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V M Soundalgekar - One of the best experts on this subject based on the ideXlab platform.
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Effects of a Radial Temperature Gradient on the stability of a wide‐gap annulus
International Journal of Energy Research, 2007Co-Authors: V M Soundalgekar, H S TakharAbstract:A numerical solution of the differential equations governing the stability of the wide-gap flow between two concentric cylinders is presented, taking into account the presence of a Radial Temperature Gradient between the two cylinders when they are maintained at different Temperatures. The critical Taylor number Tc and the critical wavenumber ac are shown graphically for different values of η (the ratio of the radii of two cylinders), μ≤O (the ratio of the angular velocities of the two cylinders) and the positive and negative Temperature Gradient given by a parameter ± N ( =Ra/T, where Ra =Rayleigh number). The results are discussed in terms of the parameters η, μ and N.
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Effects of Radial Temperature Gradient on the Stability of a Viscous Flow between Two Rotating Porous Cylinders with a Narrow Gap
Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2001Co-Authors: V M SoundalgekarAbstract:The linear stability of viscous fluid flow between two rotating concentric porous cylinders at Temperature θ 1 (of the inner cylinder) and θ 2 (of the outer cylinder) is studied in a narrow gap case. The numerical values of the critical wave number a c and the critical Taylor number T c are listed in a table for different values of μ (-0 only the inner cylinder rotating), μ (≷0, both cylinders co-rotating or counter-rotating) ratio of angular velocities Ω 2 /Ω 1 , and for different values of ±N, ±S where N is a Radial Temperature Gradient parameter based on the Temperature difference θ 2 - θ 1 >/ 0) or injection (
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effects of Radial Temperature Gradient on the stability of a viscous flow between two rotating porous cylinders with a narrow gap
Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2001Co-Authors: V M SoundalgekarAbstract:The linear stability of viscous fluid flow between two rotating concentric porous cylinders at Temperature θ 1 (of the inner cylinder) and θ 2 (of the outer cylinder) is studied in a narrow gap case. The numerical values of the critical wave number a c and the critical Taylor number T c are listed in a table for different values of μ (-0 only the inner cylinder rotating), μ (≷0, both cylinders co-rotating or counter-rotating) ratio of angular velocities Ω 2 /Ω 1 , and for different values of ±N, ±S where N is a Radial Temperature Gradient parameter based on the Temperature difference θ 2 - θ 1 >/ 0) or injection (<0) velocity. The effects of these parameters on the stability of flows are discussed.
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effect of Radial Temperature Gradient on the stability of flow in a curved channel
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1998Co-Authors: H S Takhar, V M SoundalgekarAbstract:The stability of the Dean problem in the presence of a Radial Temperature Gradient is studied in the narrow-gap case. A finite-difference method is used to solve an eigenvalue problem, and critical values of the parameters A and a are given, where a is a wavenumber and A is a parameter determining the onset of instability. The parameter M , which depends upon T 2 − T 1), where T 1 is the Temperature of the inner cylinder and T 2 is that of the outer cylinder, governs the onset of instability in such a way that an increase in (+ M ) tends to destabilize the flow, whereas an increase in (− M ) tends to stabilize the flow. The cells and the maximum value of the Radial velocity perturbation are found to move towards a cylinder with lower Temperature when M > 0.
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stability of flow between two rotating cylinders in the presence of a constant heat flux at the outer cylinder and Radial Temperature Gradient wide gap problem
Heat and Mass Transfer, 1997Co-Authors: P M Eagles, V M SoundalgekarAbstract:The stability of Couette flow of a viscous incompressible fluid between two concentric rotating cylinders in the presence of a Radial Temperature Gradient due to a constant heat flux at the outer cylinder is studied. The critical values of `a' (the wave number) and Ta (the Taylor number) are listed in a table and some critical Taylor numbers are shown graphically. It is shown that as the heat flux is increased the flow becomes more unstable for all values of μ calculated, where μ is the ratio of the angular velocity of the outer cylinder to that of the inner cylinder.
