Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

Numerical simulation of heat transfer and fluid flow over two rotating circular cylinders at low Reynolds number

This paper presents a numerical investigation of the characteristics of two‐dimensional heat transfer in a steady laminar flow around two rotating circular cylinders in a side‐by‐side arrangement. The simulation is validated by comparing our computational results for the large gap‐spacing between cylinder surfaces with the available numerical and experimental data for a single cylinder. Numerical simulations were carried out for the Reynolds number range 10≤Re ≤40, for the Prandtl number range 0.7≤Pr ≤50, and for a variety of absolute rotational speeds (|α|≤2.5) at different gap spacings. The study revealed that for the range of parameters considered the rate of heat transfer decreases with the increasing speed of rotation. An increase of the Prandtl number resulted in an increase in the average Nusselt number. The streamlines and isotherms are plotted for a numbers of cases to show the details of the velocity and thermal fields. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20293     

Numerical Simulation of Steady Mixed Convection Around Two Heated Circular Cylinders in a Square Enclosure

In this paper, a numerical study has been carried out to investigate the steady-state mixed convection around two heated horizontal cylinders in a square two-dimensional enclosure. The cylinders are located at the middle of the enclosure height and the walls of the cavity are adiabatic. Streamlines and isotherms are produced and the effects of cylinder diameter, Reynolds number, and Richardson number on the heat transfer characteristics are numerically analyzed. The average Nusselt number over the surface of cylinders and average nondimensional temperature in the enclosure are also presented. The results show that both heat transfer rates from the heated cylinders and the dimensionless fluid temperature in the enclosure increase with increasing Richardson number and cylinder diameter. However, the trend of average Nusselt number and nondimensional temperature variation is completely opposite when Reynolds number increases. In addition, by increasing the cylinders diameter and Richardson number, the left cylinder is less affected by the inlet flow than right one.     

Heat and fluid flow across a rotating cylinder dissipating uniform heat flux in 2D laminar flow regime

Free-stream flow and forced convection heat transfer across a rotating cylinder, dissipating uniform heat flux, are investigated numerically for Reynolds numbers of 20–160 and a Prandtl number of 0.7. The non-dimensional rotational velocity (α) is varied from 0 to 6. Finite volume based transient heatline formulation is proposed. For Re = 100, the reasons for the onset/suppression of vortex shedding at a critical rotational velocity is investigated using vorticity dynamics. At higher rotational velocity, the Nusselt number is almost independent of Reynolds number and thermal boundary conditions. Finally, a heat transfer correlation is proposed in the 2D laminar flow regime. Cylinder rotation is an efficient Nusselt number reduction or cylinder-surface temperature enhancement technique.     

Effect of cross-stream buoyancy and rotation on the free-stream flow and heat transfer across a cylinder

Cross-stream buoyancy-induced formation of VS (vortex shedding) past a rotating cylinder maintained at constant wall temperature is studied at Re = 40 and 100. The non-dimensional rotational velocity (α) is varied from 0 to 8 and Richardson number from 0 to 1 with air as the working fluid. Semi-explicit finite-volume method code implemented on colocated Cartesian multi-block grid is used. Buoyancy-induced onset of vortex shedding is found for stationary/rotating cylinder at sub-critical Re = 40. Steady-VS flow transition map is shown for the different rotational velocity and Ri; and reasoned using vorticity dynamics. At higher rotational velocity, origin of buoyancy-induced secondary frequency for Re = 40 at α = 6 and for 100 at α = 5 is discussed using spectral analysis and phase portrait technique. The VS frequency is much smaller at higher as compared to lower rotational velocity and increases with increasing Ri. A monotonic increase in the downward lift force and a reversal in the direction of drag force is found with increasing rotational velocity. Rotation can be used as a drag reduction and heat transfer suppression technique.     

