Three-dimensional Mixed Convection Flow Research Articles

Computational analysis of entropy generation in three-dimensional mixed convection flow with thermal dissipation and variable thermal conductivity

Entropy generation in steady three-dimensional thermal flow is investigated under the coupled influence of viscous dissipation and mixed convection. The stretching sheet with an exponential velocity profile induces the flow. In this examination, we presume that the fluid is incompressible and possesses a Newtonian behavior and temperature-dependent thermal conductivity. Using the appropriate classical similarity variables reduces the dimensional nonlinear dynamical system of governing equations to a dimensionless nonlinear dynamical set of ordinary differential equations. It’s important to note that the selection of an exponentially varying surface temperature is deliberate, as it enables precise similarity transformations to be established in situations involving both viscous dissipation and buoyancy forces. The simplified finite difference approach (SFDM) is used to solve the acquired nonlinear dynamical set of ordinary differential equations. The tridiagonal matrix approach is used to solve the resulting system of algebraic equations. In a particular situation, the present numerical simulation is numerically checked with the previously available results and observed a good agreement. The effects of physical parameters on velocity, temperature, surface stresses and heat tranfer rate, entropy generation, and the irreversibility parameter are investigated. The entropy generation rate exhibits a decreasing trend with respect to the mixed convection parameter in the vicinity of the stretching surface. Entropy reduction can be achieved by employing a working fluid with a low Prandtl number and by minimizing the fluid friction.

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

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

Prevalence of secondary flow due to hall currents on radiative squeezing flow of a CuO-water nanofluid in a rotating channel: numerical prediction

The current study describes three-dimensional incompressible mixed convection flow with convective heat and mass transport on squeezing nanofluid from a rotating channel under impact of Hall current, heat source and Soret number. The current flow model is formulated to consider water based nanofluids with nanoparticle CuO (Copper Oxide). Effectively a nanoscale formulation with the Tiwari-Das model deployed to study material properties. The basic flow equations rendered to non-dimensional form via similarity transformation for which numerical simulations utilizing the fourth-fifth order Runge-Kutta-Fehlberg scheme with the help of Maple, it is a simple iteration scheme that does not require any evaluation of perturbation and linearization for solving non-linear system of equations. Graphical results for primary velocity, secondary velocity, temperature and nanoparticle concentration distributions are presented for different controlled parameters. Furthermore, computed numerical results for skin friction, Nusselt number and Sherwood number for different emerging parameters are tabulated and discussed in detail. The results are verified for limiting cases by comparing with various investigators and found to be in excellent agreement. Outcomes reveal that decrease in secondary flow to a rising channel rotating term and Hall current term. Squeezing term improved the flow rate motion, but reduces nanoparticle conductivity and species diffusion. Thermo-diffusion term stimulated the CuO nanofluid reaction. The authors have hope that the results obtained in the present study not only provide useful information for applications, it also serves as a complement to the previous studies.

Outlining the influence of thermal and solutal stratifications on mixed convection second grade fluid flow near an irregular cylinder with induced magnetic field

In this analysis, thermal and solutal stratifications in three-dimensional mixed convection flow of second grade fluid along an irregular cylinder through porous medium is demonstrated. Effect of induced magnetic induction is considered to deal many technological and scientific problems like crude oil purification, plasma confinement, rotating magnetic stars and power generation. The flow narrating continuity, magnetic flux, momentum, magnetic induction, concentration and heat equations are modeled in the form of PDEs. Set of dimensionless conversions are introduced to replace non-linear PDEs into a set of ODEs. To predict numerical solution of considering model, we used an efficient numerical technique Bvp4c. The consequential outcomes are sketched for unlike values of dimensionless parameters. Parameters like mixed convection, second grade parameter, magnetic parameter, porosity parameter and buoyancy ratio parameter are initiated to control the flow field. Further, temperature and solutal stratification parameters, Prandtl, magnetic Prandtl and Schmidt numbers are found to control energy, magnetic induction and concentration distributions. Skin drag coefficients, heat and mass fluxes are investigated for inflating values of some sundry parameters. For justification of the model, we compared present numerical outcomes with previous published results.

