Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid

A numerical investigation of laminar mixed convection flows through a copper–water nanofluid in a square lid-driven cavity has been executed. In the present study, the top and bottom horizontal walls are insulated while the vertical walls are maintained at constant but different temperatures. The study has been carried out for the Rayleigh number 10⁴ to 10⁶, Reynolds number 1 to 100 and the solid volume fraction 0 to 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics have been investigated and discussed. It is found that at the fixed Reynolds number, the solid concentration affects on the flow pattern and thermal behavior particularly for a higher Rayleigh number. In addition it is observed that the effect of solid concentration decreases by the increase of Reynolds number.     

Influence of an inclined stretching cylinder over MHD mixed convective nanofluid flow due to chemical reaction and viscous dissipation

This paper analyzed the steady two‐dimensional magnetohydrodynamic mixed convective viscous nanofluid and heat transfer toward an inclined stretching cylinder with chemical reaction and uniform magnetic field. The governing partial differential equation in a cylindrical form is reduced to a set of nonlinear ordinary differential equations by using appropriate similarity transformation and solved numerically by spectral quasilinearization methods (SQLMs). A new approach of this method is employed to derive numerical expressions for velocity, temperature, and concentration profile. The convergence and accuracy of our numerical scheme are observed. The SQLM is employed to find out the convergent series solution. There is an increase in the temperature profiles due to the increase in the thermophoresis parameter. The increase in effective Eckert number results in the increase of the temperature profile.     

Numerical study of mixed convection in an inclined two sided lid driven cavity filled with nanofluid using two-phase mixture model

Mixed convection of a nanofluid consisting of water and SiO2 in an inclined enclosure cavity has been studied numerically. The left and right walls are maintained at different constant temperatures while upper and bottom insulated walls are moving lids. Two-phase mixture model has been used to investigate the thermal behaviors of the nanofluid for various inclination angles of enclosure ranging from θ = − 60° to θ = 60°, volume fraction from 0% to 8%, Richardson numbers varying from 0.01 to 100 and constant Grashof number 10⁴. The governing equations are solved numerically using the finite-volume approach. Results are presented in the form of streamlines, isotherms, distribution of nanoparticles and average Nusselt number. In addition, effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated. The results reveal that addition of nanoparticles enhances heat transfer in the cavity remarkably and causes significant changes in the flow pattern. Besides, effect of inclination angle is more pronounced at higher Richardson numbers.     

Effects of buoyancy assisting and opposing flows on mixed convection boundary layer flow over a permeable vertical surface

The present study deals with new similarity solution of steady mixed convection boundary layer flow over a permeable surface for convective boundary condition. It has been shown that a self similar solution is possible when the mass transfer velocity at the surface of the plate varies like x^−1/2, where x is the distance from the leading edge of the solid surface. Two point boundary value problem governed by non-linear coupled ordinary differential equations have been solved numerically using implicit finite difference scheme in combination with the quasi-linearization technique. It is interesting to note that dual solutions exist for buoyancy assisting flow, besides that usually reported in literature for buoyancy opposing flow. Further, the buoyancy assisting force causes considerable overshoot in the velocity profile and the Prandtl number strongly affects the thermal boundary layer thickness including the surface heat transfer rate.     

Numerical study of mixed convective cooling in a square cavity ventilated and partially heated from the below utilizing nanofluid

A numerical investigation of mixed convection flows through a copper–water nanofluid in a square cavity with inlet and outlet ports has been executed. The natural convection effect is attained by heating from the constant flux heat source which is symmetrical located at the bottom wall and cooling from the injected flow. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Reynolds number in the range 50 ≤ Re ≤ 1000, with Richardson numbers 0 ≤ Ri ≤ 10 and for solid volume fraction 0 ≤ ? ≤ 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. Results are presented in the form of streamlines, isotherms, average Nusselt number and average bulk temperature. In addition, the effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated and discussed. The results indicate that increase in solid concentration leads to increase in the average Nusselt number at the heat source surface and decrease in the average bulk temperature.     