Vortex structure behind highly heated two cylinders in parallel arrangements

Vortex structures behind twin, highly heated cylinders in parallel arrangements have been investigated experimentally. The experiments were conducted under the following conditions: cylinder diameter, D=4mm; mean flow velocity, U_∞ = 1.0 m/s; Reynolds number, Re=250; cylinder clearance, S/D=0.5 to 1.4; and cylinder heat flux, q=0 to 72.6kW/m². For S/D>1.2, the Karman vortex street is formed alternately behind each cylinder divided on the slit flow. The slit flow velocity increases with a decrease in S/D and decreases with increasing heat flux. For S/D < 1.2, the wake vortexes become asymmetric having small and large scale vortexes divided by the slit flow. In the small scale vortexes, the symmetric counter‐rotating twin vortexes are formed just behind the cylinders. In the large scale vortexes, the generated vortexes have a similar structure to a Karman vortex even though the Strouhal number is approximately half of the ordinary single cylinder vortex. For isothermal conditions, the transition phenomena from symmetric to asymmetric wake structures are observed in the range of 0.9 < S/D <1.2. In addition, the asymmetric vortexes are irregularly switched up and down in the case of isothermal conditions. In the highly heated condition, the switching phenomena and the transition phenomena could not be observed and the small scale vortexes always formed behind the upper cylinder. The critical S/D increases approximately 30% in the heated condition (q=72.6kW/m²). As a result, the increased local kinematic viscosity and S/D play a key role for the vortex structure and formation behind arrangements of two parallel cylinders. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20244     

Large eddy simulation of flow over square cylinder arrays in an octagonal configuration at subcritical Reynolds numbers

In this study, fluid flow over an array of eight, 0.029 m × 0.029 m, square cross‐section cylinders in an octagonal configuration is studied numerically. The mean force coefficients (drag and lift) and the vortex formation characteristics of the array are calculated numerically by utilizing a three‐dimensional large eddy simulation mathematical model for turbulence. The numerical simulation is performed with commercial software ANSYS Fluent 19R1. To investigate the parametric influences, three spacings between the cylinders (0.07, 0.14, and 0.2 m), two array attack angles (0° and 15°), and two Reynolds numbers (4060 and 45 800) are considered. The results comprise flow patterns and force coefficients' variations with Reynolds numbers. The lift force of the downstream cylinder reaches its maximum at α = 15°, and the drag force of the upstream cylinders finds its peak at α = 0°. It is observed through velocity and viscosity contour plots that vortex formation length near the cylinder increases at higher Reynolds number. Velocity vector plots are also presented to show fluid flow behavior near the cylinder. Furthermore, the predicted mean forces on the cylinders are slightly different for different Reynolds numbers, spacings, and angles of attack.     

Influence of nonlinear thermal radiation on mixed convective hybrid nanofluid flow about a rotating sphere

The present study investigates the mixed convective hybrid nanofluid flow over a rotating sphere under the impact of nonlinear thermal radiation. A model is built to examine the heat transport performance of ferrimagnetic magnetite and copper nanoparticles over a rotating sphere. Nonsimilar transformations are used to nondimensionalize the coupled nonlinear governing equations and the flow model's boundary conditions. Furthermore, the nondimensional governing equations were solved using implicit finite difference approximation and the quasilinearization technique. The impacts of the flow regime on many controlling parameters are then thoroughly addressed. Temperature patterns improve when nonlinear thermal radiation and hybrid nanofluid values increase. The fluid velocity and skin friction coefficient increase in the streamwise direction while decreasing in the rotating direction. The separation of the boundary layer is delayed as the sphere's rotation weakens. The stationary sphere has a larger boundary layer separation than the revolving sphere. The velocity distribution improves with increasing rotation parameter values while decreasing with increasing combined convection parameter values in the rotating direction. An increase in the temperature ratio parameter makes the fluid get hotter, and the Nusselt number goes down simultaneously. Nusselt number and skin friction coefficient in the rotation direction increase, while skin friction coefficient in streamwise direction reduces for increasing values of hybrid nanofluid. The velocity of the fluid enhances in the stream-wise direction while reducing in the rotational direction with the increasing values of the combined convection parameter.     

