Effect of rotating cylinder on heat transfer in a square enclosure filled with nanofluids

Convective heat transfer in a differentially heated square enclosure with an inner rotating cylinder is studied theoretically. The free space between the cylinder and the enclosure walls is filled with water–Ag, water–Cu, water–Al₂O₃ or water–TiO₂ nanofluids. The governing equations are formulated for velocity, pressure and temperature formulation and are modeled in COMSOL, a partial differential equation (PDE) solver based on the Galerkin finite element method (GFEM). The governing parameters considered are the solid volume fraction, 0.0 ? ? ? 0.05, the cylinder radius, 0 ? R ? 0.3 and the angular rotational velocity, ?1000 ? Ω ? 1000. The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the strength of the flow circulation is much stronger for a higher nanoparticle concentration, a better thermal conductivity value and a smaller cylinder with a faster, negative rotation. The maximum heat transfer are obtained at a high nanoparticle concentration with a good conductivity value, a slow positive rotation and a moderate cylinder size located in the center of the enclosure.     

Heat transfer in a small gap between co-axial rotating cylinders

This paper investigates the local heat transfer of a co-axial rotating cylinder. In the inner flow field of the rotating cylinder, the dimensionless parameters include the rotational Reynolds number (Re_Ω) and buoyancy parameter (Gr). The test rig is designed to make the rotating in the inner cylinder and stationary in the outer cylinder. The local temperature distributions of the inner and outer cylinder on axial direction were measured. Under the experimental condition, whereas the ranges of the rotational Reynolds number are 2400 ≤ Re_Ω ≤ 45,000. Experimental results reveal that the rotational Reynolds number's increase is with the heat transfer coefficient distributions increase types. Finally, the local heat transfer rate on the wall are correlated and compared with that in the existing literature.     

Bénard convection from a circular cylinder in a packed bed

Bénard convection around a circular heated cylinder embedded in a packed bed of spheres is studied numerically. The Forchheimer–Brinkman–extended Darcy momentum model with the Local Thermal Non-Equilibrium energy model is used in the mathematical formulation for the porous layer. The governing parameters considered are the Rayleigh number (10³ ≤ Ra ≤ 5 × 10⁷) and the thermal conductivity ratio (0.1 ≤ k_r ≤ 10,000). The structural properties of the packed bed are kept constant as: cylinder-to-particle diameter ratio D/d = 20 and porosity ε = 0.5, while the Prandtl number is fixed at Pr = 0.71. It is found that the presence of the porous medium suppresses significantly the strong free convection produced in the empty enclosure, and reduces considerably the high intensity of the pair of vortices generated behind the cylinder. Also, the results show that the porous medium can play the role of insulator or enhancer of heat transfer from the heat source, depending mainly on their thermal conductivities regardless of the Rayleigh number.     

Effect of Prandtl number and rotation on vortex shedding behind a circular cylinder subjected to cross buoyancy at subcritical Reynolds number

We perform a two-dimensional numerical simulation following a finite volume approach to understand the vortex shedding (VS) phenomena around a circular cylinder subjected to cross thermal buoyancy at a subcritical Reynolds number, Re = 40. The flow is considered in an unbounded medium. The cylinder may either be stationary or rotating about its centroidal axis. At the subcritical Reynolds number, the flow and thermal fields are steady without the superimposed thermal buoyancy (i.e. for pure forced flow). However, as the buoyancy parameter (Richardson number, Ri) increases, flow becomes unstable, and eventually, at some critical value of Ri, periodic VS is observed to characterize the flow and thermal fields. An extended Stuart–Landau model is used in this work for the accurate quantitative estimation of the critical Richardson number for the onset of VS. The above phenomena of VS with imposed buoyancy is strongly dependent on the type of the fluid being used. We quantify here the minimum heating requirement for the initiation of VS by choosing three different types of fluids having Prandtl numbers, Pr = 0.71, 7, and 100. The dimensionless rotational speed (Ω) ranges between 0 and 4. It is revealed that as Pr increases, heating requirement also increases for the initiation of VS. A possible explanation for the observation is provided.     

Lattice Boltzmann simulation of the double diffusive natural convection and oscillation characteristics in an enclosure filled with porous medium

This article adopts lattice Boltzmann method to investigate the double diffusive natural convection around a heated cylinder in an enclosure filled with porous medium. The heated cylinder is located at the center of the enclosure with high temperature and concentration. Four surrounding walls are assumed to be low temperature and concentration. The distributions of velocity, temperature and concentration are solved by three independent lattice Bhatnagar-Gross-Krook (LBGK) equations. The influence of Darcy number Da (10^–4 ≤ Da ≤ 10^− 2), Lewis number Le (0.2 ≤ Le ≤ 10.0) and buoyancy ratio Br (− 10.0 ≤ Br ≤ 10.0) on the double diffusive natural convection are inspected numerically. Results are presented in terms of isotherms, streamlines, isoconcentrations, average Nusselt and Sherwood numbers. At Br = − 50.0, the effect of Darcy number on unsteady flow characteristics is also investigated by the time history and phase space trajectory. It is found that the flow undergoes steady-state, unsteady doubling periodic oscillation, quasi-periodic oscillation and non-periodic oscillation when Darcy number Da is varied from 10^− 4 to 10^− 2.     

