Buoyancy-aided momentum and heat transfer in a vertical channel with a built-in square cylinder

This study focuses on the confined upward flow and heat transfer around a square cylinder under the effect of aiding buoyancy (Richardson number, Ri=0–1) in the vertical channel for Reynolds number (Re)=1–40 and blockage ratio (BR)=25–50% for the air as working fluid. Flow is found to be steady and symmetric for the range of settings. For Re≤2, no separation zone occurs for BR=25% and 30%. However, for BR=50%, no wakes are observed for Re≤3. The onset of flow separation takes place between Re=2 and 3 for BR=25% and 30%; whereas, for BR=50%, it exists between Re=3 and 4, irrespective of the value of Ri. Heat transfer correlations have also been obtained at different values of Re, BR and Ri.     

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 Channel-Confinement and Rotation on the Two-Dimensional Laminar Flow and Heat Transfer across a Cylinder

Effect of channel-confinement and rotation on the flow and heat-transfer across a cylinder is studied for various blockage ratio (β = 0–50%), nondimensional rotational velocity (α = 0–2), and Reynolds number (Re = 35–170). The cylinder is maintained at a constant wall temperature with air as the working fluid. Criss-cross motion of the shed-vortices is noticed for the channel-confined flow across a rotating cylinder at intermediate blockage ratio. The effect of channel-confinement (rotation) is an enhancement (reduction) in the drag force and heat transfer. A downward lift force is generated under the influence of counterclockwise rotation, which increases with increasing blockage ratio. Rotation and channel-confinement have a stabilizing effect and can be used for flow control.     

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.     

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.     

Power‐law flow and heat transfer over an inclined square bluff body: effect of blockage ratio

Flow and heat transfer of non‐Newtonian power‐law fluids over an inclined square cylinder placed inside a channel are studied numerically at low Reynolds numbers. In particular, calculations are carried out for Reynolds number (Re) = 1–40; power‐law index (n) = 0.4–1 and blockage ratio (β) = 12.5–50% at a Prandtl number (Pr) = 50. An increase in blockage ratio results in an increase in the total drag coefficient and decrease in the wake length. The Strouhal number and the root mean square value of the lift coefficient increase with the increasing Reynolds number for the fixed values of blockage ratio and power‐law index. The average Nusselt number increases with power‐law index and/or blockage ratio. The maximum enhancement in heat transfer is approximately 49, 41, and 35% for the values of blockages of 50, 25, and 12.5%, respectively, as compared to the corresponding Newtonian value. The average Nusselt number for the inclined square cylinder (at α = 45^°) is always greater than the average Nusselt number for the regular square cylinder (at α = 0). Finally, simple expressions of drag and Nusselt number have been established for the above range of settings. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 167‐196, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21071     

Combined convection heat transfer in a channel with two ribs attached to one wall

Two-dimensional calculations were performed for combined convection heat transfer in a channel with two ribs attached to one wall, following a previous study on the forced convection case without buoyancy. The flow is heated from the surfaces of both ribs and the present study dealt with the two cases of buoyancy-assisted flow and buoyancy-opposing flow. The effect of Reynolds number, Re_L, and modified Richardson number, Ri^*, was examined keeping the space between ribs, σ, and blockage ratio, τ, constant (σ = 3.0, τ = 0.5). Increasing the magnitude of buoyancy, unsteady flows predicted by the present calculations are stabilized in both cases. Serious deterioration of Nusselt number on the second rib suddenly occurs in a certain range of Ri^* due to the flow stabilization. This is because flow unsteadiness plays an important role for heat transfer enhancement as was described in a previous study. However, in buoyancy-assisted flow, a similar deterioration of Nusselt number also appears on the second rib even if flow remains steady. This is caused by the disappearance of a strong rotating flow which exists in the cavity between both ribs and keeps the fluid in the cavity cooler. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 379–394, 1999     

Computational study of thermal buoyancy from two confined cylinders within a square enclosure wifth single inlet and outlet ports