Analysis of vortex‐induced and stall‐induced vibrations at standstill conditions using a free wake aerodynamic code

Vortex‐induced and stall‐induced vibrations of a 2D elastically mounted airfoil at high angles of attack in the vicinity of 90° are investigated using a vortex type model. Such conditions are encountered in parked or idling operation at extreme yaw angles provoked by control system failures. At very high angles of attack, massive flow separation takes place over the entire blade span, and vortex shedding evolves downstream of the blade giving rise to periodically varying loads at frequencies corresponding to the Strouhal number of the vortices shed in the wake. As a result, vortex‐induced vibrations may occur when the shedding frequency matches the natural frequency of the blade. A vortex type model formulated on the basis of the ‘double wake’ concept is employed for the modelling of the stalled flow past a 2D airfoil. By tuning the core size of the vortex particles in the wake, the model predictions are successfully validated against averaged 2D measurements on a DU‐96‐W‐180 airfoil at high angles of attack. In order to assess the energy fed to the airfoil by the aerodynamic loads, the behaviour under imposed sinusoidal edgewise motions is analysed for various oscillation frequencies and amplitudes. Moreover, stall‐induced and vortex‐induced vibrations of an elastically mounted airfoil section are assessed. The vortex model predicts higher aeroelastic damping as compared with that obtained using steady‐state aerodynamics. Excessive combined vortex‐induced and stall‐induced edgewise vibrations are obtained beyond the wind speed of 30 m s^?1. Copyright © 2014 John Wiley & Sons, Ltd.     

Non‐Newtonian squashed flow simulation across Darcy‐Forchheimer sensor

The current mathematical formulation is dedicated to investigate the Darcy‐Forchheimer boundary layer–squeezed hydromagnetic flow of a Casson fluid passing through a sensor surface. The flow phenomenon is occurring in a locally free stream under the combined sway of heat generation and thermic radiation. The energy equation is deliberated with the assistance of Cattaneo‐Christov theory rather than using Fourier's law for conduction of heat. Here, the thermic conductivity is being presumed as a function of temperature. The governing mathematical structure consists of highly nonlinear terms, so a set of regulatory parameters is being accomplished to attain the unpretentious dimensionless equations. This nondimensional structure is then treated numerically to attain the nearly converging results. The significance of substantial parameters such as magnetic factor, radiation parameter, Casson fluid parameter, heat origination, and thermal relaxation time on the flow phenomenon is estimated and presented graphically. Besides this, the factors of engineering interest like the Prandtl number and squeezed flow index with vacillating thermic conductivity have strong effects on the flow behavior of the fluid. It is observed that the magnetic effect causes an expansion in the velocity curve while a reduction is found for squeezed flow index parameter.     

Triggering Vortex Shedding by Superimposed Thermal Buoyancy Around Bluff Obstacles in Cross-Flow at Low Reynolds Numbers

Influences of superimposed thermal buoyancy on the initiation of vortex shedding process behind bluff obstacles (such as circular and square cylinders in 2-D) in cross-flow at low Reynolds numbers (10 ≤ Re ≤ 40) are discussed. The flow which is steady and separated at this Reynolds number range eventually becomes unsteady periodic with the introduction of thermal buoyancy. The aim here is to numerically predict the critical value of the buoyancy parameter (Richardson number, Ri) for the onset of vortex shedding. The critical Ri is found to have a decreasing tendency for both types of cylinder geometries with increasing Re.     

Unsteady Mixed Convection Flow of a Rotating Second‐Grade Fluid on a Rotating Cone

In the present article, we have investigated the unsteady mixed convection flow of a rotating second‐grade fluid in a rotating cone with time‐dependent angular velocities. Two cases of heat transfer are presented which are known as (i) prescribed wall temperature (PWT) and (ii) prescribed heat flux (PHF). The governing coupled nonlinear partial differential equations are simplified with the help of transformations and non‐dimensional similar and non‐similar variables, and solved analytically with the help of the homotopy analysis method (HAM). The effects of pertinent parameters on the velocity, temperature, concentration, skin friction coefficients, Nusselt number, and Sherwood number have been examined through graphs. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 204–220, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21072     