Magneto-Convective Transport of Nanofluid in a Vertical Lid-Driven Cavity Including a Heat-Conducting Rotating Circular Cylinder

Numerical simulations are performed for the two-dimensional magneto-convective transport of Cu–H₂O nanofluid in a vertical lid-driven square cavity in the presence of a heat-conducting and rotating circular cylinder. The left wall of the cavity is allowed to translate at a constant velocity in the vertically upward direction. Both left and right walls are maintained at isothermal but different temperatures. The top and bottom walls of the enclosure are thermally insulated. At the central region of the cavity is a heat-conducting circular cylinder which can rotate either clockwise or counterclockwise. A constant horizontal magnetic field of amplitude B₀ is applied perpendicular to the vertical walls. The nanofluid is electrically conducting, while the solid walls are considered electrically insulated. Simulations are performed for various controlling parameters, such as Richardson number (0.01 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), dimensionless rotational speed of the cylinder (Ω = ±1), and nanoparticle concentration (0 ≤ ? ≤ 0.3), while Reynolds number based on lid velocity is fixed at a specific value (Re = 100). The flow and thermal fields are found to be susceptible to changes in the magnetic field and mixed convective strength, as well as nanoparticle concentration. However, the direction of cylinder rotation is observed to have little or no influence quantitatively on global hydrodynamic and thermal parameters.     

Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids

The behaviour of nanofluids is investigated numerically inside a two-sided lid-driven differentially heated square cavity to gain insight into convective recirculation and flow processes induced by a nanofluid. A model is developed to analyze the behaviour of nanofluids taking into account the solid volume fraction χ. The transport equations are solved numerically with finite volume approach using SIMPLE algorithm. Comparisons with previously published work on the basis of special cases are performed and found to be in excellent agreement. The left and the right moving walls are maintained at different constant temperatures while the upper and the bottom walls are thermally insulated. Three case were considered depending on the direction of the moving walls. Governing parameters were 0.01 < Ri < 100 but due to space constraints only the results for 0.1 < Ri < 10 are presented. It is found that both the Richardson number and the direction of the moving walls affect the fluid flow and heat transfer in the cavity. Copper–Water nanofluid is used with Pr = 6.2 and solid volume fraction χ is varied as 0.0%, 8%, 16% and 20%. Detailed results are presented for flow pattern and heat transfer curves.     

Transient natural convective heat transfer of a low-Prandtl-number fluid inside a horizontal circular cylinder with an inner coaxial triangular cylinder

A numerical study of transient natural convection of liquid gallium (Pr = 0.023) from a horizontal triangular cylinder to its coaxial cylindrical enclosure is performed. The aspect ratio is fixed at 2 and two positions of the inner triangular cylinder are considered. The development of the convective flow and heat transfer is shown via the time histories of the average Nusselt number over the outer circular wall for various Grashof numbers. Temporal phases of the flow development are identified as: initializing, developing, transitioning, and steady/quasi-steady state or oscillating. Typical flow patterns and temperature distributions at these phases are presented by means of streamlines and isotherms, respectively. Pitchfork bifurcation is present for both positions of the inner triangular cylinder when Gr ? 5 × 10⁴. The time-averaged Nusselt number over the outer circular cylinder, the flow development time, and the onset time of pitchfork bifurcation are predicted and scaled with the Grashof number. It is found that the time-averaged Nusselt number is apparently increased by horizontally placing the top side of the inner triangular cylinder for Gr ? 1 × 10⁵.     

Numerical simulation of double diffusive mixed convection in an open enclosure with different cylinder locations

This article reports numerical simulation of the double diffusive mixed convection around a cylinder in an open enclosure with an inlet and exit ports. The temperature and mass concentration of the cylinder are higher than those of the inlet flow and the cylinder can be at three different locations (lower, middle and upper) in the enclosure. The inlet flow with low temperature and mass concentration is located at the lower-left wall of the enclosure and the exit is at the upper-right wall. Other walls are assumed to be adiabatic. Effects of Lewis number Le, buoyancy ratio Br, and cylinder locations on the double diffusive mixed convection are investigated at Richardson number Ri = 1.0 and 0.01 while Prandtl number Pr is kept at 0.7. Streamlines, isotherms, isoconcentrations, and the average and local Sherwood number at different parameters are reported to characterize the double diffusive mixed convection phenomena in the open enclosure.     

