Effects Of Richardson Number Research Articles

Mixed convection heat transfer in a partial porous layered split lid-driven wavy wall cavity with Cu–H2O nanofluid

This numerical study investigates mixed convection heat transfer in a two-dimensional irregularly-shaped enclosure with a nanofluid-saturated porous medium. The enclosure has wavy vertical walls, a centered triangular block, and a lid split into two regions moving in opposite directions. Transport equations are solved using the finite element method under varied Darcy (10−5 to 10−1), Reynolds (50 to 200), Richardson (0.1 to 10), amplitude (0 to 0.2), and nanoparticle volume fraction (0 to 0.1) numbers. Results demonstrate the combined effects of forced convection from lid motion and natural convection from temperature differences significantly enhance heat transfer. The wavy walls induce secondary flows and periodic disruption of thermal boundary layers. Increasing Darcy number enables deeper penetration into the porous block. Copper nanoparticles incrementally improve conductive heat transfer. Richardson number effects are more prominent at higher Reynolds numbers as buoyancy forces influence vertical convection. This study provides novel insights into synergistically utilizing wavy geometries, nanofluids, porous media, and active pumping for optimizing heat transfer in irregular enclosures for electronics cooling and thermal management.

Heat transfer enhancement in lid-driven cavity with rotating cylinder: Exploring NEPCMs and magnetic field effects

This numerical study investigates the influence of magnetic field orientation and Nano-Encapsulate Phase Change Materials (NEPCMs) on heat flow in mixed convection. The physical model consists of a cavity with a square lid and an isothermal rotating cylinder and Ga@SiO2 is selected as the NEPCM material. The numerical predictions are achieved by finite volume method. The governing equations are resolved employing the finite volume method. The credibility of the prevailing method is affirmed through a comparison of its predictions with findings from existing literature. The analysis focuses on assessing the effects of Richardson number (Ri), temperature of fusion position (θf), and magnetic field orientation angles (α). The findings reveal that optimal heat transfer occurs within the fusion position range of 0.3 to 0.6. Moreover, the incorporation of NEPCM results in a substantial increase in the Nusselt number by >20%. Although the magnetic field generally diminishes heat transfer, specific α and Ri ranges exhibit enhancements of up to 3.34%.

Effect of Richardson number on transient double diffusive mixed convection: A thermo-hydrodynamic study

Effect of Richardson number on transient double diffusive mixed convection: A thermo-hydrodynamic study

Double Diffusive Casson Fluid Flow, Heat and Mass Transfer due to Porous Media with Effects of Richardson Number and Thermal Radiation

Double Diffusive Casson Fluid Flow, Heat and Mass Transfer due to Porous Media with Effects of Richardson Number and Thermal Radiation

Effect of Richardson number on double-diffusive mixed convective slip flow, Heat and Mass transfer of MHD Casson fluid

An analysis of the heat and mass transfer in a mixed-convective double diffusive flow with convective boundary conditions is carried out in this paper. The governing equations are solved numerically by using Runge-Kutta method with shooting procedure with Matlab software. An accuracy of the numerical procedure has been validated through a results of the current work when compared with prior available results in the literature. The values of shear surface stress, Nusselt and Sherwood number are increasing with increasing values of Prandtl number. The effect of Biot number [Formula: see text] on flow and heat transfer are also investigated and further it is observed that friction coefficient, Nusselt number and Sherwood number are increasing due to enhancing values of Biot number. In the present paper it is noticed that the increasing in estimations of Casson parameter slowdown the heat transfer rate and accelerates mass transfer rate. The results are in good agreement with existing findings The impact of pertinent constraints on distinct flow parameters are determined and analysed through tables and graphs.

Effect of Richardson number on stagnation point flow of double diffusive mixed convective slip flow ofmagnetohydrodynamicCasson fluid: A numerical study

An analysis of stagnation point flow of heat and mass transfer of double diffusive mixed-convective stream with radiating vertical plate and convective boundary conditions. The Runge–Kutta method with shooting procedure is used to solve the transformed equations mathematically. An accuracy of the numerical procedure has been validated through a restriction of the current work compared with prior available results. The shear surface stress, Nusselt and Sherwood number are increased with increase in Prandtl number. The Biot number Bi > 0.1 is investigated and observed that to increase the Prandtl number, the friction coefficient, Nusselt number and Sherwood number are increased. The impact of pertinent constraints on distinct flow parameters are determined and analyzed through tables and graphs.

