Inclination Angle Of Cavity Research Articles

Natural convection in fully open parallelogrammic cavity filled with Cu–water nanofluid and heated locally from its bottom wall

The natural convection in fully open parallelogrammic cavity filled with Cu–water nanofluid and heated locally from its bottom wall is investigated numerically for the first time in the present paper. The finite volume method together with the body fitted coordinates system are used to deal with the governing non-linear partial differential equations. The top wall of the cavity is considered fully open to the surrounding, while a specific location in the bottom wall is subjected to a local hot heat source. The other regions of the bottom wall are kept adiabatic. Both right and left sidewalls of the cavity are considered inclined and maintained to an isothermal cold temperature. The nanofluid entering form the top wall is considered cold, while it leaves in adiabatic condition from the same wall. The flow and thermal fields together with the Nusselt number are investigated for various values of Rayleigh number (103≤Ra≤105), heat source location (0.2≤δ≤0.8), cavity inclination angle (0°≤θ≤60°), volume fraction of nanoparticles (0≤φ≤0.2). The results show that for both pure and nanofluids the highest counter-clockwise circulation occurs at (δ=0.8) and (θ=0°) for all Rayleigh numbers, while the highest clockwise circulation occurs at (δ=0.5) and (θ=30°) for Ra=103 and at (δ=0.8) and (θ=30°) for Ra=105. In order to increase the heat transfer for both pure and nanofluids in the cavity, it is recommended to select (θ=60°) and make the heat source adjacent to the left sidewall (δ=0.2).

Experimental and numerical analysis of convective heat losses from spherical cavity receiver of solar concentrator

Spherical cavity receiver of solar concentrator is made up of Cu tubing material having cavity diameter 385 mm to analyze the different heat losses such as conduction, convection and radiation. As the convection loss plays major role in heat loss analysis of cavity receiver, the experimental analysis is carried out to study convective heat loss for the temperature range of 55-75?C at 0?, 15?, 30?, 45?, 60?, and 90? inclination angle of downward facing cavity receiver. The numerical analysis is carried out to study convective heat loss for the low temperature range (55-75?C) as well as high temperature range (150-300 ?C) for no wind condition only. The experimental set-up mainly consists of spherical cavity receiver which is insulated with glass wool insulation to reduce the heat losses from outside surface. The numerical analysis is carried out by using CFD software and the results are compared with the experimental results and found good agreement. The result shows that the convective loss increases with decrease in cavity inclination angle and decreases with decrease in mean cavity receiver temperature. The maximum losses are obtained at 0? inclination angle and the minimum losses are obtained at 90? inclination angle of cavity due to increase in stagnation zone in to the cavity from 0? to 90? inclination. The Nusselt number correlation is developed for the low temperature range 55-75?C based on the experimental data. The analysis is also carried out to study the effect of wind speed and wind direction on convective heat losses. The convective heat losses are studied for two wind speeds (3 m/s and 5 m/s) and four wind directions [? is 0? (Side-on wind), 30?, 60?, and 90? (head-on wind)]. It is found that the convective heat losses for both wind speed are higher than the losses obtained by no wind test. The highest heat losses are found for wind direction ? is 60? with respect to receiver stand and lowest heat losses are found for wind direction ? is 0? (side-on wind). The heat losses obtained for wind direction, ?, is 30? condition are higher than the heat losses obtained for wind direction ? is 0? (side-on wind) condition, while the heat losses obtained by wind direction ? is 90? (head-on wind) condition are less than the heat losses obtained for wind direction, ?, is 60? condition.

Lattice Boltzmann analysis of MHD natural convection of CuO-water nanofluid in inclined C-shaped enclosures under the effect of nanoparticles Brownian motion

In this study, Magneto-Hydro-Dynamic (MHD) natural convection heat transfer has been analyzed for an inclined C-shaped cavity filled with nanofluid. The Lattice Boltzmann Method (LBM) is used to solve the governing equations. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo-Kleinstreuer-Li) correlation. The influence of pertinent parameters such as Rayleigh number, Hartmann number, the cavity inclination angle, nanoparticle volume concentration and the cavity aspect ratio on the flow and heat transfer characteristics have been examined. From this work, it is found that the heat transfer enhances when considering the Brownian motion effect of nanoparticles, whereas presence of magnetic field tries to retard convection. Moreover, the numerical results demonstrate that the average Nusselt is increased when increasing cavity aspect ratio, cavity angle and volume fraction of nanofluid. Also, the results demonstrate that the enclosure with an inclination angle of γ=π/2, has the maximum heat transfer coefficient.