Assessment of dissipative particle dynamics to simulate combined convection heat transfer: Effect of compressibility

The current study explored the capability of a discrete particle method known as dissipative particle dynamics with energy conservation (eDPD) to simulate combined convection heat transfer in a vertical lid driven cavity. The study investigated two cases of aiding and opposing buoyancy mechanisms in the lid driven cavity. The eDPD results were compared against the finite volume solutions for the range of Richardson number, 10^− 2 ≤ Ri ≤ 10². The method showed good comparison for the range of Richardson number 10^− 2 ≤ Ri ≤ 10¹. However, the eDPD method showed deviation from the FV solutions for a high value of Richardson number, Ri = 10², and this deviation is attributed to the compressibility of eDPD system experienced at such high value of Richardson number. Parametric study on the influence of the Richardson number (Ri) on the eDPD compressibility was conducted and presented via temperature isotherms, streamlines, velocity contours, velocity vectors, temperature and velocity profiles.     

Rotation effects on non-Darcy convection in an enclosure filled with porous medium

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper taking into consideration the Forchheimer–Brinkman-extended Darcy model. The enclosure is filled with a fluid-saturated porous medium and executes a steady counterclockwise angular velocity about its longitudinal axis. The staggered grid arrangement together with the Marker and Cell (MAC) method was employed to solve the governing equations. The governing parameters considered are the porosity, 0.4 ≤ ϵ ≤ 0.99, the Darcy number, 0.005 ≤ Da ≤ 0.01 and the Taylor number, 8.9 × 10⁴ ≤ Ta ≤ 3.8 × 10⁵, and the centrifugal force is assumed weaker than the Coriolis force. It is found that higher porosities have weaker flow circulation when the Coriolis effect is smaller than the buoyancy effect. The global quantity of the heat transfer rate increases by increasing the porosity and the Darcy number and decreases by increasing the Taylor number.     

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.     

Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–Water nanofluid

This work focuses on the study of natural convection heat transfer characteristics in a differentially-heated enclosure filled with a CuO–EG–Water nanofluid for different published variable thermal conductivity and variable viscosity models. The problem is given in terms of the vorticity–stream function formulation and the resulting governing equations are solved numerically using an efficient finite-volume method. Comparisons with previously published work are performed and the results are found to be in good agreement. Various results for the streamline and isotherm contours as well as the local and average Nusselt numbers are presented for a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 6%), and enclosure aspect ratios (½ ≤ A ≤ 2). Different behaviors (enhancement or deterioration) are predicted in the average Nusselt number as the volume fraction of nanoparticles increases depending on the combination of CuO–EG–Water variable thermal conductivity and viscosity models employed. In general, the effects the viscosity models are predicted to be more predominant on the behavior of the average Nusselt number than the influence of the thermal conductivity models. The enclosure aspect ratio is predicted to have significant effects on the behavior of the average Nusselt number which decreases as the enclosure aspect ratio increases.     

Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures

Heat transfer enhancement utilizing nanofluids in a two-dimensional enclosure is investigated for various pertinent parameters. The Khanafer's model is used to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersion. Transport equations are model by a stream function-vorticity formulation and are solved numerically by finite-difference approach. Based upon the numerical predictions, the effects of Rayleigh number (Ra) and aspect ratio (AR) on the flow pattern and energy transport within the thermal boundary layer are presented. The diameter of the nanoparticle d_p is taken as 10 nm in nanofluids. The buoyancy parameter is 10³ ≤ Ra ≤ 10⁶ and aspect ratios (AR) of two-dimensional enclosure are 1/2, 1, 2. Results show that increasing the buoyancy parameter and volume fraction of nanofluids cause an increase in the average heat transfer coefficient. Finally, the empirical equation was built between average Nusselt number and volume fraction.     

Numerical study of swirling flows in a cylindrical container with co-/counter-rotating end disks under stable temperature difference

A numerical study was conducted to investigate swirling flows of a Boussinesq fluid confined in a cylindrical container with co-/counter-rotating end disks. A vertically stable temperature gradient is imposed, with the stationary sidewall assumed as adiabatic. Flows are studied for a range of parameters: the Reynolds number, Re, 100 ⩽ Re ⩽ 2000; the Richardson number, Ri, 0 ⩽ Ri ⩽ 1.0; and the Prandtl number, Pr, Pr = 1.0. The ratio of the angular velocity of the top disk to the bottom disk, s, −1.0 ⩽ s ⩽ 1.0. The cylinder aspect ratio: h = 2.0. For the case of negligibly small temperature difference (Ri ∼ 0) and high Re, interior fluid rotates with an intermediate angular velocity of both end disks when they are co-rotating (s > 0). When end disks are counter-rotating (s < 0), shearing flow with meridional recirculation is created. For the case of large temperature difference (Pr · Ri ∼ O(1)), the Ekman suction is suppressed and the sidewall boundary layer disappears at mid-height of the cylinder. For all the values of s considered in the present study, the bulk of the fluid is brought close to rest with the fluid in the vicinity of both end disks rotating in each direction. The secondary flow in the meridional section of the cylindrical container exhibits various types of vortices as the governing parameters are varied. These flow patterns are presented in the form of diagrams on the (s, Re) plane and (s, Ri) plane. The average Nusselt number is computed and presented as functions of Ri, Re and s.     

