The Effect of Aiding/Opposing Buoyancy on Two-Dimensional Laminar Flow Across a Circular Cylinder

The effect of thermal buoyancy on the upward flow and heat transfer characteristics around a heated/cooled circular cylinder is studied. A two-dimensional finite-volume model is deployed for the analysis. The influence of aiding/opposing buoyancy is studied for the range of parameters ?0.5 ≤ Ri ≤ 0.5, 50 ≤ Re ≤ 150, and the blockage ratios of B = 0.02 and 0.25. The flow shows unsteady periodic nature in the chosen range of Reynolds numbers for the forced convective cases (Ri = 0), and the vortex shedding stops completely at some critical values of Richardson numbers.     

Effect of Thermal Buoyancy on Fluid Flow and Heat Transfer Across a Semicircular Cylinder in Cross-Flow at Low Reynolds Numbers

The influence of superimposed thermal buoyancy on hydrodynamic and thermal transport across a semicircular cylinder is investigated through numerical simulation. The cylinder is fixed in an unconfined medium and interacted with an incompressible and uniform incoming flow. Two different orientations of the cylinder are considered: one when the curved surface is exposed to the incoming flow and the other when the flat surface is facing the flow. The flow Reynolds number is varied from 50 to 150, keeping the Prandtl number fixed (Pr = 0.71). The effect of superimposed thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ Ri ≤ 2. The unsteady two-dimensional governing equations are solved by deploying a finite volume method based on the PISO (Pressure Implicit with Splitting of Operator) algorithm. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds and Richardson numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag, lift and pressure coefficients, and Nusselt numbers are presented and discussed. Substantial differences in the global flow and heat transfer quantities are observed for the two different configurations of the obstacle chosen in the study. Additionally, intriguing effects of thermal buoyancy can be witnessed. It is established that heat transfer rate differs significantly under the superimposed thermal buoyancy condition for the two different orientations of the obstacle.     

Effect of Thermal Buoyancy on the Two-Dimensional Upward Flow and Heat Transfer Around a Square Cylinder

The effect of aiding/opposing buoyancy on the two-dimensional upward flow and heat transfer around a heated/cooled cylinder of square cross section is studied in this work. The finite-volume-based commercial computational fluid dynamics (CFD) software FLUENT is used for the numerical simulation. The influence of aiding/opposing buoyancy is studied for Reynolds and Richardson numbers ranges of 50 to 150 and –1 to 1, respectively, and the blockage parameters of 2% and 25%. The flow exhibits unsteady periodic characteristics in the chosen range of Reynolds numbers (except for Reynolds number of 50 and blockage parameter of 25%) for the forced convective cases (Richardson number of 0). However, the vortex shedding is observed to stop completely at some critical value of Richardson number for a particular Reynolds number, below which the shedding of vortices into the stream is quite prominent. Representative streamlines and isotherm patterns for different blockage parameters are systematically presented and discussed. The critical Richardson and average Nusselt numbers are plotted against the Reynolds and Richardson numbers, respectively, to elucidate the role of thermal buoyancy on flow and heat transfer characteristics. It is observed that the vortex shedding frequency (Strouhal number) increases with increased heating and suddenly reduces to zero at the critical Richardson number. The critical Richardson number is again found to increase with Reynolds number for a particular blockage ratio, and the higher the blockage ratio, the less is the critical Richardson number. The results obtained from the commercial solver are extensively validated with the available numerical results in the literature and an excellent agreement is observed.     