Innocent Mutabazi - One of the best experts on this subject based on the ideXlab platform.
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a large thermal turbulent taylor couette thetaco facility for investigation of turbulence induced by simultaneous action of rotation and Radial Temperature Gradient
Review of Scientific Instruments, 2019Co-Authors: Harminder Singh, Arnaud Prigent, Antoine Bonnesoeur, Hugues Besnard, Claude Houssin, Olivier Crumeyrolle, Innocent MutabaziAbstract:A thermal turbulent Taylor-Couette facility has been designed to investigate turbulent flows generated by differential rotation and Radial Temperature Gradient. It consists of a cylindrical annulus with a rotating inner cylinder and a fixed outer cylinder. The electric heating system is installed inside the inner cylinder, and the annulus is immersed in a large cylindrical container filled with cooling fluid. Temperature regulators independently control the Temperature of the inner surface of the inner cylinder and that of the cooling fluid. The facility allows us to reach values of the Reynolds number (Re ∼ 5 × 105) and of the Rayleigh number (Ra ∼ 3 × 106) for water as the working fluid. The facility provides torque measurements, a full optical access at the side and from the bottom for velocity measurements using particle image velocimetry (2D, stereoscopic, and tomographic). Temperature measurements in the flow can be performed by thermochromic liquid crystals or laser induced fluorescence.A thermal turbulent Taylor-Couette facility has been designed to investigate turbulent flows generated by differential rotation and Radial Temperature Gradient. It consists of a cylindrical annulus with a rotating inner cylinder and a fixed outer cylinder. The electric heating system is installed inside the inner cylinder, and the annulus is immersed in a large cylindrical container filled with cooling fluid. Temperature regulators independently control the Temperature of the inner surface of the inner cylinder and that of the cooling fluid. The facility allows us to reach values of the Reynolds number (Re ∼ 5 × 105) and of the Rayleigh number (Ra ∼ 3 × 106) for water as the working fluid. The facility provides torque measurements, a full optical access at the side and from the bottom for velocity measurements using particle image velocimetry (2D, stereoscopic, and tomographic). Temperature measurements in the flow can be performed by thermochromic liquid crystals or laser induced fluorescence.
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Dielectrophoretic buoyancy and heat transfer in a dielectric liquid contained in a cylindrical annular cavity
Journal of Applied Physics, 2019Co-Authors: Changwoo Kang, Innocent MutabaziAbstract:The effect of a thermoelectric body force on the flow of a dielectric fluid with a Radial Temperature Gradient and an alternating electric voltage in a cylindrical annular cavity has been studied by a direct numerical simulation. The Radial Temperature Gradient induces a vertical ascending flow near the hot surface and descending flow near the cold surface. A Radial dielectrophoretic force with the electric field acting induces a thermoelectric convection in the form of columnar vortices that can transfer heat from the hot surface to the cold one. The heat transfer coefficient in the dielectric fluid significantly increases with the applied electric voltage.The effect of a thermoelectric body force on the flow of a dielectric fluid with a Radial Temperature Gradient and an alternating electric voltage in a cylindrical annular cavity has been studied by a direct numerical simulation. The Radial Temperature Gradient induces a vertical ascending flow near the hot surface and descending flow near the cold surface. A Radial dielectrophoretic force with the electric field acting induces a thermoelectric convection in the form of columnar vortices that can transfer heat from the hot surface to the cold one. The heat transfer coefficient in the dielectric fluid significantly increases with the applied electric voltage.
