled, nonlinear ordinary （similar） differential equations, which are then solved numerically for the Prandtl number Pr = 6.2. The skin friction coeffi- cient, the local Nusselt number, and the velocity and temperature profiles are presented graphically and discussed. Effects of the solid volume fraction φ and the mixed convection parameter λ on the fluid flow and heat transfer characteristics are thoroughly examined. Different from an assisting flow, it is found that the solutions for an opposing flow are non-unique. In order to establish which solution branch is stable and physically realizable in practice, a stability analysis is performed.

Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

The effect of nonlinear mixed convection in stretched flows of rate-type nonNewtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

Mixed convection flow in vertical channel with boundary conditions of third kind in presence of heat source/sink

The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique. The velocity, temperature, skin friction, and Nusselt num- bers at the plates are discussed numerically and presented through graphs.

Non-uniform slot suction/injection into mixed convection boundary layer flow over vertical cone

The aim of this work is to study the effect of non-uniform single and double slot suction/injection into a steady mixed convection boundary layer flow over a vertical cone, while the axis of the cone is inline with the flow. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar trans- formations. The resulting coupled non-linear partial differential equations are solved nu- merically by employing the quasi-linearization technique and an implicit finite-difference scheme. Numerical computations are performed for different values of the dimensionless parameters to display the velocity and temperature profiles graphically. Also, numerical results are presented for the skin friction and heat transfer coefficients. Results indicate that the skin friction and heat transfer coefficients increase with non-uniform slot suction, but the effect of non-uniform slot injection is just opposite.

Darcy-Forchheimer Hybrid Nano Fluid Flow with Mixed Convection Past an Inclined Cylinder

This article aims to investigate the Darcy Forchhemier mixed convection flow of the hybrid nanofluid through an inclined extending cylinder.Two different nanoparticles such as carbon nanotubes(CNTs)and iron oxide Fe3O4 have been added to the base fluid in order to prepare a hybrid nanofluid.Nonlinear partial differential equations for momentum,energy and convective diffusion have been changed into dimensionless ordinary differential equations after using Von Karman approach.Homotopy analysis method(HAM),a powerful analytical approach has been used to find the solution to the given problem.The effects of the physical constraints on velocity,concentration and temperature profile have been drawn as well for discussion purpose.The numerical outcomes have been carried out for the drag force,heat transfer rate and diffusion rate etc.The Biot number of heat and mass transfer affects the fluid temperature whereas the Forchhemier parameter and the inclination angle decrease the velocity of the fluid flow.The results show that hybrid nanofluid is the best source of enhancing heat transfer and can be used for cooling purposes as well.

Transient mixed convection flow arising due to thermal and mass diffusion over porous sensor surface inside squeezing horizontal channel

The double diffusion effect on the mixed convection flow over a horizontal porous sensor surface placed inside a horizontal channel is analyzed. With the appropriate transformations, the unsteady equations governing the flow are reduced to non-similar boundary layer equations which are solved numerically for the time-dependent mixed convection parameter. The asymptotic solutions are obtained for small and large values of the time-dependent mixed convection parameter. The results are discussed in terms of the skin friction, the heat transfer coefficient, the mass transfer coefficient, and the velocity, temperature, and concentration profiles for different values of the Prandtl number, the Schmidt number, the squeezing index, and the mixed convection parameter.

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

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

Mixed convection heat transfer in horizontal channel filled with nanofluids

The laminar fully developed nanofluid flow and heat transfer in a horizonal channel are investigated. Highly accurate solutions for the temperature and nanopavticle concentration distributions are obtained. The effects of the Brownian motion parameter Nb, the thermophoresis parameter Nt, and the Lewis number Le on the temperature and nanoparticle concentration distributions are discussed. The current analysis shows that the nanoparticles can improve the heat transfer characteristics significantly for this flow problem.

Finite Element Analysis of Magnetohydrodynamic Mixed Convection in a Lid-Driven Trapezoidal Enclosure Having Heated Triangular Block

A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (Rot = 0° - 90°) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed U0. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ Pr ≤ 2), Reynolds number (60 ≤ Re ≤ 120), Rayleigh number (Ra = 103) and Hartmann number (Ha = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of Nuav of hot bottom wall and θav in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.

Numerical Investigation of a Mixed Convection Flow in a Lid-Driven Cavity

This study is devoted to the computational fluid dynamics (CFD) modeling of steady laminar mixed convection flow and heat transfer in lid driven cavity (10 ≤ Re ≤ 1000). The ratio of the height to the width of the cavity is ranged over H/L = 0.5 to 1.5. The governing equations are solved using commercial finite volume package FLUENT to visualize the nature of the flow and estimate the heat transfer inside the cavity for different aspect ratio. The simulation results are presented in terms of average Nusselt number of the hot wall, velocity profile, and temperature contours. It was found that the average Nusselt number inside the cavity is strongly governed by the aspect ratio as well as the Reynolds number. A parametric study is conducted to demonstrate the effect of aspect ratio on the flow and heat transfer characteristics. It is found that heat transfer enhancement was obtained by decreasing the aspect ratio and/or increasing the Reynolds number.

Unsteady mixed convection flow over stretching sheet in presence of chemical reaction and heat generation or absorption with non-uniform slot suction or injection

The article examines the unsteady mixed convection flow over a vertical stretching sheet in the presence of chemical reaction and heat generation or absorption with non-uniform mass transfer. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Non-similar solutions are obtained nu- merically by solving the coupled nonlinear partial differential equations using the quasi- linearization technique in combination with an implicit finite difference scheme. To reveal the tendency of the solutions, typical results for the local skin friction coefficient and the local Nusselt and Sherwood numbers are presented for different values of parameters. The effects of various parameters on the velocity, temperature, and concentration distributions are discussed here. The present numerical results are compared with the previously published work, and the results are found to be in excellent agreement.

Darcy-Forchheimer flow with nonlinear mixed convection

An analysis of the mixed convective flow of viscous fluids induced by a nonlinear inclined stretching surface is addressed.Heat and mass transfer phenomena are analyzed with additional effects of heat generation/absorption and activation energy,respectively.The nonlinear Darcy-Forchheimer relation is deliberated.The dimensionless problem is obtained through appropriate transformations.Convergent series solutions are obtained by utilizing an optimal homotopic analysis method(OHAM).Graphs depicting the consequence of influential variables on physical quantities are presented.Enhancement in the velocity is observed through the local mixed convection parameter while an opposite trend of the concentration field is noted for the chemical reaction rate parameter.