Numerical prediction of flow and heat transfer of power-law fluids in a plane channel with a built-in heated square cylinder

Structure of unsteady laminar flow and heat transfer of power-law fluids in two-dimensional horizontal plane channel with a built-in heated square cylinder is studied numerically. The governing equations are solved using a control volume finite element method (CVFEM) adapted to the staggered grid. Computations are performed over a range of Reynolds and Richardson numbers from Re = 20 to 200 and from Ri = 0 to 8, respectively at fixed Prandtl number Pr = 50 and blockage ratio value β′ = 1/8. Three different values of the power-law index (n = 0.5, 1 and 1.4) are considered in this study to show its effect on the value of the critical Reynolds number defining the transition between two different flow regimes (symmetrical and periodic flows), the variations of Strouhal number, drag and lift coefficients and the heat transfer from the square cylinder as function of Reynolds number. Heat transfer correlations are obtained through forced convection. A discussion about the buoyancy effect on the flow pattern and the heat transfer for different power-law index is also presented.     

Effects of viscous dissipation during forced convection of power-law fluids in microchannels

The effect of viscous dissipation in forced convection of power-law fluids through microchannels of different cross-sectional geometries is studied numerically over the ranges of power-law index, 0.8 ≤ n ≤ 1.2 and Brinkman number, 0.001 ≤ Br ≤ 0.1 while keeping Péclet number constant at Pe = 10. Two types of thermal boundary conditions, namely, uniform wall temperature (T₂) and uniform heat flux (H₂), have been employed at the microchannel wall and the results of the temperature fields are expressed in terms of Nusselt number. The interplay between the fluid rheology and viscous dissipation effect gives rise to significant alteration in the net convective transport and thus can be beneficial in the thermal design of biofluidic devices.     

Convective Transport Around a Rotating Square Cylinder at Moderate Reynolds Numbers

Two-dimensional numerical simulation is performed to analyze the thermofluidic transport around a rotating square cylinder in an unconfined medium. The convective transport originates as a consequence of the interaction between a uniform free-stream flow and the flow evolving due to the rotation of the sharp-edged body. A finite volume-based method and a body-fitted grid system along with the moving boundaries are used to obtain the numerical solution of the incompressible Navier–Stokes and energy equations. The Reynolds number based on the free-stream flow is considered in the range 10 ≤ Re ≤ 200, and the dimensionless rotational speed of the cylinder is kept 0 ≤ Ω ≤ 5. Depending on the Reynolds number and the rotational speed of the cylinder, the transport characteristics change. For the range 10 ≤ Re < 50, the flow remains steady irrespective of the rotational speed. In the range 50 ≤ Re ≤ 200, regular low-frequency Kármán vortex shedding (VS) is observed up to a critical rate of rotation (Ω_cr ). Beyond Ω_cr , the global convective transport shows a steady nature. The rotating circular cylinder also shows likewise degeneration of Kármán VS at some critical rotational speed. However, the heat transfer behavior varies significantly with a rotating circular cylinder. Such thermofluidic transport around a spinning square in an unconfined free-stream flow is reported for the first time.     

Mixed convection flow and heat transfer across a square cylinder under the influence of aiding buoyancy at low Reynolds numbers

In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re = 1–40 and Richardson number, Ri = 0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re = 1–2, between Re = 2–3 and between Re = 3–4 for Ri = 0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work.     

Convective heat transfer on a rotating finned cylinder with transverse airflow

The present experimental investigation relates to the convective heat transfer determination around annular fins mounted on a rotating cylinder with air crossflow. The mean convective heat transfer coefficient can be identified by solving the inverse conduction heat transfer problem during the fin cooling process. We used an inverse method, based on the mean squared error, to develop a model of mean convective heat transfer, taking lateral conduction into account. Tests were carried out for rotational Reynolds numbers Re_ω between 2150 and 17,200, air crossflow Reynolds numbers Re_U between 0 and 39,600, and fin spacings u in the range 10 mm to ∞, u = ∞ corresponding to the single disk case. For each fin spacing, the relative influences of the rotational and airflow forced convections on the heat transfer were analyzed and correlations of the mean Nusselt number on the fin, relative to both Reynolds numbers, are proposed. Moreover, an efficiency definition, that allows optimal geometrical configurations of the finned cylinder to be identified for the given operating conditions, is proposed.