FINITE ELEMENT SOLUTION OF HYDROMAGNETIC MIXED CONVECTION IN A NANOFLUID FILLED VENTED GROOVED CHANNEL

The mixed convection flow in a differentially heated grooved channel filled with water based nanofluid under the influence of external magnetic field has been analyzed numerically in this study. Nanofluid’s thermal conductivity model has been modified to develop a new physical problem and finite element method has been implemented to solve the dimensionless governing equations. Numerical simulations have been performed for different values of pertinent parameters. Fluid flow and temperature distributions have been exhibited in terms of streamlines and isotherms due to the variation of Richardson number, Hartmann number and concentration of nanoparticles in base fluid water. The results show that flow field and temperature distributions within the channel affected significantly with the effects of Richardson number, Hartmann number and concentration of nanoparticles. In addition, it is found that heat transfer rate increases and decreases respectively with the increase in strength of magnetic field which depends strongly on Richardson number. Moreover, heat transfer rate accelerates effectively for increasing volume fraction, Reynolds number and Richardson number. The present simulation has been validated by comparing the present results with other published works on the basis of special cases.

Prandtl and Richardson Number Effects on Mixed Convection in a Vented Enclosure on Application to the Cooling of the Fins

In the present study, a numerical investigate the transport mechanism of laminar mixed convection in a vented enclosure. The walls of the cavity were kept adiabatic except the right vertical wall which was equipped with three fins dissipating the heat at a constant temperature. The equations of considered phenomenon were established and discretized by the finite difference method. The sweeping method line-by-line and the Thomas Algorithm (TDMA) were used for the resolution of the system of discretized equations. The results obtained showed that both the variations of the Prandtl and Richardson number have important effects on the flow structure and on the heat transfer.

Analysis of unsteady mixed convection of Cu\u2013water nanofluid in an oscillatory, lid-driven enclosure using lattice Boltzmann method

The unsteady physics of laminar mixed convection in a lid-driven enclosure filled with Cu–water nanofluid is numerically investigated. The top wall moves with constant velocity or with a temporally sinusoidal function, while the other walls are fixed. The horizontal top and bottom walls are, respectively, held at the low and high temperatures, and the vertical walls are assumed to be adiabatic. The governing equations along with the boundary conditions are solved through D2Q9 fluid flow and D2Q5 thermal lattice Boltzmann network. The effects of Richardson number and volume fractions of nanoparticles on the fluid flow and heat transfer are investigated. For the first time in the literature, the current study considers the mechanical power required for moving the top wall of the enclosure under various conditions. This reveals that the power demand increases if the enclosure is filled with a nanofluid in comparison with that with a pure fluid. Keeping a constant heat transfer rate, the required power diminishes by implementing a temporally sinusoidal velocity on the top wall rather than a constant velocity. Reducing frequency of the wall oscillation leads to heat transfer enhancement. Similarly, dropping Richardson number and raising the volume fraction of the nanoparticles enhance the heat transfer rate. Through these analyses, the present study provides a physical insight into the less investigated problem of unsteady mixed convection in enclosures with oscillatory walls.

Thermal analysis of nanofluid saturated in inclined porous cavity cooled by rotating active cylinder subjected to convective condition

Convective heat transfer in a porous cavity conjugated with an active rotating cylinder is investigated in this paper. Copper–water nanofluid fills the porous cavity. The rotating active cylinder is positioned in such a way conveying heat from the cavity and discharges it outside. The vertical walls of the cavity are thermally insulated while the bottom wall is moving to the right and kept at a constant high temperature. The governing equations are facilitated with the ability to study the tilt of the cylinder-cavity assembly. The effects of Richardson number, Darcy number, inclination angle, conductivity ratio, rotational speed, and nanofluid volume fraction are studied at a constant Rayleigh number of 105. Galerkin finite element method of weak formulation is used to solve the dimensionless governing equation with appropriate boundary conditions. Darcy–Brinkman–Forchheimer model is adopted to govern the flow inside porous medium. Results show that the rotation of the cylinder can enlarge the average Nusselt number more than 223%, while ten times increase of thermal conductivity ratio amplifies Nusselt number by 136%. It is also found that the Richardson number plays an adverse role on the average Nusselt number. Physical explanations and thorough validations are given in the paper.

Augmentation of VIVACE by means of Thermal Buoyancy

The present numerical simulation is carried out to evaluate the effect of Richardson Number on cylinder displacement and in turn the power extraction from the movement of cylinder. An in-house code based on arbitrary Lagrangian Euler scheme is used to tackle fluid structure interaction. The following fluid parameters is used in a present study Reynolds Number (Re) = 100, Prandtl Number (Pr) = 7.1 and Richardson number (Ri) = [-1, 0]. Structural parameters are as follows Reduced velocities (Ured) = 3 and 8, Reduced mass (Mred) = 2, damping coefficient (ξ′) is set to be zero. With the aid of thermal buoyancy there is significant increase in power is obtained.

