Effect of channel-confinement and aiding/opposing buoyancy on the two-dimensional laminar flow and heat transfer across a square cylinder

The effect of channel-confinement of various degree (blockage ratio of 10%, 30% and 50%) on the upward flow and heat transfer characteristics around a heated/cooled square cylinder is studied by considering the effect of aiding/opposing buoyancy at −1 Ri 1, for Re = 100 and Pr = 0.7. With increasing blockage ratio, the minimum heating (critical Ri) required for the suppression of vortex shedding decreases up to a certain blockage ratio (=30%), but thereafter increases. The influence of buoyancy and channel-confinement on the recirculation length, drag and lift coefficient, pumping power, Strouhal number and heat transfer from the cylinder, is also investigated.     

Vortex shedding and heat transfer dependence on effective Reynolds number for mixed convection around a cylinder in cross flow

The influence of surface heating of a circular cylinder on the wake structure and heat transfer in the range of Reynolds number (Re) for which parallel vortex shedding occurs, is investigated numerically for different values of the buoyancy parameter, Gr. The role of buoyancy induced baroclinic vorticity on the wake formation is addressed in the present study. The variation of Strouhal number and Nusselt number with the ’effective Reynolds number’, is analyzed for different values of cylinder to free stream temperature ratio. Both Strouhal number and the rate of heat transfer increases monotonically with the increase of the effective Reynolds number. The validity of the correlations, which have been established by several authors, between the effective Reynolds number and Strouhal/ Nusselt number for forced convection, is examined in the mixed convection regime. The curves between the effective Reynolds number and the computed data for Strouhal number and Nusselt number do not collapse for the range of temperature ratio considered here. The flow field is found to be asymmetric and the cylinder experiences a negative lift. The drag coefficient increases steadily with the rise of surface temperature.     

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.     

Buoyancy-aided/opposed convection heat transfer for unsteady turbulent flow across a square cylinder in a vertical channel

The Large Eddy Simulation (LES) and SIMPLE-C method coupled with preconditioned conjugate gradient methods have been employed to study the effect of aiding/opposing buoyancy on the turbulent flow field and heat transfer across a square cylinder in a vertical channel. The level of wall-confinement (blockage ratio of 10%, 30% and 50%) was changed with a constant Reynolds number (5000) under various Richardson numbers (−1 to 1). With increasing blockage ratio, the buoyancy effect is becoming weaker on the Nusselt number for the square cylinder. The turbulent heat transfer past the square cylinder can be improved by increasing the blockage ratio.     

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.     

Effect of Buoyancy Ratio on Double-Diffusive Natural Convection in a Porous Rhombic Annulus

This paper reports on the effect of buoyancy ratio due to both heat and mass transfer on natural convection in a porous enclosure between two isothermal concentric cylinders of rhombic cross sections. For negative values of the buoyancy ratio, buoyancy forces due to heat and mass transfer are in opposite directions (opposing mode), while for positive values they are in the same direction (aiding mode). Numerical results demonstrate that the flow strength increases as the absolute value of the buoyancy ratio increases. In the opposing mode, the eye of the vortex flow is located in the lower half of the enclosure, while in the aiding mode it is positioned in the upper part of the annulus. The average Nusselt and Sherwood number values increase as the absolute value of the buoyancy ratio moves away from 1, with values obtained in the aiding mode being higher than corresponding values achieved in the opposing mode. A comparison is also made between the computed average Nusselt and Sherwood number values and similar ones obtained in a circular annulus having the same inner and outer perimeters as the rhombic enclosure. Predictions indicate large percent difference in values, demonstrating that circular geometries cannot be exploited to accurately predict heat and mass transfer in complex geometries.     

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.     

Mixed Convection Heat Transfer From an Equilateral Triangular Cylinder in Cross Flow at Low Reynolds Numbers

A two-dimensional numerical study is undertaken to investigate the influences of cross buoyancy on the vortex shedding phenomena behind a long heated equilateral triangular cylinder for the low-Reynolds-number laminar regime. The flow is considered in an unbounded medium; however, fictitious confining boundaries are chosen on the lateral sides to make the problem computationally feasible. Numerical calculations are performed by using a finite-volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid system. The range of Reynolds number is chosen to be 10–100 with a fixed Prandtl number, 0.71. The mixed convection effect is studied for the Richardson number range of 0–1. The effects of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as the overall drag and lift coefficients, local and surface average Nusselt numbers, and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers.     