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short wavelength local instabilities of a circular couette flow with Radial Temperature Gradient
Journal of Fluid Mechanics, 2017Co-Authors: Oleg N Kirillov, Innocent MutabaziAbstract:We perform a linearized local stability analysis for short-wavelength perturbations of a circular Couette flow with the Radial Temperature Gradient. Axisymmetric and nonaxisymmetric perturbations are considered and both the thermal diffusivity and the kinematic viscosity of the fluid are taken into account. The effect of the asymmetry of the heating both on the centrifugally unstable flows and on the onset of the instabilities of the centrifugally stable flows, including the flow with the Keplerian shear profile, is thoroughly investigated. It is found that the inward Temperature Gradient destabilizes the Rayleigh stable flow either via Hopf bifurcation if the liquid is a very good heat conductor or via steady state bifurcation if viscosity prevails over the thermal conductance.
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thermal convection in a cylindrical annulus under a combined effect of the Radial and vertical gravity
Comptes Rendus Mecanique, 2017Co-Authors: Antoine Meyer, Christoph Egbers, Marcel Jongmanns, Martin Meier, Innocent MutabaziAbstract:Abstract The stability of the flow of a dielectric fluid confined in a cylindrical annulus submitted to a Radial Temperature Gradient and a Radial electric field is investigated theoretically and experimentally. The Radial Temperature Gradient induces a vertical Archimedean buoyancy and a Radial dielectrophoretic buoyancy. These two forces intervene simultaneously in the destabilization of the flow, leading to the occurrence of four types of modes depending on the relative intensity of these two buoyancies and on the fluid's properties: hydrodynamic and thermal modes that are axisymmetric and oscillatory, stationary columnar modes and electric modes which are stationary and non-axisymmetric modes. Experiments performed in a parabolic flight show the existence of non-axisymmetric modes that should be either columnar or helicoidal vortices.
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the effect of Radial Temperature Gradient on the circular couette flow
Journal of computational fluids engineering, 2009Co-Authors: Changwoo Kang, Kyungsoo Yang, Innocent MutabaziAbstract:Numerical simulation has been carried out to investigate the influence of Radial Temperature Gradient on the Circular-Couette flow. Varying the Grashof number, we study the detailed flow and Temperature fields. The current numerical results show good agreement with the analytical and experimental results currently available. It turns out that spiral vortices are generated by increasing Temperature Gradient. We classify the flow patterns for various Grashof number based on the characteristics of flow fields and spiral vortices. The correlation between Richardson number with wave number shows that the spiral angle and size of spiral vortices increase with increasing Richardson number.
H S Takhar - One of the best experts on this subject based on the ideXlab platform.
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Effects of a Radial Temperature Gradient on the stability of a wide‐gap annulus
International Journal of Energy Research, 2007Co-Authors: V M Soundalgekar, H S TakharAbstract:A numerical solution of the differential equations governing the stability of the wide-gap flow between two concentric cylinders is presented, taking into account the presence of a Radial Temperature Gradient between the two cylinders when they are maintained at different Temperatures. The critical Taylor number Tc and the critical wavenumber ac are shown graphically for different values of η (the ratio of the radii of two cylinders), μ≤O (the ratio of the angular velocities of the two cylinders) and the positive and negative Temperature Gradient given by a parameter ± N ( =Ra/T, where Ra =Rayleigh number). The results are discussed in terms of the parameters η, μ and N.
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effect of Radial Temperature Gradient on the stability of flow in a curved channel
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1998Co-Authors: H S Takhar, V M SoundalgekarAbstract:The stability of the Dean problem in the presence of a Radial Temperature Gradient is studied in the narrow-gap case. A finite-difference method is used to solve an eigenvalue problem, and critical values of the parameters A and a are given, where a is a wavenumber and A is a parameter determining the onset of instability. The parameter M , which depends upon T 2 − T 1), where T 1 is the Temperature of the inner cylinder and T 2 is that of the outer cylinder, governs the onset of instability in such a way that an increase in (+ M ) tends to destabilize the flow, whereas an increase in (− M ) tends to stabilize the flow. The cells and the maximum value of the Radial velocity perturbation are found to move towards a cylinder with lower Temperature when M > 0.