Cattaneo-Christov Heat Flux Model of Eyring Powell fluid along with Convective Boundary Conditions

Heat and mass transfer effects in three-dimensional mixed convection flow of Eyring Powell over an exponentially stretching surface with convective boundary conditions are inspected. Cattaneo-Christov Heat Flux model is a modified version of the classical Fourier’s law that takes into account the interesting aspect of thermal relaxation time. First order chemical reaction effects are also taken into account. Similarity transformations are invoked to reduce the leading boundary layer partial differential equations into the ordinary differential equations. The nonlinear, coupled ordinary differential equations with boundary conditions has been analyzed numerically by using Finite Element Method. Similarity transformations are invoked to reduce the leading boundary layer partial differential equations into the ordinary differential equations.

Three-Dimensional MHD Mixed Convection Flow of Casson Nanofluid with Hall and Ion Slip Effects

The intention of the present study is to scrutinize the three-dimensional MHD mixed convection flow of Casson nanofluid over an exponentially stretching sheet using the impacts of Hall and ion slip currents. Moreover, the impacts of thermal radiation and heat source are considered in this study. The governing partial differential equations are transformed into a system of joined nonlinear ordinary differential equations using similarity transformations, and they are solved numerically employing a spectral relaxation method (SRM). The obtained results are contrasted with existing specific cases, and a reasonable harmony is established. The impacts of noteworthy physical parameters on the velocities, thermal and concentration distributions, skin friction coefficients, local Nusselt number, and local Sherwood number are investigated graphically. It is found that the rise in Casson fluid and magnetic field parameters reduce the velocity profiles along bothx−andy−directions while the reverse tendency is observed with an increment in Hall, ion slip, and mixed convection parameters. Moreover, the increase in both radiation and heat source parameters enhances the temperature profile. It is also observed that both the skin friction coefficients reduced with an increase in Casson fluid, Hall, and ion slip parameters. Furthermore, the local Nusselt number enhances with an augment in radiation parameter, whereas the opposite trends of local Nusselt and Sherwood numbers are found with an increase in heat source parameter.

Three-dimensional mixed convection flow with variable thermal conductivity and frictional heating

In this article, three-dimensional mixed convection flow over an exponentially stretching sheet is investigated. Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity. Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations. Resulting nonlinear ordinary differential equations are solved numerically employing the Runge–Kutta shooting method. In order to check the accuracy of the method, these equations are also solved using bvp4c built-in routine in Matlab. Both solutions are in excellent agreement. The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs. The novelty of this analysis is the self-similar solution of the three-dimensional boundary layer flow in the presence of mixed convection, viscous dissipation and variable thermal conductivity.

Mixed convection flow of Oldroyd-B nano fluid with Cattaneo-Christov heat and mass flux model with third order slip

This study reports the three-dimensional mixed convection flow of an Oldroyd-B nanofluid past a bidirectional stretching surface. Nonlinear partial differential equations obtained from the flow problem were converted into nonlinear ordinary differential equations using similarity transformation, and then, the numerical solutions of these ODEs with corresponding boundary conditions were obtained by employing a bvp4c solver. The effect of governing parameters on nondimensional velocity along x- and y-directions, temperature, particle concentration, local Nusselt number, and Sherwood number was presented through graphs and tables. It can be seen that the increasing values of the Brownian motion parameter Nb and thermophoresis parameter Nt lead to an increase in the temperature field and thermal boundary layer thickness, while the opposite behavior is observed for concentration field and concentration boundary layer thickness. As the Deborah number β1 increases, the concentration profile as well as concentration boundary layer thickness increase. However, the effects of β2 on the concentration profile are opposite to those of β1. An increase in δt, Pr, and α results in a decrease in temperature. It is reported that the local Nusselt number increases when β and Pr increase, whereas it decreases when λ, Nb, Nt, and Sc increase. An increase in Biot number Bi results in an increase in the Nusselt number, and an increase in Nt results in an increase in the Sherwood number. The results of the present analysis were compared with the available works in particular situations, and more agreement has been noted.