This article is devoted to investigating the mixed convection arising from two equally hot circular cylinders embedded in a square cavity of adiabatic surfaces. This cavity is filled with an incompressible fluid and contains single entry and outlet orifices. The heated cylinders are assumed to be arranged side-by-side with a fixed gap within the square cavity. Based on some simplifying assumptions, the nonlinear governing equations that express the principle of conservation of mass, momentum, and energy are obtained and numerically solved using a Computational fluid dynamics package ANSYS-CFX with finite volume technique. Pertinent results showing the roles of embedded parameters such as Richardson number (Ri = 0 to 1) and Reynolds number (Re = 1 to 40) at Prandtl number (Pr = 1) on the overall fluid flow and temperature patterns are graphically depicted in the form of representative streamlines and isotherms. The values of average Nusselt number and total drag coefficient (C_D) for both representative cylinders are also computed and discussed. Generally, an increase in buoyancy force augments the effectiveness of heat transfer only of the down cylinder. Also, a rise in Re and/or Ri numbers augment the flow instability.     

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.     

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.     

Two-dimensional laminar fluid flow and heat transfer in a channel with a built-in heated square cylinder

A numerical investigation was conducted to analyze the unsteady flow field and heat transfer characteristics in a horizontal channel with a built-in heated square cylinder. Hydrodynamic behavior and heat transfer results are obtained by the solution of the complete Navier–Stokes and energy equations using a control volume finite element method (CVFEM) adapted to the staggered grid. The Computation was made for two channel blockage ratios (β=1/4 and 1/8), different Reynolds and Richardson numbers ranging from 62 to 200 and from 0 to 0.1 respectively at Pr=0.71. The flow is found to be unstable when the Richardson number crosses the critical value of 0.13. The results are presented to show the effects of the blockage ratio, the Reynolds and the Richardson numbers on the flow pattern and the heat transfer from the square cylinder. Heat transfer correlation are obtained through forced and mixed convection.     

Effects of shear-thinning nature and opposing buoyancy from a square geometry in a confined framework

Numerical computations were brought up to study the effect of opposing buoyancy mixed convection (Ri?=?0 to ??1) flow of power law shear-thinning fluids past a confined cooled square bluff body at Prandtl numbers (Pr)?=?1, 50 and Reynolds numbers (Re)?=?1–40. Irrespective of the n, Ri, Pr, and Re, the flow separation is delayed with increasing confinement (β). The vortex shedding and flow separation start earlier for shear-thinning fluids than Newtonian fluid. For opposing buoyancy (Ri?Pr (except for n?=?0.2, Ri?=??1). Also, the periodic unsteady transition appears at some higher value of Re on increasing Ri for fixed Pr. The drag coefficient (C_D) value reduces with the decrease in n, whereas the maximum C_D is noted for Newtonian fluids. The maximum augmentation in the heat transfer was reached about 9 and 36% on comparing with Newtonian fluids and forced convection case, respectively, and also the corresponding maximum compression in heat transfer was found about 15 and 5%, respectively. The numerical results have also been correlated for C_D and the Colburn j_h factor values for various Re, Pr, Ri, and n. In surplus, the effects of wall confinement ranging from β?=?25 to 50% on flow separation and engineering output parameters were studied in a steady regime.     

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.     

Accurate numerical simulation for non-Darcy double-diffusive mixed convection in a double lid-driven porous cavity using SEM

The non-Darcy double-diffusive mixed convection in a double lid-driven porous cavity with two thermosolutal sources is numerically investigated in this article, depicting the effects of different physical parameters on heat and mass transfer in the drying chamber. The flow is generated due to the motion of the horizontal moving lids and the buoyancy produced by the temperature and concentration gradients. The governing equations are discretized by the Legendre spectral element method (SEM) with high accuracy, and an improved time-splitting method is developed to deal with the coupled pressure and velocity in the Brinkman-Forchheimer extended Darcy model. The effects of Darcy number (Da?=?10^?5～10^?1), Richardson number (Ri?=?10^?2～10¹), and buoyancy ratio (Br = ?5?～?5) are investigated, and numerical results are analyzed by contours of streamline, isotherm, heatline, isoconcentration, and massline in detail. Results reveal the pattern of heat and mass transfer with the variation on significant parameters by the average Nusselt and Sherwood numbers on the moving lids of the cavity.     