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the effect of Radial Temperature Gradient and axial magnetic field on the stability of couette flow the narrow gap problem
International Journal of Energy Research, 1992Co-Authors: H S Takhar, V M SoundalgekarAbstract:A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under the following conditions: (i) the inner cylinder rotating with the outer cylinder stationary, (ii) corotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, (v) conducting and nonconducting walls, and (vi) the presence of a Radial Temperature Gradient. Results for the critical wave number ac, and the critical Taylor number Tc, are presented. The variation of Tc is shown on graphs for both the conducting and nonconducting walls and for different values of ±μ (= Ω2/Ω1, where Ω2 is the angular velocity of the outer cylinder, and Ω1 is the angular velocity of the inner cylinder), the magnetic field parameter Q, which is the square of the Hartmann number and ± N (= Ra/Ta, where Ra is the Rayleigh number). The effects of ±μ, N and Q on the stability of flow are discussed. It is seen that the effect of the magnetic field is to inhibit the onset of instability, this being more so in the presence of conducting walls and a negative Temperature Gradient.
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effects of Radial Temperature Gradient on mhd stability of couette flow between conducting cylinders a wide gap problem
1992Co-Authors: H S Takhar, V M SoundalgekarAbstract:Stability of Couette flow under different conditions and assuming a narrow gap annulus has received great attention in the past. Notable among these are studies by Taylor (1923), Chandrasekhar (1953, 1954, 1961), Edwards (1958), Becker and Kaye (1962), Lai (1962), Kurzweg (1963), Harris and Reid (1964), Krueger, Gross and DiPrima (1966), Hassard, Cheng and Ludford (1972), Bahl (1972), Soundalgekar, Takhar, Smith (1981), Takhar, Smith and Soundalgekar (1985). Takhar, Ali and Soundalgekar (to be published) presented the study of MHD stability of Couette flow on taking into account the presence of Radial Temperature Gradient and the axial magnetic field, in a narrow-gap annulus. The corresponding stability of Couette flow in a wide-gap annulus has been studied by very few researchers because of its complex nature. Notable among these are studies by Chandrasekhar (1958). Chandrasekhar and Elbert (1962), Walowit, Tsao and DiPrima (1964), Sparrow, Munro and Jonsson (1964), Astill and Chung (1976), Takhar, Ali and Soundalekar (1988), Chandrasehkar (1958) derived results for \(\eta = \frac{1}{2}\) = (i.e. \({R_1} = \frac{1}{2}{R_2}\)) whereas in other papers, Chandrasekhar and Elbert (1962) simplified the numerical procedure by considering the corresponding adjoint eigenvalue problem. Walowit et al. (1964) simplified the method of solution of an eigenvalue problem by giving an algebraic series solution instead of Chandrasekhar’s trigonometric series solution. Sparrow et al., Takhar et al. solved the eigenvalue problem numerically using the Runge-Kutta method, whereas Asti11 and Chung solved it by a finite-difference method. The only paper which deals with MHD stability of wide-gap problem is the one by Chang and Sartory (1967). It deals with the stability of the flow of an electrically conducting fluid in a wide-gap of permeable, perfectly conducting cylinders. In the narrow gap case, there are many papers on the MHD stability of Taylor flows with both conducting and non-conducting walls of the two concentric cylinders. So Ali, Soundalgekar and Takhar (to be published) solved this MHD stability of Taylor flow for both conducting and non-conducting impermeable cylinders separated by a wide-gap. This eigenvalue problem was solved numerically following the method of Harris and Reid (1964) and Sparrow et al. (1964). In Chang and Sartory’s (1967) paper, the basic velocity was assumed to be A/r, where A is a constant. We have assumed the basic velocity of the form Ar + B/r to solve this eigenvalue problem. Hence a comparison is not possible between our results and those of Chang and Sartory (1967).