Momentum and Heat Transfer Characteristics for the Flow of Power-Law Fluids over a Semicircular Cylinder

In this study, the two-dimensional steady flow of power-law fluids past a semicircular cylinder (flat face oriented upstream) has been investigated numerically. The governing equations (continuity, momentum, and energy) have been solved in the steady symmetric flow regime over the range of the Reynolds number (0.01 ≤ Re ≤ 25), power-law index (0.2 ≤ n ≤ 1.8), and Prandtl number (0.72 ≤ Pr ≤ 100). Extensive new results reported here endeavor to elucidate the role of power-law index (0.2 ≤ n ≤ 1.8) on the critical Reynolds number denoting the onset of flow separation (Re ^c ) and of vortex shedding (Re _c ). In shear-thinning fluids, both of these transitions are seen to be delayed than that in Newtonian and shear-thickening fluids. Furthermore, the influence of the Reynolds and Prandtl numbers, power-law index on drag phenomenon, and heat characteristics of semicircular cylinder have been studied in the steady flow regime. Finally, the present numerical values of the critical Reynolds numbers and the average Nusselt number have been correlated by simple forms which are convenient for interpolating these results for the intermediate values of the governing parameters in a new application.     

Momentum and Heat Transfer from a Semi-Circular Cylinder to Power-Law Fluids in the Vortex Shedding Regime

Flow and heat transfer from a semi-circular cylinder to power-law fluids has been studied in the laminar vortex shedding regime for the range of conditions as follows: Reynolds number, 40 ≤ Re ≤ 140; Prandtl number, 0.7 ≤ Pr ≤ 50; and power-law index, 0.2 ≤ n ≤ 1.8. Extensive results are presented in terms of the streamline, vorticity and isotherm profiles, drag and lift coefficients, Strouhal number, and Nusselt number. The influence of Reynolds number, Prandtl number, and power-law index are seen to be more prominent in shear-thinning fluids (n < 1) than that in shear-thickening (n > 1) fluids. The shear-thinning fluid behavior enhances the rate of heat transfer, whereas shear-thickening fluid behavior impedes it.     

Flow past an Equilateral Triangular Bluff Obstacle: Computational Study of the Effect of Thermal Buoyancy on Flow Physics and Heat Transfer

The effect of thermal buoyancy on the wake dynamics and heat transfer characteristics of an isolated equilateral triangular cylinder in cross-flow configuration is considered here. Utilizing air (Pr = 0.71) as an operating fluid computations are carried out for wide ranges of the Reynolds number (80 ≤ Re ≤ 160) and the Richardson number (?1 ≤ Ri ≤ 1). In the range of conditions studied here, flow was found to be two-dimensional and unsteady. Detailed flow physics and temperature field are visualized in terms of the streamlines, vorticity, and isotherm contours in close proximity to the cylinder. Further insights are provided by analyzing the influence of buoyancy on the overall force coefficients, and the time-averaged Nusselt number.     

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.     

Magnetoconvective Transport in a Vertical Lid-Driven Cavity Including a Heat Conducting Square Cylinder with Joule Heating

The hydromagnetic mixed convection flow and heat transfer in a vertical lid-driven square enclosure is numerically simulated following a finite volume approach based on the SIMPLEC algorithm. Both the top and bottom horizontal walls of the enclosure are insulated, and the left and right vertical walls are kept isothermal with different temperatures. The left vertical wall is translating in its own plane at a uniform speed, while all other walls are stationary. Two cases of translational lid motion, viz. vertically upward and downward, are considered. A uniform magnetic field is applied along the horizontal direction normal to the translating wall. A heat conducting horizontal solid square cylinder is placed centrally within the outer enclosure. Simulations are conducted for various controlling parameters, such as the Richardson number (1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), and Joule heating parameter (0 ≤ J ≤ 5), keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, J, and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number, and bulk fluid temperature are also plotted to show the effects of Ha, J, and Ri on them.     

Effect of the Buoyancy Ratio on Oscillatory Double-Diffusive Convection in Binary Mixture

In this work, a numerical study of double-diffusive convection in binary mixture has been presented. A square cavity filled with a binary mixture and exposed to opposition solute and thermal gradients has been considered. The following flow parameters were considered: Prandtl number Pr = 10, Lewis number Le = 10, and buoyancy ratio varies 0 ≤ N ≤ 2. The finite volume method with SIMPLER algorithm was used to solving numerically the mathematical model. Our computer code is validated and shows a good agreement with literature available results. The obtained results show a strongest dependence of the thermal structure and solute effect with the buoyancy ratio. The oscillatory double-diffusive flow appeared from periodic time-evolution where the phenomena retuned in each period time. A critical thermal Rayleigh number Ra_Tcr and corresponding dominated frequency for the onset of oscillatory double-diffusive convection were determined for each buoyancy ratio N, and the results show a strongest dependence between the buoyancy ratio and critical Rayleigh number. Also, the dominance of solute force increases the intensity of the flow better than the case of the dominance of thermal force.     