Laminar boundary-layer analysis of simultaneous mass and heat transfer in natural convection around A horizontal cylinder

An analytical study is presented of the combined heat and mass transfer characteristics of natural convection flow around a horizontal circular cylinder. The surface of the cylinder is assumed to be at uniform temperature and uniform concentration. Specific cases of diffusion of water vapour and naphthalene into air are studied. The results indicate that the local Nusselt number and the local wall shear stress increase and decrease from the pure free convection values as the buoyancy force from species diffusion assists and opposes, respectively, the thermal buoyancy force. The local Nusselt number and the local wall shear stress are found to increase with the decrease of the Schmidt number, whereas the surface mass transfer increases with increasing Schmidt number. The Sherwood number is found to become more effective as the thermal buoyancy force increases. The cumulative tangential mass flow rate is found to increase with the increase of the polar angle from the lower pole and is strongly dependent on the nature and magnitude of the concentration to thermal buoyancy force ratio, especially at low Schmidt number.     

Effect of wall proximity on forced convection in a plane channel with a built-in triangular cylinder

A numerical investigation has been carried out to analyze the effect of wall proximity of a triangular cylinder on the heat transfer and flow field in a horizontal channel. Computations have been carried out for Reynolds numbers (based on triangle width) range of 100–450 and gap widths (a/h) 0.5, 0.75 and 1. Results are presented in the form of instantaneous contours of temperature, vorticity, with some characteristics of fluid flow and heat transfer; such as time-averaged and instantaneous local Nusselt number, skin friction coefficient along bottom channel's wall, and drag coefficient. Results show that approaching triangular cylinder in the wall, removes vortex shedding and subsequently the heat transfer rate decreases at low Reynolds number. By decreasing the vortex shedding, drag coefficient decrease as triangular cylinder approaches the wall of the channel. The variation of vortex formation has a more significant suppression effect on the skin friction coefficient than the Nusselt number.     

Steady mixed convective flow and heat transfer from tandem square cylinders in a horizontal channel

The two-dimensional laminar steady mixed convective flow and heat transfer around two identical tandem square cylinders confined in a horizontal channel are simulated by the high-accuracy multidomain pseudo-spectral method. The blockage ratio of the channel is chosen as 0.1, whereas the spacing between the cylinders is fixed with four widths of the cylinder. The Prandtl number is fixed at 0.7, the Reynolds number (Re) is studied in the range 5?≤?Re?≤?60, and the Richardson number (Ri) demonstrating the influence of thermal buoyancy ranges from 0 to 1. Numerical results reveal that, with the thermal buoyancy effect, the mixed convective flow remains steady. The variations of the overall drag and lift coefficients and the Nusselt numbers, are presented and discussed. Furthermore, the influence of thermal buoyancy on fluid flow and heat transfer is discussed and analyzed.     

Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration

This work examines the natural convection heat and mass transfer near a sphere with constant wall temperature and concentration in a micropolar fluid. A coordinate transformation is used to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. For micropolar fluids, higher viscosity tends to retard the flow and thus decreases the natural convection heat and mass transfer rates from the sphere with constant wall temperature and concentration. Moreover, the natural convection heat and mass transfer rates from a sphere in Newtonian fluids are higher than those in micropolar fluids.     

Numerical Investigation of Flow and Heat Transfer Characteristics of Two Tandem Circular Cylinders of Different Diameters

Unsteady laminar flow and heat transfer characteristics from a downstream cylinder of two tandem circular cylinders of different in diameters are numerically investigated. The working fluid is air, and the downstream cylinder is isothermal while the upstream cylinder is kept adiabatic. Two-dimensional numerical simulations are carried out for Reynolds numbers of 100 and 200. The ratio of the upstream to downstream cylinder diameters (diameter ratio) and the ratio of the gap distance to the downstream cylinder diameter (gap ratio) are considered in the range of 0.3 to 2 and 0.5 to 4, respectively. Numerical solutions are obtained using the FLUENT® software. The flow parameters such as the rms lift/drag coefficients and Strouhal numbers are computed and analyzed for the diameter ratio and gap ratio intervals investigated. The iso-vorticity lines and isotherms are also generated to understand, identify and analyze the flow and heat transport characteristics. Four basic flow structures are observed and classified as (i) over-shoot, (ii) symmetric-reattachment, (iii) front-side reattachment and (iv) co-shedding flow. The critical spacing, which marks the minimum gap spacing for the vortex formation to begin, depends on the diameter ratio and Reynolds number, and it decreases with increasing Reynolds number. The convective heat transfer phenomenon is observed to be strongly influenced by diameter ratio, gap ratio and Reynolds number. The mean and the local Nusselt number along the perimeter of isothermal cylinder are computed and discussed in connection with the flow characteristics.     