Effects of inclination angle on mixed convective nanofluid flow in a double lid-driven cavity with discrete heat sources

In the present study, numerical simulations are performed to examine the effect of inclination angle on the heat transfer of Al2O3–water nanofluid for mixed convection flows in a partially heated double lid driven inclined cavity. At the lower wall of the cavity, two heat sources are fixed with the condition that the remaining part of the bottom wall is kept insulated. Top wall and vertically moving walls are maintained at constant cold temperature. Buoyant force is responsible for the flow along with two moving vertical walls. The governing equations are discretized with the help of finite element method in space and the Crank–Nicolson in time. For the spatial discretization, nonconforming Stokes element Q∼1/Q0 of 2nd order accuracy for velocity, temperature and 1st order accuracy for pressure is utilized. The discretized nonlinear systems of equations are treated by using the Newton method and the associated linear subproblems are solved using Gaussian elimination method in each time level. Numerical results are presented and analyzed by means of streamlines, isotherms, tables and some useful plots. Impact of emerging parameters on the flow, in specific ranges such as Reynolds number (1⩽Re⩽100), Richardson number (0.01⩽Ri⩽10), nanoparticle volume fraction (0⩽ϕ⩽0.04) as well as inclination angle of cavity (0°⩽γ⩽45°) are investigated and findings are exactly of the same order as that of the previously performed analysis in the literature. Calculations of average Nusselt number, average temperature, average entropy generation due to heat transfer and fluid friction and kinetic energy are the main focus of our study.

GPU accelerated numerical study of PCM melting process in an enclosure with internal fins using lattice Boltzmann method

Latent heat thermal energy storage (LHTES) has many applications in engineering fields such as electronic cooling, thermal storage of solar energy, heating and cooling in buildings, waste heat utilization and so on. The advantages of LHTES over sensible thermal energy storage or chemical energy storage techniques are high energy density and phase change at nearly constant temperature. Unfortunately, the low thermal conductivity of PCMs increases the thermal gradient in the energy storage system and impedes the heat transfer efficiency. However, high thermal conductivity fins could be used to promote the melting process in PCM enclosures. As a powerful numerical method developed during the past two decades, lattice Boltzmann method (LBM) was used to simulate the conjugate heat transfer in the solid walls, fins and PCM region. By changing the velocity field and diffusivities, only one distribution function was needed to simulate the melting with natural convection in PCMs and conduction in fins and enclosure surfaces. As a result, the thermal boundary conditions on the interfaces of PCMs, fins and solid walls were satisfied automatically. By using enthalpy-based multiple-relaxation-time (MRT) LBM model, the iteration steps for the latent-heat source term were avoided. Under this case, the conjugate convective heat transfer with phase change is modeled efficiently. The graphics processing units (GPU) computing becomes attractive since the advent of CUDA which includes both hardware and programming environment in 2007. Consequently, the developed MRT LBM code is further implemented to run on GPU. High computation speed was achieved. The melting process in PCMs was investigated for different materials of fins and walls, number of fins, fin configurations, hot wall temperature, thermal boundary conditions, and inclination angle of the PCM cavity. Lattice Boltzmann method implemented on GPU was demonstrated as an efficient approach to study the PCM melting process with internal fins.