Mixed Convection 3D Radiating Flow and Mass Transfer of Eyring-Powell Nanofluid with Convective Boundary Condition

Three-dimensional mixed convection flow, heat and mass transfer of Eyring-powell fluid over a convectively heated stretched sheet is inspected in this paper. The encouragement of Brownian motion, Thermophoresis and thermal radiations are accounted. Appropriate transformations are used to reduce the principal PDE’s into set of coupled highly non-linear ODE’s which are then solved numerically using RKF fourth-fifth order method. The consequence of several parameters on flow, heat and mass transfer characteristics are deliberated with the help of graphs and tables. It is observed that, the temperature and concentration profiles diminish for higher values mixed convection parameter.

Three-Dimensional Magnetohydrodynamic Mixed Convection Flow of Nanofluids over a Nonlinearly Permeable Stretching/Shrinking Sheet with Velocity and Thermal Slip

In this paper, the steady three-dimensional magnetohydrodynamic (MHD) mixed convection flow of nanofluids over a permeable vertical stretching/shrinking sheet with slip conditions is investigated in a numerical manner. As such, two types of nanofluids, Cu-water and Ag-water, had been considered. A similarity transformation was employed to reduce the governing equations to ordinary differential equations, which were then solved numerically using the MATLAB (Matlab R2015a, MathWorks, Natick, MA, USA, 1984) programme bvp4c. The numerical solutions derived from the ordinary differential equations subjected to the associated boundary conditions, were obtained to represent the values of the mixed convection parameter. Dual (upper and lower branch) solutions were discovered in the opposing flow region of the mixed convection parameter. A stability analysis was carried out to prove that the upper branch solution was indeed stable, while the lower branch solution was unstable. The significant effects of the governing parameters on the reduced skin friction coefficients, the reduced local Nusselt number, as well as the velocity and temperature profiles, were presented graphically and discussed in detail.

3D analysis of the combined effects of thermal buoyancy and viscous dissipation on the mixed convection of Bingham plastic fluid in a rectangular channel

The present study investigates numerically the three-dimensional mixed convection flow behavior of a Bingham plastic fluid within a rectangular horizontal duct. The latter has a square cross section, which is symmetrically heated at uniform wall temperature. The effect of the viscous dissipation on the hydrodynamic and thermal fields is taking into account through the energy equation. The finite volume method is used to discretize the governing equations, and the resulting algebraic system is solved iteratively by TDMA algorithm. The simulations are conducted for different values of the Grashof number (104 ≼ | Gr | ≼ 5 × 105), the Brinkman number (0 ≼ | Br | ≼ 10), and the Bingham number (10 ≼ | Bn | ≼ 20), for Re = 100 and Pr = 50. The results are analyzed through the distribution of the Nusselt number, the temperature and velocity profiles as well as unyielded plugs. For Br = 0, the Grashof number variation affects greatly the heat transfer and the fluid flow, in particular at the duct intermediate region. However, for Br ≠ 0, the Grashof number variation effect is noticeable in both the central and the fully developed regions. Moreover, the combination of Grashof, Brinkman, and Bingham numbers constitutes pertinent parameters control of the unyielded plugs.

Three-dimensional mixed convection flow of Sisko nanoliquid

This article deals a model to investigate the mixed convection flow of Sisko nanofluid driven by bidirectionally stretched surface. Features of Brownian motion and thermophoresis have been described. Convective conditions model the heat and mass transfer process. Transformations yield ordinary differential systems. Convergence of derived local similar series solutions for resulting problems is verified. Intervals of convergence in the series solutions are explicitly determined. Impact of numerous sundry variables for velocity, temperature and nanoparticles concentration is explored by plotting graphs. Computations for heat and mas transfer rates are declared and inspected for the influence of emerging variables. It is inspected that higher mixed convection variable results to enhance the velocity distribution whereas it diminishes fluid temperature and concentration. The results of presented analysis are compared with the available works in particular situations and good agreement has been noted.