Augmentation of heat transfer from a solid cylinder wrapped with a porous layer

In the present study, the heat transfer from a porous wrapped solid cylinder is considered. The heated cylinder is placed horizontally and is subjected to a uniform cross-flow. The aim is to investigate the heat transfer augmentation through the inclusion of a porous wrapper. The porous layer is of foam material with high porosity and thermal conductivity. The mixed convection is studied for different values of flow parameters such as Reynolds number (based on radius of solid cylinder and stream velocity), Grashof number, permeability and thermal conductivity of the porous material. The optimal value of porous layer thickness for heat transfer augmentation and its dependence on other properties of the porous foam is obtained. The flow field is analyzed through a single domain approach in which the porous layer is considered as a pseudo-fluid and the composite region as a continuum. A pressure correction based iterative algorithm is used for computation. Our results show that a thin porous wrapper of high thermal conductivity can enhance the rate of heat transfer substantially. Periodic vortex shedding is observed from the porous shrouded solid cylinder for high values of Reynolds number. The frequency of oscillation due to vortex shedding is dampened due to the presence of the porous coating. Beyond a critical value of the porous layer thickness, the average rate of heat transfer approaches asymptotically the value corresponding to the case where the heated cylinder is embedded in an unbounded porous medium.     

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.     

Forced convection heat transfer from a circular cylinder in crossflow to air and liquids

Local and average heat transfer by forced convection from a circular cylinder is studied for Reynolds number from 2 × 10³ to 9 × 10⁴ and Prandtl number from 0.7 to 176. For subcritical flow, the local heat transfer measurement indicates three regions of flow around the cylinder: laminar boundary layer region, reattachment of shear layer region and periodic vortex flow region. The average heat transfer in each region is calculated and correlated with the Reynolds number and the Prandtl number. The Nusselt number in each region strongly depends on the Reynolds number and the Prandtl number with different power indices. An empirical correlation for predicting the overall heat transfer from the cylinder is developed from the contributions of heat transfer in these three regions.     

Storage Silos Self Ventilation: Interlinked Heat and Mass Transfer Phenomenon

This work is to better understand heat and mass transfer by natural convection in a vertical, open ended, and porous cylinder. The effects of buoyancy forces and chemical reaction on the natural convection are studied numerically and discussed for a large range of Rayleigh number (Ra _T ), buoyancy ratio (N), and reaction rate (Ak). A map diagram (Ra _T , A, Ak) of the two observed flow types, with and without fluid recirculation, was obtained. The analysis shows that the results strongly depend on the controlling parameters and demonstrates the effect on the recirculating possible flow. Thus, it's confirmed that the rate of heat transfer increases with increasing Rayleigh, and it is particularly sensitive to the values of dimensionless reaction rate (Ak) and aspect ratio (A).     

Natural convective flow of a chemically reacting fluid in an annulus

We examine the heat transfer and flow properties induced by natural convection in an annulus between a square enclosure and a circular cylinder filled with a chemically reacting fluid. During the exothermic reaction process in the reacting fluid, there generates heat that induces natural convection in the annulus. The problem is developed defining the vorticity‐stream function. We solve it with the use of the finite difference method. The results show that two counter‐rotating vortices generate in each half about the vertical symmetry line through the center of the inner cylinder. The lower eddies of the inner vortices get closer and closer with the decrease of the aspect ratio and the increase of the Rayleigh number, Frank‐Kamenetskii number, buoyancy force parameter, and Lewis number. Besides this, the eyes of the outer vortices expose similar characteristics for increasing values of the Rayleigh number and buoyancy force parameter, and for decreasing values of the aspect ratio and the Lewis number. It is remarkable that the flow field and the Nusselt number demonstrate completely distinct characteristics for the Lewis number unity, the aspect ratio equal to 0.1, and in the absence of the buoyancy force parameter.