Natural convection and entropy generation of Al2O3–water nanofluid in an inclined wavy-wall cavity

A numerical investigation is performed into the natural convection heat transfer performance and entropy generation of Al2O3–water nanofluid in an inclined wavy-wall cavity. The simulations focus specifically on the effects of the cavity inclination angle, nanoparticle volume fraction, Rayleigh number and wave amplitude of the wavy surface on the flow streamlines, isotherm distribution, Nusselt number and entropy generation within the cavity. The range of the studied parameters is as follows: cavity inclination angle from 0° to 360°, nanoparticle volume fraction from 0% to 4%, Rayleigh number from 102 to 106, wavy-surface amplitude from 0.0 to 0.5. The results show that the inclination angle has a strong effect on the flow streamlines, isotherms, local entropy generation and heat transfer performance; particularly at higher Rayleigh numbers. In addition, it is shown that for a given Rayleigh number and cavity inclination angle, the mean Nusselt number increases and the total entropy generation decreases as the volume fraction of Al2O3 nanoparticles increases. Finally, it is shown that for a constant Rayleigh number and inclination angle, the Nusselt number in a wavy-surface cavity is higher than that in a regular cavity, while the total energy generation is lower.

Three-dimensional unsteady natural convection and entropy generation in an inclined cubical trapezoidal cavity with an isothermal bottom wall

Numerical computation of unsteady laminar three-dimensional natural convection and entropy generation in an inclined cubical trapezoidal air-filled cavity is performed for the first time in this work. The vertical right and left sidewalls of the cavity are maintained at constant cold temperatures. The lower wall is subjected to a constant hot temperature, while the upper one is considered insulated. Computations are performed for Rayleigh numbers varied as 103⩽Ra⩽105, while the trapezoidal cavity inclination angle is varied as 0°⩽Φ⩽180°. Prandtl number is considered constant at Pr=0.71. Second law of thermodynamics is applied to obtain thermodynamic losses inside the cavity due to both heat transfer and fluid friction irreversibilities. The variation of local and average Nusselt numbers is presented and discussed, while, streamlines, isotherms and entropy contours are presented in both two and three-dimensional pattern. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. Also, the inclination angle effect on the total entropy generation becomes insignificant when the Rayleigh number is low. Moreover, when the Rayleigh number increases the average Nusselt number increases.

Heatline visualization of natural convection heat transfer in an inclined wavy cavities filled with nanofluids and subjected to a discrete isoflux heating from its left sidewall

Natural convection visualization by heatlines in three types of inclined wavy cavities filled with Al2O3–water and Ag–water nanofluids and subjected to a discrete isoflux heating from its left sidewall is investigated numerically in this work. The right sidewall together with remaining regions in the left sidewall is insulated. The solution is based on the finite volume method. The upper and lower cavity walls are maintained at a constant cold temperature and follow a profile of sine wave. Numerical computations are carried out for various values of the solid volume fraction [φ=0, 0.05, 0.1, 0.15 and 0.2], number of undulations [N=1, 2 and 3], Rayleigh number [Ra=103–107], the ratio of heating element length to the cavity height [ε=0.2, 0.4, 0.6, 0.8 and 1.0], the cavity inclination angle [Φ=0°, 30°, 60° and 90°] and the wave amplitude [γ=0.1, 0.15 and 0.2]. The results are presented in terms of heatlines, isotherms, streamlines together with local and average Nusselt numbers. It is found that the geometry of the wavy cavity has a cursive role on the flow and thermal fields pattern. The results also explained that streamlines and isotherms were affected significantly for high Rayleigh number and vertical cavity position [Φ=90°]. Also, when the solid volume fractions and wave amplitudes increase, the local Nusselt number along the heat source increases. Furthermore, velocity profiles increase as [ε] increases near the left sidewall of the cavity while they decrease as [ε] increases near the right sidewall of the cavity. For all three types of horizontal wavy cavities the heat functions increase for both nano and base fluids when the wave amplitude increases. Finally, results of the present work indicated that both heatlines and heat functions techniques are applied efficiently to describe the natural convection heat transfer inside wavy cavities filled with nanofluid.