Three-dimensional mixed convection stagnation-point flow over a permeable vertical stretching/shrinking surface with a velocity slip

This paper reports on the findings of a study attempting to investigate the steady three-dimensional mixed convection stagnation-point flow past a permeable vertical stretching/shrinking sheet with a velocity slip. In doing so, similarity transformations had to be used to help transform the partial differential equations into ordinary (similarity) differential equations, which were then solved numerically using MATLAB programme bvp4c with different values of the governing parameters. The findings of the study revealed that it was the ordinary (similarity) differential equations that had dual (upper and lower branch) solutions within a certain range of the mixed convection parameter, stretching/shrinking parameter, suction parameter and velocity slip parameter. A stability analysis was implemented in order to test the stability of the branch solutions. The effects of the governing parameters on the reduced skin friction coefficients, reduced local Nusselt number, dimensionless velocity and temperature profiles are presented graphically and discussed in detail.

Effect of Viscous Dissipation and Joule Heating on Three-Dimensional Mixed Convection Flow of Nano Fluid Over a Non-Linear Stretching Sheet in Presence of Solar Radiation

Effect of Viscous Dissipation and Joule Heating on Three-Dimensional Mixed Convection Flow of Nano Fluid Over a Non-Linear Stretching Sheet in Presence of Solar Radiation

Convective heat and mass transfer in three-dimensional mixed convection flow of viscoelastic fluid in presence of chemical reaction and heat source/sink

Heat and mass transfer effects in the three-dimensional mixed convection flow of a viscoelastic fluid with internal heat source/sink and chemical reaction have been investigated in the present work. The flow generation is because of an exponentially stretching surface. Magnetic field normal to the direction of flow is considered. Convective conditions at the surface are also encountered. Appropriate similarity transformations are utilized to reduce the boundary layer partial differential equations into the ordinary differential equations. The homotopy analysis method is used to develop the solution expressions. Impacts of different controlling parameters such as ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed. The local Nusselt and Sherwood numbers are sketched and examined.

Thermophoresis and MHD mixed convection three-dimensional flow of viscoelastic fluid with Soret and Dufour effects

Heat and mass transfer effects in three-dimensional mixed convection flow of viscoelastic fluid over a stretching surface with convective boundary conditions are investigated. The fluid is electrically conducting in the presence of constant applied magnetic field. Conservation laws of energy and concentration are based upon the Soret and Dufour effects. First order chemical reaction effects are also taken into account. By using the similarity transformations, the governing boundary layer equations are reduced into the ordinary differential equations. The transformed boundary layer equations are computed for the series solutions. Dimensionless velocity, temperature, and concentration distributions are shown graphically for different values of involved parameters. Numerical values of local Nusselt and Sherwood numbers are computed and analyzed. It is found that the behaviors of viscoelastic, mixed convection, and concentration buoyancy parameters on the Nusselt and Sherwood numbers are similar. However, the Nusselt and Sherwood numbers have qualitative opposite effects for Biot number, thermophoretic parameter, and Soret-Dufour parameters.

Effects of chemical reaction and partial slip on the three-dimensional flow of a nanofluid impinging on an exponentially stretching surface

The three-dimensional mixed convection boundary layer flow of a nanofluid induced by an exponentially stretching sheet is numerically investigated in the presence of thermal radiation, heat source/sink and first-order chemical reaction effects. The adopted nanofluid model incorporates the effects of Brownian motion and thermophoresis into the mathematical model. The first-order velocity slip boundary conditions are also taken into account. The governing boundary layer equations are transformed into a set of nonlinear ordinary differential equations by employing suitable similarity variables. The resultant equations are solved numerically using the Runge-Kutta-Fehlberg method. Obtained solutions are compared with previous results in a limiting sense from the literature, demonstrating an excellent agreement. To show the typical trend of the solutions, a parametric study is conducted. The axial velocity, transverse velocity, temperature and nanoparticle volume fraction profiles as well as the skin-friction coefficient, Nusselt and Sherwood numbers are demonstrated graphically as a representative set of numerical results and discussed comprehensively.