Numerical study on mixed convection in an inclined lid-driven cavity with discrete heating

The present investigation deals with numerical analysis on mixed convection in an inclined square cavity with different sizes and locations of the heater. The left wall is heated fully or partially with higher temperature whereas the opposite wall is kept with lower temperature. In the left wall, three different sizes and locations of the heater are considered. The governing transformed equations are solved numerically using the finite volume method. Simulations are performed on different Richardson numbers, different sizes and locations of the heater and the cavity inclination angles. It is observed that the high heat transfer is found at cavity inclination angle of γ = 30° in the buoyancy convection dominated regime when the heater is located at the middle of the cavity.     

Numerical investigation for natural convection of a nanofluid in an inclined L-shaped cavity in the presence of an inclined magnetic field

The problem of natural convection in an inclined L-shaped enclosure filled with Cu/water nanofluid that operates under differentially heated walls in the presence of an inclined magnetic field is presented in this paper. The fully implicit finite difference method is used to solve the governing equations. A comparison with previously published results in special case of the present study is performed and a very good agreement is found. Heat transfer and fluid flow are examined for parameters of the Hartmann number (0 ≤ Ha ≤ 100), the nanoparticles volume fraction (0% ≤ ϕ ≤ 20%), the cavity inclination angle (0° ≤ ϑ ≤ 300°), the magnetic field inclination angle (0° ≤ γ ≤ 270°), the cavity aspect ratio (0.25 ≤ AR ≤ 0.6) and the Rayleigh number (10³ ≤ Ra ≤ 10⁶). It is found that, the presence of the magnetic field in the fluid region causes a significant reduction in the fluid flow and heat transfer characteristics. Also, a good enhancement in the heat transfer rate can be obtained by adding the copper nanoparticles to the base fluid.     

Analysis of mixed convection in an inclined square cavity using nanofluids with Vajjha and Das' nanofluid model

In this article, the effects of angle of inclination on heat transfer by mixed convection have been analyzed numerically in a square cavity packed with a CuO nanofluid. Cavity boundaries are constructed by having sinusoidal varying temperature on sidewalls, inactive horizontal walls, and the hot passing plate at the center of the cavity. The transport equations for fluid and heat are solved using the finite-volume method with SIMPLE algorithm. The Richardson number (Ri) varying from 0.01 to 100, inclination angle (γ) from 0° to 90°, wall speed ratios (λ) from 0 to 3 and volume fraction of nanoparticles (φ) from 0.0 to 0.1 are given and represented in the form of flow fields, temperature fields, and mean heat transfer graphs. It is detected that the principal flow constraints have a substantial impact on the flow lines and thermal lines. Specifically, the structures of cavity inclination, existence of copper nanoparticles, and the hot wall in motion at the midpoint of the cavity are established to enrich the overall rate of heat transfer. Correspondingly, in the present study, the Vajjha and Das model is taken into account for the effective thermal conductivity and viscosity of the nanofluid; application of this model is beneficial for the industries working in a high-temperature environment.     

Numerical study of mixed convection nanofluid in an annulus enclosure between outer rotating cylinder and inner corrugation cylinder

Numerical investigations are presented for mixed convection problems in a concentric inner sinusoidal cylinder and an outer rotating circular cylinder, which were kept at constant hot and cold temperatures, respectively. The free space between the cylinders and the enclosure walls was filled with a water‐Cu nanofluid. The governing equations are formulated for velocity, pressure, and temperature formulation and are modeled in COMSOL5.2a, a partial differential equation solver based on the Galerkin finite element method. The governing parameters considered are the solid volume fraction, [0, 0.02, 0.04, and 0.06], Re (1, 25, 100, 200, and 300), and Ra (less than 10⁴), and the inner cylinder corrugation frequencies varied from (N = 3, 6, and 9). According to the calculations, the Reynolds number, the Rayleigh number, the nanoparticle volume fraction, and the number of corrugations play an important role of forming the stream and isothermal lines, the local and the average Nusselt number inside the annulus enclosure. The average Nusselt number decreases with increasing Reynolds number and the number of corrugations, while it increases as the Rayleigh number and the volume fraction increase.     