Investigation of Mixed Convection in a Ventilated Cavity in the Presence of a Heat Conducting Circular Cylinder

The study is aimed to investigate the mixed convective transport within a ventilated square cavity in presence of a heat conducting circular cylinder. The fluid flow is imposed through an opening at the bottom of the left cavity wall and is taken away by a similar opening at the top of the right cavity wall. The cylinder is placed at the center of the cavity. Two cases are considered depending on the thermal conditions of the cavity walls. In the first case, the left and right vertical walls are kept isothermal with different temperatures and the top and bottom horizontal walls are considered as thermally insulated. For the second case, the top and bottom walls are maintained at different constant temperatures and the left and right walls are considered adiabatic. Heat transfer due to forced flow, thermal buoyancy, and conduction within the cylinder are taken into account. Effect of the cylinder size (0.1 ≤ D ≤ 0.5) and the solid–fluid thermal conductivity ratio (0.1 ≤ K ≤ 10) are explored for various values of Richardson number (0 ≤ Ri ≤ 5) at fixed Reynolds (Re = 100) and Prandtl (Pr = 0.71) numbers. The fluid dynamic and thermal transport phenomena are depicted through streamline and isotherm plots. Additionally, the global thermal parameters such as the average Nusselt number and average fluid temperature of the cavity are presented. It is found that the aforementioned parameters have significant influences on the fluid flow and heat transfer characteristics in the cavity.     

MHD Mixed Convection in a Lid-Driven Cavity Including Heat Conducting Solid Object and Corner Heaters with Joule Heating

The hydromagnetic mixed convection flow and heat transfer in a top sided lid-driven square enclosure is numerically simulated in this paper following a finite volume approach based on the SIMPLEC algorithm. The enclosure is heated by corner heaters which are under isothermal boundary conditions with different lengths in bottom and right vertical walls. The lid is having lower temperature than heaters. The other boundaries of the enclosure are insulated. A uniform magnetic field is applied along the horizontal direction. A heat conducting horizontal solid object (a square cylinder) is placed centrally within the outer enclosure. Shear forces through lid motion, buoyancy forces due to differential heating and magnetic forces within the electrically conducting fluid inside the enclosure act simultaneously. Heat transfer due to forced flow, thermal buoyancy, Joule dissipation and conduction within the solid object are taken into account. Simulations are conducted for various controlling parameters such as the Richardson number (0.1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50) and Joule heating parameter (0 ≤ J ≤ 5) keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, J and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number and bulk fluid temperature are also plotted to show the effects of Ha, J and Ri on them.     

Dual role of thermal buoyancy in controlling boundary layer separation around bluff obstacles

We establish through numerical simulation a dual role played by the superimposed thermal buoyancy in controlling the boundary layer separation around bluff obstacles. The work essentially demonstrates the influence of superimposed thermal buoyancy on flow around bluff obstacles of circular and square cross sections in aiding/opposing and cross buoyancy configurations. For the aiding/opposing configuration we show two phenomena such as the suppression of flow separation which occurs at relatively low Reynolds numbers (10–40) and the suppression of vortex shedding at a moderate range of Reynolds numbers (50–150). In the cross buoyancy configuration, the initiation of vortex shedding by the introduction of thermal buoyancy is shown at relatively low Reynolds numbers (10–40). Hence, depending on the direction of interaction with the free stream flow, the buoyancy sometimes stabilizes the flow and sometimes destabilizes the flow. Accordingly, there is a dual role of superimposed thermal buoyancy in controlling the boundary layer separation around bluff obstacles. Such duality cannot be observed in case of other agents such as rotation, magnetic force which also control the boundary layer separation around bluff obstacles.     