Mixed convection inside a fluid‐porous composite cavity with centrally rotating cylinder

The mixed convection in a fluid‐porous composite medium lying inside a square cavity with a centrally rotating cylinder has been investigated in the present work. The bottom half of the cavity is filled with a porous material and the top half is filled with a clear fluid. The bottom wall of the cavity is at a higher temperature, and the top wall is at a lower temperature. The vertical walls are thermally insulated. The convection inside the cavity sets through the combined mechanisms of the thermal buoyancy force and the shearing action of the centrally rotating cylinder. The relative importance of each driving mechanism over the other is featured through the Richardson number. The Darcy–Brinkman–Forchheimer equation is used for the flow modeling in the porous medium, and a single‐domain approach is adopted for the numerical solution in the fluid‐porous composite medium. The simulation is carried out with ANSYS Fluent software, and a parametric analysis involving the Rayleigh number (), Richardson number (), and the Darcy number () is conducted showing their effects on the flow and heat transfer. The phenomena are quite interesting at higher Darcy number and Rayleigh number. The distributions of isotherms, streamlines, and vector plots are plotted, along with the local Nusselt numbers for different parameters, to explore the underlying physics of the phenomenon. The system is found stable at lower Darcy number, and the heat transfer is minimum around Ri = 10. From the numerical study, an empirical correlation for the average Nusselt number is developed as a function of the other dimensionless numbers.     

Effect of Joule heating on MHD non‐Newtonian fluid flow past an exponentially stretching curved surface

The current endeavor examines the convective heat transfer characteristics on magnetohydrodynamic stagnation point flow of micropolar fluid past an exponential curved surface. The flow is supposed to be laminar and time‐independent. The influence of radiation, irregular heat source/sink, Joule heating, and variable thermal conductivity are supposed. Suitable similarity renovations are considered to transform the original partial differential equations as ordinary ones and then resolved by shooting and fourth‐order Runge–Kutta methods. Graphs are drawn to inspect the impacts of sundry nondimensional parameters on the distributions of velocity, microrotation, and temperature. We detect that there is an escalation in temperature with Eckert number and variable heat source/sink parameters. Also, it is motivating to comment that Biot number is an increasing function of local Nusselt number.     

A numerical study of fluid flow passes two heated/cooled square cylinders in a tandem arrangement via lattice Boltzmann method

In this paper, the fluid flow pass two heated/cooled square cylinders in a tandem arrangement is simulated via the Multiple-Relaxation-Time lattice Boltzmann method. The distance between the upstream and downstream cylinder varies from the rear of the upstream one to 5 times of the cylinder width. The numerical experiments are done under different Richardson numbers (Ri, represents the effect of the buoyancy force) for two typical Re = 100, 60. The buoyancy effect on the flow and heat transfer around the two cylinders is mainly investigated. As is shown, if the force is in the same direction of incoming flow, the vortex street is always suppressed and no critical spacing seems to exist. However, if the force is in the opposite direction of the incoming flow, the vortex street can always be generated and the critical spacing always seems to exist. Correspondingly, the heat transfer around the cylinders measured by the Nusselt number on the surfaces of the two cylinders also shows different characteristics for various Ri s.     

Significance of thermal radiation on dusty fluid flow over a stretching rotating disk with convective boundary condition

This paper explores the flow of dusty fluid over a stretching rotating disk with thermal radiation. Further, the convective boundary condition is considered in this modeling. The described governing equations are reduced to ordinary differential equations by using apt similarity transformations and then they are numerically solved using Runge–Kutta–Fehlberg-45 scheme. To gain a clear understanding of the current boundary layer flow problem, the graphical results of the velocity and thermal profiles, shear stresses at the disk, and Nusselt number are drawn. Results reveal that the increase in the value of the porosity parameter reduces the velocity of both particle and fluid phases. The increase in the value of the Biot number improves the temperature gradient of both particle and fluid phases. The rise in the value of the radiation parameter advances the heat transference of both phases. The rise in the value of the Biot number improves the rate of heat transfer. Finally, increasing the value of the radiation parameter improves the rate of heat transfer.     