Finite Element Analysis of Unsteady Natural Convective Heat Transfer and Fluid Flow of Nanofluids inside a Tilted Square Enclosure in the Presence of Oriented Magnetic Field

In this paper, the problem of unsteady natural convective heat transfer flow of nanofluids having various sizes of nanoparticles inside an inclined square enclosure in the presence of oriented magnetic field is investigated numerically. The Brownian motion of nanoparticles is taken into consideration in the thermal conductivity model construction. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. Galerkin weighted residual finite element technique has been employed to solve the governing nonlinear dimensionless equations. In order to ensure the accuracy of the present numerical code, comparisons with previously published works are performed and excellent agreement is obtained. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, inclination angle of magnetic field, inclination angle of the geometry, diameter and Brownian motion of the nanoparticles on the fluid flow and heat transfer are investigated. The results indicate that an increment in Rayleigh number and nanoparticle volume fraction increases the heat transfer rate in a significant way, whereas, an increment in Hartmann number decreases the overall heat transfer rate. It is also observed that the heat transfer enhancement strongly depends on the diameter of the nanoparticles as well as the types of the nanofluids. It is observed that the time taken to reach the steady state is controlled by the different model parameters and in particular, it is longer for low Rayleigh number and shorter for high Rayleigh number. A comparison between the two studies of with and without Brownian motion shows that when Brownian motion is considered, the solid volume fraction has more significant effects on the heat transfer rate at all Rayleigh numbers considered in the square cavity. Finally, the distribution of average heat transfer rate for different cavity inclination angle along with various model parameters has been found as almost parabolic shape.

Unsteady double diffusive convection in an inclined rectangular lid-driven enclosure with different magnetic field angles and non-uniform boundary conditions

The effect of buoyancy ratio on an unsteady double diffusive natural convection flow in an inclined lid-driven enclosure with different magnetic field angles is studied. The enclosure is non-uniformly heated and concentrated from the bottom side and uniformly heated and concentrated from the left vertical side. The right vertical wall is insulated and the top wall is cooled. The top wall moves in the positive direction with a constant speed from left to right. The governing equations have been solved numerically using the staggered grid finite-difference method to obtain streamlines, isotherms, iso-concentrations, average Nusselt and Sherwood numbers for various values of the buoyancy ratio and different magnetic field angles for three different cavity inclination angles. The results indicate that the flow pattern, temperature and concentration fields are significantly depend on the magnetic field and cavity inclination angles. It was found that different angles of the magnetic field may suppress the convection flow and that the direction of the magnetic field influences the flow pattern. Computations of the average Nusselt numbers at the left hot wall are made and these compare favorably with previously published results. The change in streamline, isotherm and iso-concentration patterns with time is described here.

Lid-Driven and Inclined Square Cavity Filled With a Nanofluid: Optimum Heat Transfer

AbstractThis paper reports a numerical study on mixed convection within a square enclosure, filled with a mixture of water and Cu (or Ag) nanoparticles. It is assumed that the temperature difference driving the convection comes from the side moving walls, when both horizontal walls are kept insulated. In order to solve the general coupled equations, a code based on the finite volume method is used and it has been validated after comparison between the present results and those of the literature. To make clear the effect of the main parameters on fluid flow and heat transfer inside the enclosure, a wide range of the Richardson number, taken from 0.01 to 100, the nanoparticles volume fraction (0% to 10%), and the cavity inclination angle (0º to 180º) are investigated. The phenomenon is analyzed through streamlines and isotherm plots, with special attention to the Nusselt number.