Effect of Richardson Number on Unsteady Mixed Convection in a Square Cavity Partially Heated From Below

Abstract: The objective of the present study is to analyze the laminar mixed convection in a square cavity with a side length L and moving cooled vertical sidewalls. A constant flux heat source with relative length l is placed in the center of the lower wall and all the other horizontal sides of the cavity are considered adiabatic. The numerical method used is based on a finite difference technique where the spatial partial derivatives and boundary conditions of the phenomenon governing equations are discretized using a high order scheme, and time advance is dealt with by the fourth order Runge Kutta method. The Richardson number (Ri), which represents the relative importance of the natural and forced convection, is chosen as the bifurcation parameter. The effect of the Richardson number on the behavior of the fluid flow and the heat transfer has been analyzed. Although the geometry and boundary conditions concerning the velocity and the temperature are symmetrical relative to the vertical axis passing through the center of the cavity, analysis of the results allowed us to detect the existence of symmetric and asymmetric structures of the flow, completely different, depending on the value of the Richardson number.

MHD Mixed Convection and Entropy Generation in a Lid-Driven Triangular Cavity for Various Electrical Conductivity Models.

In this study, effects of different electrical conductivity models for magneto- hydrodynamic mixed convection of nanofluids in a lid-driven triangular cavity was numerically investigated with a finite element method. Effects of Richardson number and Hartmann number on the convective heat transfer characteristics were analyzed for various electrical conductivity models of nanofluids. Average Nusselt number decreases for higher Hartmann and Richardson numbers. Discrepancies in the local and average heat transfer exist between different electrical conductivity models, which is higher for higher values of Richardson number and Hartmann number. The total entropy generation rate was found reduced with higher values of Richardson number and Hartmann number while discrepancies exist between various electrical conductivity models. When the magnetic field is imposed, different behaviors of entropy generation rate versus solid particle volume fraction curve is obtained and it is dependent upon the range of solid particle volume fraction.

Entropy generation due to the transient mixed convection in a three- dimensional right-angle triangular cavity

Entropy generation of the mixed convection in a 3D air -filled right-angle triangular cavity is investigated numerically for the first time by using finite volume method. The vertical right wall of the cavity is considered moving either to the cavity center (+Vp) or downward (−Vp) or towards the cold inclined wall (Vp = 0) with a constant velocity. It is maintained at an isothermal hot temperature (Th). While, the inclined left wall is considered fixed and kept at an isothermal cold temperature (Tc). With respect to the bottom wall, it is considered hot and fixed also. The effects of Richardson number, movement direction of the right vertical wall, entropy generation, Nusselt and Bejan numbers on the flow and thermal fields are illustrated through streamlines, isotherms and entropy generation contours. It is found that the flow field inside the cavity is influenced significantly with the direction of the moving wall. The Bejan number decreases as the Richardson number increases. Moreover, it is observed that highest value of the average Nusselt number can be get when the right hot vertical wall is considered moving to the cavity center (+Vp).

Simulation of Mixed Convection in Eccentric Annulus: A Combined Lattice Boltzmann and Smoothed Profile Approach

ABSTRACTLattice Boltzmann Method is used to simulate mixed convection between two horizontal cylinders. This geometry is created using Smoothed Profile Method which produces proper fluid-solid interaction force as well as heat exchange. A two dimensional double distribution function lattice Boltzmann method is employed to simulate fluid flow and heat transfer simultaneously. In order to implement the velocity and temperature boundary conditions, the force term and heat source/sink are included in the evolution equations. While fixed Eulerian lattice nodes are employed, while different eccentricities are considered for inner cylinder. In order to simulate mixed convection, the radius ratio is set to be 2.5. Furthermore, the effect of Richardson number by choosing 0.01, 1, 100 and Prandtl number of 0.716 for air and 6.2 for water are investigated. Isotherms, streamlines and mean Nusselt numbers are given for each case. The results are in good agreement with previous related publications.

Numerical study of laminar mixed convection flow in a lid-driven square cavity filled with porous media

PurposeThe purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure.Design/methodology/approachThe authors used the finite volume method.FindingsThe authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the heat transfer rate of mixed convection flow in a porous medium.Originality/valueA comparison between Darcy–Brinkman–Forchheimer model and Darcy–Brinkman model is discussed and analyzed. The authors finally conclude that the Darcy–Brinkman model overestimates the heat transfer rate.