Numerical simulation of mixed convection flows in a square lid-driven cavity partially heated from below using nanofluid

The present numerical study deals with mixed convection in a square lid-driven cavity partially heated from below and filled with water-base nanofluid containing various volume fractions of Cu, Ag, Al₂O₃ and TiO₂. Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely, Reynolds number, solid volume fraction, different values of the heat source length and different locations of the heat source on the streamlines and isotherms contours as well as Nusselt number and average Nusselt number along the heat source were considered. The present results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed.     

Second law analysis for mixed convection nanofluid flow in an inclined channel with convectively heated walls

In this study, entropy generation analysis for Cu–water nanofluid mixed convective flow in an inclined channel occupied with a saturated porous media with Navier slip and convective boundary conditions is explored. The governing equations composed of equations of velocity and temperature are nondimensionalized and then solved utilizing the technique of homotopy analysis. Temperature and velocity profile expressions are acquired, which are then used to calculate the entropy produced in the scheme. The impacts of the corresponding fluid parameters are addressed in‐depth on velocity, temperature, entropy generation, Bejan number, Nusselt number, skin friction, volume flow rate, and heat carried out by the fluid for nanofluid concentration. Entropy has been observed to be minimal in all cases just above the channel center and maximum at the channel's bottom wall. Fluid friction‐generated entropy has been discovered to have a higher influence on entropy generation. We also provide a comparative study with existing literature to validate our current results.     

Numerical study of laminar mixed convection of a nanofluid in horizontal curved tubes

Fully developed laminar mixed convection of a nanofluid consisting of water and Al₂O₃ in a horizontal curved tube have been studied numerically. Three-dimensional elliptic governing equations have been used. Simultaneous effects of the buoyancy force, centrifugal force and nanoparticles concentration has been presented and discussed. The nanoparticles volume fraction does not have a direct effect on the secondary flow, axial velocity and the skin friction coefficient. However, its effect on the entire fluid temperature could affect the hydrodynamic parameters when the order of magnitude of the buoyancy force becomes significant compared to the centrifugal force. For a given Reynold number, buoyancy force has a negative effect on the Nusselt number while the nanoparticles concentration has a positive effect on the heat transfer enhancement and also on the skin friction reduction.     

Melting effect on mixed convective heat transfer with aiding and opposing external flows from the vertical plate in a liquid-saturated porous medium

In this paper, melting effect on mixed convective heat transfer from a porous vertical plate with uniform wall temperature in the liquid-saturated porous medium with aiding and opposing external flows is numerically examined at steady state. The resulting boundary value problems (BVPs) are comprehensively solved by Runge–Kutta–Gill method and Newton’s iteration for similarity solutions. As shown in the results, for aiding and opposing external flows, it is all found that the rate of convective heat transfer at the interface of solid and liquid phases is reduced with increasing melting strength. Additionally, the melting phenomenon decreases the thermal boundary layer regions of mixed convection in a porous medium. With melting effect, the heat transfer rate is also shown to be asymptotically approaching the forced or free convection as the value of Gr/Re approaches the limits of zero and infinity for aiding external flow; and the criteria for pure forced and mixed convection from an isothermal vertical flat plate in porous media with aiding and opposing external flows are established in melting process.     