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effects of Radial Temperature Gradient on the stability of a narrow gap annulus flow
Journal of Mathematical Analysis and Applications, 1990Co-Authors: H S Takhar, V M SoundalgekarAbstract:Abstract An eigenvalue problem of the stability of Couette flow between two concentric cylinders in relative motion in the presence of a positive (T2 > T1) and a negative (T2 ± μ (= Ω 2 Ω 1 , where Ω 2 is the angular speed of the outer cylinder and Ω 1 is the angular speed of the inner cylinder) and ±N (ratio of the Rayleigh and Taylor numbers). The Radial eigenfunction and the cell patterns are shown graphically for different values of ± μ and ±N. It is observed that the flow is more stable in the presence of a negative Temperature Gradient for both ±μ. The stabilising effect is more promising when the two cylinders are counterrotating. The magnitude of ac also increases steeply in the presence of counterrotating cylinders and a negative Radial Temperature Gradient (T2
A S Gupta - One of the best experts on this subject based on the ideXlab platform.
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effect of Radial Temperature Gradient on the stability of taylor dean flow between two arbitrarily spaced concentric rotating cylinders
International Journal of Heat and Mass Transfer, 2013Co-Authors: Tapas Ray Mahapatra, Samir Kumar Nandy, A S GuptaAbstract:Abstract The effect of a Radial Temperature Gradient on the stability of Taylor–Dean flow of an incompressible viscous fluid between two arbitrarily spaced concentric rotating circular cylinders driven by a constant azimuthal pressure Gradient is studied. Here the ratio of representative pumping and rotation velocities β is varied from −6.1613 to 1.00 and both positive and negative values of the Temperature Gradient parameter N are considered, where N depends on the Temperature differences T2 − T1 between the outer and inner cylinders. The linearized stability equations form an eigenvalue problem which is solved by using a classical Runge–Kutta scheme combined with a shooting technique, termed unit disturbance method. It is found that as the gap width between the cylinders increases, the critical Taylor number progressively increases for given values of β and N. It is also found that for given values of η (the ratio of the radii of inner and outer cylinders) and β, the flow becomes more and more unstable with increase in N(>0). In the present work, emphasis is given on the point as to whether the two neutral stability curves cross at some point for given value of N for which the flow is completely stable.
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Effect of Radial Temperature Gradient on the stability of Taylor–Dean flow between two arbitrarily spaced concentric rotating cylinders
International Journal of Heat and Mass Transfer, 2013Co-Authors: Tapas Ray Mahapatra, Samir Kumar Nandy, A S GuptaAbstract:Abstract The effect of a Radial Temperature Gradient on the stability of Taylor–Dean flow of an incompressible viscous fluid between two arbitrarily spaced concentric rotating circular cylinders driven by a constant azimuthal pressure Gradient is studied. Here the ratio of representative pumping and rotation velocities β is varied from −6.1613 to 1.00 and both positive and negative values of the Temperature Gradient parameter N are considered, where N depends on the Temperature differences T2 − T1 between the outer and inner cylinders. The linearized stability equations form an eigenvalue problem which is solved by using a classical Runge–Kutta scheme combined with a shooting technique, termed unit disturbance method. It is found that as the gap width between the cylinders increases, the critical Taylor number progressively increases for given values of β and N. It is also found that for given values of η (the ratio of the radii of inner and outer cylinders) and β, the flow becomes more and more unstable with increase in N(>0). In the present work, emphasis is given on the point as to whether the two neutral stability curves cross at some point for given value of N for which the flow is completely stable.