Mixed convection with entropy generation of nanofluid in a lid-driven cavity under the effects of a heat-conducting solid wall and vertical temperature gradient

Mixed convection combined with entropy generation of an alumina–water nanofluid in a lid-driven cavity with a bottom solid wall of finite thickness and conductivity has been examined numerically. Governing equations formulated in dimensionless stream function and vorticity variables on the basis of a single-phase nanofluid model under the effect of Brownian diffusion have been solved by finite difference method of the second-order accuracy. The effects of Richardson number (Ri = 0.01–10.0), thermal conductivity ratio (1.0 ≤ K ≤ 20.0), solid wall thickness (0.1 ≤ δ ≤ 0.3) and nanoparticles volume fraction (0 ≤ ϕ ≤ 0.05) on streamlines, isotherms and isentropic lines as well as average Nusselt number at solid–fluid interface and rate of fluid flow have been analyzed. It has been found that an increase in nanoparticles volume fraction leads to the heat transfer enhancement and reduction of the average Bejan number.

Numerical assessment of the mixed convection and volumetric radiation in a vertical channel with MRT-LBM

PurposeThe paper aims to focus on modeling of combined mixed convection and volumetric radiation within a vertical channel using a hybrid thermal lattice Boltzmann method (LBM). The multiple relaxation time LBM (MRT-LBM) is used to compute the dynamical field. The thermal field is determined by a finite difference method (FDM), and the simple relaxation time-LBM (SRT-LBM) serves to calculate the radiative part. The geometry considered concerns a vertical channel defined by two diffuse and isothermal walls. The active fluid represents a gray gas participating in absorption, emission and isotropically scattering. The parametrical study conducted aims to highlight the effect of Richardson number (Ri), Planck number (Pl) and the optical thickness (τ) on dynamical and thermal fields. It is found that radiation affects greatly heat transfer.Design/methodology/approachMRT-LBM is used to compute the dynamical field. The thermal field is determined by FDM, and SRT-LBM serves to calculate the radiative part.FindingsThis study has shown the strong capability of this approach to simulate similar problems. The Planck number largely affects the streamlines and isotherms distribution. Also, it causes disappearance of reversal flow, undesirable in most industrial applications, for low Planck numbers. The optical thickness causes the disappearance of reversal flow, in the case in which it appears, for lower opacity. However, for higher opacity it leads to a recurrence of reversed flow.Originality/valueThe use of a new original method composed of MRT-LBM to solve the fluid velocity, FDM to handle the temperature equation and extended SRT-LBM to compute the radiative part of the energy equation.

MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid

In this paper, the steady mixed convection flow and heat transfer of water-copper oxide nanofluid in an open C-shaped enclosure is investigated numerically. The enclosure is under constant magnetic field. Effects of Richardson number, magnetic and nanofluid volume fraction parameters are studied and discussed. The nanofluid with a cold temperature of T C and a velocity of u c enters the enclosure from the top right corner and exits from the bottom right corner. The vertical wall of the left side is subjected to a hot and constant temperature T h . Also, other walls are insulated. It is found that the heat transfer is increased via increasing the Hartmann and Reynolds numbers. For low Reynolds numbers, the enhances of the Hartman number leads to a slightly increases of the average Nusselt number, but for high Reynolds numbers, the average Nusselt number gets an ascending trend and the increase in the Hartmann number shows its effect more pronounced. Also, with increase in Ri, the effect of nanofluid on the heat transfer increases. Due to practical impotence, the study of mixed convection heat transfer in enclosures and various shaped of cavities has attracted remarkable attentions in the past few decades. Significant applications of the mixed convection flow can be found in atmospheric flows, solar energy storage, heat exchangers, lubrication technology, drying technologies, cooling of the electronic devices, etc. The present results are original and new for the problem of MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid. Comparison of the obtained results with those from the open literature (Mahmoodi et al. [24]) is acceptable.

Investigating heat transfer and entropy generation for mixed convection of CuO–water nanofluid in an inclined annulus

Mixed convection of the CuO–water nanofluid inside an inclined annulus is investigated based on the first and second laws of thermodynamics. The Boussinesq approximation is employed, and all properties (except the density) are considered to be constant. The same heat fluxes are employed on both walls of the annulus. The effects of Richardson number, volume fraction and inclination angle on the second law characteristics and heat transfer are evaluated. The Bejan number and entropy generation rates are calculated to investigate the irreversibility types due to friction and heat transfer. At greater Richardson numbers, the velocity profile becomes flatter owing to easy formation of the natural convection. The results show that increase of the inclination angle from 0° to 75° leads to increase of convective heat transfer and decrease of total entropy generation and consequently, a proper heat exchange together with a low irreversibility are achieved. Additionally, with increment of Richardson number, both total entropy generation and convective heat transfer increase. Meanwhile, frictional entropy generation decreases while thermal entropy generation increases with the concentration increment. In all the cases, Bejan number is close to 1, which proves dominance of the heat transfer in entropy generation.