Numerical study of double diffusive natural convective heat and mass transfer in an inclined rectangular cavity filled with porous medium

Two-dimensional double-diffusive natural convective heat and mass transfer in an inclined rectangular porous medium has been investigated numerically. Two opposing walls of the cavity are maintained at fixed but different temperatures and concentrations; while the other two walls are adiabatic. The generalized model with the Boussinesq approximation is used to solve the governing equations. The flow is driven by a combined buoyancy effect due to both temperature and concentration variations. A finite volume approach has been used to solve the non-dimensional governing equations and the pressure velocity coupling is treated via the SIMPLER algorithm. The results are presented in streamline, isothermal, iso-concentration, Nusselt and Sherwood contours for different values of the non-dimensional governing parameters. A wide range of non-dimensional parameters have been used including, aspect ratio (2 ≤ A ≤ 5), angle of inclination of the cavity (0 ≤ ? ≤ 85), Lewis number (0.1 ≤ Le ≤ 10), and the buoyancy ratio (− 5 ≤ N ≤ 5).     

Numerical simulation of Dufour and Soret impacts on MHD Williamson nanofluid flow through an inclined surface

The carry-outs of Dufour and Soret, as well as radiation, and chemical response on a non-Newtonian MHD Williamson nanofluid flow through an inclined extended plane are discussed in this article. Keller-box analysis is being used to explore the influence of the Williamson factor here on the fluid domain quantitatively. Ordinary differential equations (ODEs) are recovered from boundary flow equations using appropriate similarity transformations. These ODEs are numerically addressed. Graphs and comparisons are used to simulate and study the features of flow characteristics such as velocity, temperature, and concentration of Williamson nanofluids distributions in response to various emerging parameters. The numerical computations show that our results are in reasonable harmony with previous studies. The numerical computations revealed that for the time being, the density of the momentum fluid layers is diminishing for the values of $ᴦ$, Le, $\Omega$, M, and increasing for Gc, Gr. The thickness of the thermal boundary layer is decreasing for Sr, Df, Pr, Gc, and Gr. M, $ᴦ$, $\Omega$, R, N, and Le are all on the rise. The concentration profile for R, Le, Nb, Nt, Gr, Gc, and N is decreasing, while Pr, Df, Sr, M, $ᴦ$, and $\Omega$ are increasing.     

Turbulent convective heat transfer with molten salt in a circular pipe

In order to understand the heat transfer characteristics of molten salt and testify the validity of the well-known empirical convective heat transfer correlations, an experimental study on turbulent convective heat transfer with molten salt in a circular tube was conducted in this paper. Molten salt circulations were realized and operated in a specially designed system over 1000 h. The flow rates and temperatures of molten salt and mineral oil at the inlet and outlet in the test section were measured and the average forced convective heat transfer coefficients of molten salt were determined by least-squares method. Finally, heat transfer correlations of turbulent flow with molten salt in a circular tube were obtained. Good agreement was observed between the experimental data of molten salt and the existing well-known correlations. The experimental data of molten salt in the present work are consistent with experimental results reported by different references in a wide range of Prandtl numbers from 0.7 to 59.9.     

Numerical study of thermal instability in mixed convection flow over horizontal and inclined surfaces

This paper presents numerical study of thermal instability in mixed convection flow over horizontal and inclined plates. The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, wave number, and the inclined angle φ from the horizontal. The flow is found to become more stable to the vortex mode of instability as the value of inclined angle increases, owing to a decrease in buoyancy force in the normal direction. However, the Prandtl number has a destabilizing effect on the flow. The results of the present numerical prediction show reasonable agreement with the experimental data in the literature.     

Fully developed mixed convection flow of a nanofluid through an inclined channel filled with a porous medium

In this paper, the steady fully developed mixed convection flow of a nanofluid in a channel filled with a porous medium is presented. The walls of the channel are heated by a uniform heat flux and a constant flow rate is considered through the channel. The equations of the problem are made non-dimensional and are observed to depend on the dimensionless parameters, namely the mixed convection parameter λ, the Péclet number Pe, the inclination angle of the channel to the horizontal γ and the nanoparticle volume fraction ?. The effects of these parameters on the fluid and heat transfer characteristics are in detail discussed for three different nanofluids as Cu–water, Al₂O₃–water and TiO₂–water.