Investigation of Heat Loss from a Solar Cavity Receiver

Abstract This study examines experimentally the heat loss from a model solar cavity receiver. For this purpose, laboratory-scale cylindrical cavity models with geometric aspect ratios (cavity length to diameter) of 1 and 2, and aperture opening ratios(aperture diameter to cavity diameter) of 0.5 and 1, were built. Each cavitywas subjected to constant boundary heat inputvia heating cables, and was operated at various downward inclinations. A carefully-applied coating of Pyromark-2500 heat resistant paint on the cavity surface, in conjunction with steady-state experimental temperatures, enabled accurate calculation of the radiative loss from the cavities. The experimental technique allowed precise control of the operating parameters, resulting in determination of the conduction loss, and subsequently, the convection heat loss.Operation at temperatures up to 650 o C allowed for a better understanding of the interaction between radiation and convection heat loss mechanisms. Experimental data obtained in this study are shown to be consistent with the concept of stagnation and convection zone development in cavities, with increasing cavity inclination angle. A qualitative assessment of the impact of these zones on the cavity surface temperatures is presented. Whereas thermocouples located in stagnation region show uniform temperature distribution, the surfaces which are exposed to convective flows exhibit larger temperature variations. The temperature distribution along the cavitywalls and its effect on radiative loss calculation is also investigated in this work. It is seen that radiative loss predictions which consider an average cavity temperature in their model can overestimate the losses due to this mechanism by up to 20%, in comparison to models which use experimental temperatures along the cavity interior. Convection loss from the cavity is calculated and compared with results from correlations proposed in the literature.It is seen that correlations based on surface areas of the stagnation and convection zones are better at predicting the experimental results.

Mixed-convection flow and heat transfer in an inclined cavity equipped to a hot obstacle using nanofluids considering temperature-dependent properties

Mixed-convection fluid flow and heat transfer in a square cavity filled with Al2O3–water nanofluid have been numerically investigated using the finite volume method (FVM) and SIMPLER algorithm. The geometry is a lid-driven square enclosure with an interior rectangular heated obstacle. The bottom, top, and left walls are adiabatic while the right wall has a constant low temperature (Tc). The upper lid of the cavity moves in a positive direction. Effects of different key parameters such as Richardson number, position and height of the block, the volume fraction of the nanoparticles, and cavity inclination angles on the fluid flow and heat transfer inside the cavity are investigated. It is observed that the average Nusselt number for all ranges of solid volume fraction increases with a decrease in the Richardson number. The results elucidate irregular changes of mean Nusselt number at different Richardson numbers versus variation of inclination angles in any case.

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.

Mixed convection in an inclined lid-driven cavity with non-uniform heating on both sidewalls

The present work reports a numerical simulation of mixed convection in an inclined square cavity. The vertical sidewalls are assumed to have a nonuniform temperature distribution. The finite volume method is used to solve dimensionless governing equations. Simulations are performed for different Richardson numbers, amplitude ratios, phase deviations, and cavity inclination angles. The results are presented graphically. The mean heat transfer significantly increases in the buoyancy-dominated mode on increasing cavity inclination angle if both walls have identical heating and cooling zones.

Vibrational Suspension of Light Sphere in a Tilted Rotating Cylinder with Liquid

The dynamics of a light sphere in a quickly rotating inclined cylinder filled with liquid under transversal vibrations is experimentally investigated. Due to inertial oscillations of the sphere relative to the cavity, its rotation velocity differs from the cavity one. The intensification of the lagging motion of a sphere and the excitation of the outstripping differential rotation are possible under vibrations. It occurs in the resonant areas where the frequency of vibrations coincides with the fundamental frequency of the system. The position of the sphere in the center of the cylinder could be unstable. Different velocities of the sphere are matched with its various quasistationary positions on the axis of rotating cavity. In tilted rotating cylinder, the axial component of the gravity force appears; however, the light sphere does not float to the upper end wall but gets the stable position at a definite distance from it. It makes possible to provide a vibrational suspension of the light sphere in filled with liquid cavity rotating around the vertical axis. It is found that in the wide range of the cavity inclination angles the sphere position is determined by the dimensionless velocity of body differential rotation.

Analysis of Spherical Cavity Receiver of Solar Concentrator for Heat Losses

In this paper, analysis of total heat losses has done by constructing an experimental set up of electrically heated spherical cavity receiver of solar concentrator. Hollow spherical cavity receiver of copper material having diameter 385mm and thickness 1.5mm is used in the experimental set up. The numerical analysis has done by using the MATLAB programming. The effect of different opening ratio (0.2, 0.3, 0.4, and 0.5), different cavity inclination angles (00, 250, 500, 750, and 900) and different operating temperatures (100°C to 600°C) are studied for total heat losses for spherical cavity receiver. The maximum convective losses are found at 0 degree inclination angle of cavity while the minimum convective losses are found at 90 degree inclination angle of cavity because of decrease in convective zone of air and increase in stagnation zone of air in to the cavity. Conduction and radiation losses are independent of cavity inclination angles. The convective losses are also found to be decrease with decrease in opening ratio from 0.5 to 0.2 for different cavity surface temperatures. Experimental results of spherical cavity receiver are compared with numerical results and good agreement is found between the experimental results and numerical results.