Cross-Buoyancy Mixed Convection Around a Confined Triangular Bluff Body

Two-dimensional numerical simulations are carried out to understand the effects of cross-buoyancy on the confined flow and heat transfer characteristics over an equilateral triangular bluff body at low and intermediate Reynolds numbers (Re). For a fixed Richardson number (Ri), an average cylinder Nusselt number increases with increasing Re. However, the average Nusselt number shows a soft response toward increasing Ri. The critical Re for the onset of periodic unsteady flow increases with increasing cross-buoyancy (Ri). A simple heat transfer correlation is also obtained to relate the values of average cylinder Nusselt number, Re, and Ri.     

Effect of triangular porous layer on the transfer of heat and species in a channel-open cavity

This paper addresses the heat and species transfer in a composite cavity linked with a horizontal channel. The cavity comprises a triangular porous layer and one of its vertical sides is exposed to a high temperature and concentration. The mathematical conservation equations are solved numerically using the Galerkin finite element method. The ranges of Reynolds and Richardson numbers are taken to ascertain laminar flow, Re = 50–250 and Ri = 0.1–100. The size of the porous layer is quantified by the thickness of the porous layer H_p = 0.25–1. The problem is studied for two cases of heat and species sources; the opposing case, when the active side is on the right, and assisting case, when the active side is on the left. Results reveal that for specified conditions, the triangular porous layer increases Nusselt and Sherwood numbers by 30% and 32%, respectively, more than the horizontal porous layer. The opposing case gives maximum convective heat transfer, where for Ri = 0.01, the Nusselt number is higher by 61% and 134% for Re = 50 and 250, respectively, while for Ri = 100, the percentages increase are 67% and 43%.     

MHD heat transfer and entropy production of an Al2O3-water nanofluid in a horizontal cylinder

This paper deals with the effect of magnetic fields (B_r, B_θ, B_z) applied in r-, θ-, z-directions, respectively, on entropy production and heat transfer and in a horizontal cylinder filled with an Al₂O₃-water nanofluid. The results are verified using literature data. For different Richardson, Ri, and Hartmann numbers, Ha, the nanoparticles (NP) ϕ, and magnetic field orientation combined effect provide a better understanding of heat transfer and entropy optimization. The results indicate that entropy production and heat transfer and rates depend on magnetic field intensity and direction. Also, increasing Ri and NP increases entropy generation and heat transfer. Finally, applying a radial magnetic field promotes a better convective heat transfer and minimizes entropy production.     

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.     

Heat transfer enhancement in a cubical cavity filled with a hybrid nanofluid

Mixed convection heat transfer in a cubical cavity with an isothermally heated blockage inside filled with a hybrid nanofluid (HBNF) is numerically studied. The natural convection is created by the temperature difference between the hot block and the cold lateral walls, while the forced convection is generated by moving the upper wall. The influence of some variables, like the aspect ratio (0.1 ≤ r ≤ 0.5), Richardson number (0 ≤ Ri≤ 20), Reynolds number (50 ≤ Re ≤ 200), volume concentration of nanoparticles (0 ≤ ϕ ≤ 0.06), and the concentration ratio (2:8, 5:5, and 8:2) on the flow field and heat transfer is analyzed. A comparison between hybrid and mono nanofluids (NFs) is realized to investigate the energy transport enhancement. Results show that the increase of each parameter causes an increase of average Nusselt number Nu_avg and improves the heat transfer; besides the use of HBNF gives better Nu_avg values. Three correlations of the effect of r, ϕ, Ri, and Re on Nu_avg are determined for both hybrid and mono NFs.     

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.