Effect of thermal buoyancy on vortex shedding past a circular cylinder in cross-flow at low Reynolds numbers

This paper demonstrates the vortex shedding process behind a heated cylinder in a cross-flow at low Reynolds numbers under the influence of thermal buoyancy. The simulations were performed using an SUPG-based finite element technique. The range of Reynolds numbers was chosen to be 10–45. The flow was steady in the absence of thermal buoyancy. The eddy length and the separation angle were computed for the steady separated flow in the above range of Reynolds numbers. The results were in agreement with those reported in the literature. The Nusselt number distribution around the heated cylinder was also computed in the above range of Reynolds numbers for forced convective flows. The results compared fairly well with available experimental results. The effect of superimposed thermal buoyancy in the same range of Reynolds numbers was studied for various Richardson numbers. The steady separated flows become unsteady periodic in the presence of superimposed thermal buoyancy. For the unsteady periodic flows, the Strouhal numbers were computed. The separation angles and average Nusselt number for such unsteady flows were found to vary with time.     

Mixed Convection Heat Transfer from Tandem Square Cylinders in a Vertical Channel at Low Reynolds Numbers

The fluid flow and heat transfer characteristics around two isothermal square cylinders arranged in a tandem configuration with respect to the incoming flow within an insulated vertical channel at low Reynolds number range (1 ≤ Re ≤ 30) are estimated in this article. Spacing between the cylinders (S) is fixed at four widths of the cylinder dimension (d) and, the blockage parameter (B) is set to 0.25. The buoyancy-aided/opposed convection is examined for the Richardson number (Ri) ranges from ?1 to 1 with a fixed Prandtl number (Pr) of 0.7. The transient numerical simulation for this two-dimensional, incompressible, laminar flow and heat transfer problem is carried out by a finite volume code based on the PISO algorithm in a collocated grid system. The results suggest that the flow remains steady for the entire range of parameters chosen in this study. The representative streamlines, vorticity, and isotherm patterns are presented to interpret the flow and thermal transport visualization. Additionally, the time average drag coefficient (C _D ) as well as time and surface average Nusselt number (Nu) for the upstream and downstream cylinders are determined to elucidate the effects of Re and Ri on flow and heat transfer phenomena.     

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.     

Double-Diffusive Natural Convection in a Closed Annulus

A numerical study for steady laminar double-diffusive natural convection within a vertical closed annulus is examined with constant temperature and mass species (concentration) differences imposed across the vertical walls. The annulus has an aspect ratio of 1 and a curvature ratio of 2, while the fluid Prandtl number is 7. In this paper the problem is defined and the numerical solution procedure is validated. Moreover, the effect of buoyancy ratio on the flow structure and rite resulting heal and mass transfer rates is presented. It is determined that buoyancy ratio is the primary factor that defines flow structure, including concentration—dominated (buoyancy force) opposing flow, transitional flow, thermal-dominated flow, or concentration-dominated aiding flow. The relationship for buoyancy ratios, in the range -10 ≤ n ≤ 10, and the average NusseU and Sherwood numbers have been obtained for a thermal Rayleigh number of 50,000 and a Lewis number of 5. Future papers wilt include the effect of thermal Rayleigh number, Lewis number, and various geometric parameters on the flow structure and heat and nusi transfer.     

MHD Mixed Convection in a Channel with a Triangular Cavity

A numerical study has been carried out in an open channel, which have a heated triangular cavity at the bottom wall. The remaining walls of the channel are adiabatic. Flow inlets to the channel with uniform velocity and fully developed flow are accepted at the exit of the channel. Steady state mixed convection by laminar flow has been studied by numerically solving governing equations to obtain flow field and temperature distribution under the magnetic field and Joule effect. Equations are solved via the Galerkin weighted residual finite element technique. Calculations are performed for different governing parameters such as Hartmann number (10 ≤ Ha ≤ 100), Reynolds number (100 ≤ Re ≤ 2,000), Rayleigh number (10³ ≤Ra ≤ 10⁵), Joule parameter (0 ≤ J ≤ 5), and Prandtl number (1 ≤ Pr ≤ 10). It is found that heat transfer decreases with an increasing of the Hartmann number especially at higher values of Rayleigh number. Fluid temperature at the exit of the channel also decreases with increasing of Hartmann number. Fluid temperature at the outlet of the channel becomes higher at low Reynolds number and higher Rayleigh number. However, it decreases with the decreasing of the Reynolds number.     