Mixed convection of copper–water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method

The goal of this work is to study the laminar mixed convection of water–Cu nanofluid in an inclined shallow driven cavity using the lattice Boltzmann method. The upper lid of the cavity moves with constant velocity, U0, and its temperature is higher than that of the lower wall. The side walls are assumed to be adiabatic. The effects of different values of the cavity inclination angle and nanoparticles volume fraction at three states of free, force and mixed convection domination are investigated while the Reynolds number is kept fixed as Re=100 and Re=10. Validation of present results with those of other available ones shows a suitable agreement. Streamlines, isotherms, Nusselt numbers, and velocity and temperature profiles are presented. More Nusselt numbers can be achieved at larger values of the inclination angle and nanoparticles volume fraction at free convection domination. Results imply the appropriate ability of LBM to simulate the mixed convection of nanofluid in a shallow inclined cavity.

MIXED CONVECTION FLOW AND HEAT TRANSFER IN A VENTILATED INCLINED CAVITY CONTAINING HOT OBSTACLES SUBJECTED TO A NANOFLUID

The present study focuses on the problem of mixed convection fl uid fl ow and heat transfer of nanofl uid in a ventilated square cavity. The cavity contains two heated blocks subjected to external Al2O3–water (with particle diameter of 47 nm)nanofl uid, while temperature and nanoparticle concentration are dependent on thermal conductivity and eff ective viscosity insidea square cavity. The governing equations have been solved utilizing the fi nite volume method,while the SIMPLER algorithm is used to couple velocity and pressure fi elds. The natural convection eff ect is obtained by heating from the blocks on the bott om wall and cooling from the inlet fl ow. Using the developed code, the eff ect of Richardson number, the aspect ratio of hot blocks, solid volume fraction, and cavity inclination angles on the thermal behavior and fl uid fl ow inside the cavity are studied. The study has been executed for the Richardson number in the range of 0.1 ≤ Ri ≤ 10, solid volume fraction 0 ≤ φ ≤ 0.06, aspect ratio 0.5 ≤ AR ≤ 1, and cavity inclination angles between 0° and 90°.The obtained results are presented in the form of streamline and isotherm counter and Nusselt diagrams. It was observed from the results that for both obstacles and in all ranges of the parameters in this study, adding nanoparticles to the base fl uid or increasing the volume fraction of the nanoparticles causes the Nusselt number increases. Also, the rate of heat transfer increases when the Reynolds number increases.

MIXED CONVECTION HEAT TRANSFER IN A DOUBLE LID-DRIVEN INCLINED SQUARE ENCLOSURE SUBJECTED TO Cu-WATER NANOFLUID WITH PARTICLE DIAMETER OF 90 nm

In this article, mixed convection flow in a two-sided lid-driven cavity at different inclination angles filled with Cu−water nanofluid (with diameter of 90 nm) is studied numerically using the finite volume method. For different values of solid volume fraction of nanoparticles, flow is induced by the top and right-hand sidewalls sliding at constant speed. The left-hand sidewall is kept constant at higher temperature (Th), while the right moving wall is maintained at a lower temperature (Tc), thereby introducing natural convection. In this study, bottom and top walls were assumed isolated; Richardson number ranged from 0.001 to 10, nanoparticles solid volume fraction (φ) up to 0.06 were investigated, and cavity inclination angle from 0° to 90° was considered and the Grashof number was set to 104. The influence of inclination angle and φ of the nanofluids on hydrodynamic and thermal characteristics is discussed. The results indicated that increase in φ for a constant Ri enhances heat transfer. Also, heat transfer was increased as Ri was decreased for a particular φ. Moreover, where natural convection is dominant (i.e., higher Ri), the flow form seems to be influenced more by φ.