A numerical study of convective heat transfer from a rotating cylinder with cross-flow oscillation

This article presents a numerical investigation of convective heat transfer from a rotating cylinder with cross-flow oscillation. A finite element analysis using Characteristic Based Split method (CBS) is developed to solve governing equations involving continuity, Navier–Stokes, and energy equations. Dynamic unstructured triangular grid is used employing improved lineal and torsional spring analogy which is coupled with the solver by the Arbitrary Lagrangian–Eulerian (ALE) formulation. After verifying the numerical code accuracy, simulations are conducted to study convective heat transfer past a rotating cylinder with cross-flow oscillation at Reynolds numbers of 50, 100, and 200. Different rotational speeds of the cylinder normalized by free stream velocity, in the range of 0–2.5 are considered at various oscillating amplitudes and frequencies and three different Prandtl numbers of 0.7, 6, and 20. Effects of oscillation and rotation of cylinder on the temperature and flow field, vortex lock-on, mean Nusselt number, and the pattern of vortex shedding are investigated in detail considering iso-temperature and iso-flux boundary conditions on the cylinder surface. It is found that similar to the fixed cylinder, beyond a critical rotating speed, vortex shedding is mainly suppressed. Also by increasing the non-dimensional rotational speed of the cylinder, both the Nusselt number and the drag coefficient decrease rapidly. However, in vortex lock-on region, the Nusselt number increases in a large amount.     

Finite-difference solution of heat transfer in developing flow in an annulus of two rotating cylinders

Finite-difference analysis of the heat transfer in the developing flow of an annulus bounded by two concentric and rotating cylinders is carried out. The two cylinders are assumed to be at unequal temperatures. Numerical results for temperature profiles, mixing-cup temperature θ_m and the Nusselt number Nu are derived for different values of Re²/Ta (Re = axial Reynolds number; Ta = Taylor number), θ (ratio of the angular velocities of two cylinders) and N (ratio of the two radii). Temperature profiles are shown graphically, whereas the numerical values of θ_m and Nu are listed in tables. The effects of these parameters are discussed.     

Numerical Simulation of Fluid Flow and Heat Transfer on the Lubricating Surface with Micro‐Groove

The effect of the lubricant flow in the micro‐grooves which resulted from the machining can be expressed in the flow fluid and heat transfer during the mechanical lubrication process. In this paper, a thermal lattice Boltzmann model (LBM), which consists of the heat viscous dissipation term, was proposed to investigate on the lubricants flow and heat transfer in the micro‐grooves. The heat, generated in the lubricating flowing process, was equivalent to a heat source R (x, t) within the fluid and added to the internal energy distribution function. The effect of the heat generated by the fluid on the flow and temperature field can be derived by comparing these two models. The results showed that the fluid temperature rises slower than the mainstream area on account of the vortex motion in the grooves. When the heat source is added to the function, the vortex became larger and the solid boundary was heated by the fluid. Thus, the improved thermal lattice Boltzmann method can accurately simulate the flow of lubricants.     

Stability analysis between two concentric rotating cylinders with heat and mass transfer

The stability of the liquid/vapor interface between two concentric revolving cylinders is examined. The transfer of heat/mass is allowed at the interface. Both the cylinders rotate with different angular velocities. The fluids inside the annular region are taken as incompressible and viscous. The theory of viscous potential flow analysis is used to add the viscous effects. The normal mode technique is used to calculate the growth of perturbations. If we rotate the inner cylinder, it is seen that asymmetric disturbances have a destabilizing character at the interface but the rotation of the outer cylinder has a stabilizing effect. We found that an asymmetric disturbance destabilizes the interface if the inner cylinder rotates. It is found that the arrangement gets destabilized on rotating of the inner cylinder but rotation of the outer cylinder induces stability, and the most stable case is found when the inner cylinder is stationary and the outer cylinder is rotating.