Mixed convection from a spheroid in Bingham plastic fluids: Effect of buoyancy-assisted flow

ABSTRACT

In this work, laminar mixed convection from an isothermal spheroidal particle immersed in a Bingham plastic fluid is studied numerically in the buoyancy-assisted regime. The results reported herein encompass the following ranges of conditions: Reynolds number, 0.1 ≤ Re ≤ 100; Prandtl number, 10 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 100; Richardson number, 0 ≤ Ri ≤ 8; and aspect ratio of the spheroid, 0.2 ≤ e ≤ 5. In particular, consideration is given to the effect of shape and orientation of the particle on the detailed flow and temperature fields (in terms of streamlines, iso-vorticity, and isotherm contours), morphology of the yielded–unyielded regions, and the local and surface-averaged Nusselt number. All else being equal, the propensity for flow separation is seen to be greater for oblates (e < 1) than that for prolates (e > 1). In both cases, this reduces with the increasing Bingham number and/or the Richardson number. Both drag coefficient and the Nusselt number show a positive dependence on the Bingham number as well as on the Richardson number. Overall, the drag coefficient increases as the particle shape changes from an oblate to prolate, whereas the reverse trend is obtained for the average Nusselt number, which is in line with the general inference that more drag corresponds to more heat transfer. Finally, the average Nusselt number is correlated with the pertinent dimensionless parameters (Re, Pr, Bn, Ri, e) via a simple correlation, thereby enabling its prediction for intermediate values of the parameters and/or in a new application.     

Forced Convection Heat Transfer in Power-Law Fluids Around a Semicircular Cylinder at Incidence

Two-dimensional steady flow and convective heat transfer of power-law fluids past a semicircular cylinder are investigated in the reported work. The heated semicircular cylinder is placed in an unconfined domain at different angles facing the incoming free-stream flow of power-law fluids having a generalized Prandtl number (Pr) = 100. Particular emphasis is given to studying the effect of angle of incidence (0 ≤ α ≤ 180°) on fluid dynamics and thermal transport around the semicircular object for varying Reynolds number (10 ≤ Re ≤ 40) and power-law index (0.4 ≤ n ≤ 1.8). A finite volume-based method is adopted for the numerical computation. The flow and heat transfer phenomena are visualized through the streamline and isotherm profiles at various operating conditions. Also, the pressure coefficient, drag coefficient, and Nusselt number on the surface of the object are presented and discussed.     

Mixed Convection in a Vertical Channel with Discrete Heat Sources Using a Porous Matrix

In this work, we present the mixed convection air-cooling of two identical heat sources mounted in a vertical channel by using a porous matrix. The flow field is governed by the Navier–Stokes equation in the fluid region, the Darcy–Brinkman–Forchheimer equation in the porous region, and the thermal field by the energy equation. The effects of the Richardson number, Darcy number, thermal conductivity, and thickness of the porous matrix on the flow and heat transfer were studied. Results show that a better cooling is obtained for the channel completely filled with a porous material, except the components, with the Richardson number (Ri = Gr/Re² = 0.25), where Gr = 10⁴ is the Grashof number and Re = 200 is the Reynolds number, and for all Darcy numbers (10^?5 ≤ Da ≤ 10^?3). It was also seen that for Gr/Re² = 20, where the buoyancy effect is stronger, the average Nusselt number with porous matrix is higher than without porous matrix for all Richardson numbers (Ri = 0.25, 1, 10, and 20). As a result, we can economize the energy of the fan. Finally, the insertion of the porous matrix with high thermal conductivity ameliorates the cooling of the heat sources.