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stability of viscous flow driven by an azimuthal pressure Gradient between two porous concentric cylinders with Radial flow and a Radial Temperature Gradient
Acta Mechanica, 2007Co-Authors: Rudra Kanta Deka, A S GuptaAbstract:The effect of a Radial Temperature Gradient on the stability of viscous flow between two porous concentric circular cylinders driven by a constant azimuthal pressure Gradient is studied when a Radial flow through the permeable walls of the cylinders is present. The Radial Reynolds number β based on the Radial velocity at the inner cylinder and the inner radius R1 is varied from −130 to 30 and both positive and negative values of the parameter N are taken, where N depends on the Temperature difference T2 − T1 between the outer and inner cylinders. The linearized stability equations form an eigenvalue problem, which are solved by using a classical Runge-Kutta scheme combined with a shooting method, termed unit disturbance method. It is found that for a given value of N the Radially outward flow (β > 0) has a stabilizing effect and the stabilization is more as the gap between the cylinders increases. But the inward throughflow (β 0, the flow becomes more and more unstable with an increase in N.
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Stability of viscous flow driven by an azimuthal pressure Gradient between two porous concentric cylinders with Radial flow and a Radial Temperature Gradient
Acta Mechanica, 2007Co-Authors: Rudra Kanta Deka, A S GuptaAbstract:The effect of a Radial Temperature Gradient on the stability of viscous flow between two porous concentric circular cylinders driven by a constant azimuthal pressure Gradient is studied when a Radial flow through the permeable walls of the cylinders is present. The Radial Reynolds number β based on the Radial velocity at the inner cylinder and the inner radius R _1 is varied from −130 to 30 and both positive and negative values of the parameter N are taken, where N depends on the Temperature difference T _2 − T _1 between the outer and inner cylinders. The linearized stability equations form an eigenvalue problem, which are solved by using a classical Runge-Kutta scheme combined with a shooting method, termed unit disturbance method. It is found that for a given value of N the Radially outward flow ( β > 0) has a stabilizing effect and the stabilization is more as the gap between the cylinders increases. But the inward throughflow ( β < 0) has a destabilizing influence when | β | increases up to a certain critical value and thereafter the throughflow is stabilizing with further increase in | β |. When the outer cylinder is kept at a lower Temperature than the inner one ( N < 0), the flow becomes more and more stable with an increase in | N |. On the other hand, for N > 0, the flow becomes more and more unstable with an increase in N .
Insu Kang - One of the best experts on this subject based on the ideXlab platform.
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experimental study on Radial Temperature Gradient effect of a taylor couette flow with axial wall slits
Experimental Thermal and Fluid Science, 2011Co-Authors: Insu KangAbstract:Abstract The flow between two concentric cylinders with the inner cylinder rotating and an imposed Radial Temperature Gradient was studied using a digital particle image velocimetry method. The flow transition process under both a positive and negative Temperature Gradient with four different models of a stationary outer cylinder without and with differing numbers of slits (6, 9 and 18) was studied. The results showed that the buoyant force due to the Temperature Gradient clearly generated a helical flow when the rotating Reynolds number was small. For the plain and 6-slit models, the transition to a turbulent Taylor vortex flow was not affected by the Temperature Gradient considered in this study. In addition, the transition process of a larger number of slits (9-, 18-slit models) was accelerated due to the slit wall. As the Temperature Gradient became larger, the critical Reynolds number of the transition process decreased.
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Experimental study on Radial Temperature Gradient effect of a Taylor–Couette flow with axial wall slits
Experimental Thermal and Fluid Science, 2011Co-Authors: Insu KangAbstract:Abstract The flow between two concentric cylinders with the inner cylinder rotating and an imposed Radial Temperature Gradient was studied using a digital particle image velocimetry method. The flow transition process under both a positive and negative Temperature Gradient with four different models of a stationary outer cylinder without and with differing numbers of slits (6, 9 and 18) was studied. The results showed that the buoyant force due to the Temperature Gradient clearly generated a helical flow when the rotating Reynolds number was small. For the plain and 6-slit models, the transition to a turbulent Taylor vortex flow was not affected by the Temperature Gradient considered in this study. In addition, the transition process of a larger number of slits (9-, 18-slit models) was accelerated due to the slit wall. As the Temperature Gradient became larger, the critical Reynolds number of the transition process decreased.