Unsteady three-dimensional mixed convection flow with variable viscosity and thermal conductivity

An analysis has been carried out to investigate the influence of variable viscosity and thermal conductivity in the mixed convection three-dimensional flow of viscous fluid by an exponential stretching surface with heat transfer. Temperature distribution of the surface is also assumed to vary exponentially. The governing system is transformed into ordinary differential equations by appropriate transformations and non-similar solutions are computed. The effects of pertinent parameters on the flow field and heat transfer characteristics have been examined qualitatively through graphs and numerical values. Comparisons of the present work is shown with the existing previous results in the limiting sense.

Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid

Purpose – The purpose of this paper is to numerically solve the problem of an unsteady squeezing three-dimensional flow and heat transfer of a nanofluid in rotating vertical channel of stretching left plane. The fluid is assumed to be Newtonian, incompressible and electrically conducting embedded with nanoparticles. Effect of internal heat generation/ absorption is also considered in energy equation. Four different types of nanoparticles are considered, namely, copper (Cu), alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) with the base fluid as water. Maxwell-Garnetts and Brinkman models are, respectively, employed to calculate the effective thermal conductivity and viscosity of the nanofluid. Design/methodology/approach – Using suitable similarity transformations, the governing partial differential equations are transformed into set of ordinary differential equations. Resultant equations have been solved numerically using Runge-Kutta-Fehlberg fourth fifth order method for different values of the governing parameters. Effects of pertinent parameters on normal, axial and tangential components of velocity and temperature distributions are presented through graphs and discussed in detail. Further, effects of nanoparticle volume fraction, squeezing parameter, suction/injection parameter and heat source/sink parameter on skin friction and local Nusselt number profiles for different nanoparticles are presented in tables and analyzed. Findings – Squeezing effect enhances the temperature field and consequently reduces the heat transfer rate. Large values of mixed convection parameter showed a significant effect on velocity components. Also, in many heat transfer applications, nanofluids are potentially useful because of their novel properties. They exhibit high-thermal conductivity compared to the base fluids. Further, squeezing and rotation effects are desirable in control the heat transfer. Originality/value – Three-dimensional mixed convection flows over in rotating vertical channel filled with nanofluid are very rare in the literature. Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid is first time investigated.

Numerical Study of Turbulent Mixed Convection of Nanofluids in Three-Dimensional Horizontal Concentric Annuli

Three-dimensional turbulent mixed convection flow using nanofluids in horizontal concentric annuli is numerically simulated. The continuity, Navier-Stokes and energy equations are solved using finite volume method (FVM) and the SIMPLE algorithm scheme is applied to examine the effects of turbulent flow on heat transfer characteristics. In this study, several parameters such as different types of nanoparticles (Al2O3, CuO, SiO2 and ZnO), different volume fractions in the range of 1% to 4%, different nanoparticles diameter in the range of 20 to 80 nm were used. Reynolds numbers are considered in the turbulent range of 6000 =Re = 18000. Different nanoparticle shapes (i.e., blades, platelets, cylindrical, bricks, and spherical), and effects of inner cylinder and outer cylinder heat fluxes were analyzed. Hydraulic diameter ratio was also examined. The numerical results indicate that the nanofluid with SiO2 has the highest Nusselt number and pressure drop compared with other nanofluids types. Heat transfer characteristic increases as the volume fraction of nanoparticles increases while it decreases as the nanoparticles diameter increases. Effects of hydraulic diameter ratio, nanoparticle shapes and location of applying heat flux on heat transfer characteristics are significant.