Simulation for flow across heated square cylinders

The thermal lattice Boltzmann method is used to examine forced convection heat transfer from six inline heated square cylinders for Re = 100 at 0.5 ≤ s/d ≤ 4.0, where s is the distance between the surfaces of two cylinders and d is the cylinder size. Such a heat transfer is transient in nature for which the present work reports heat transfer regimes such as synchronous, quasiperiodic and chaotic. For 0.5 ≤ s/d ≤ 1.5 the heat transfer is synchronous, for 1.5 ≤ s/d ≤ 3.0 it is quasiperiodic and for 3.0 ≤ s/d ≤ 4.0 it is chaotic in nature at Re = 100. These regimes are confirmed through cylinder Nusselt number signals, its power spectra, and heat wake interference. The appearance of heat transfer regimes for inline heated cylinders is similar to the appearance of flow regimes for inline unheated cylinders except for the fact that transition from synchronous to quasiperiodic regime occurs at s/d = 1.5 for heat transfer and at s/d = 1.1 for flow. The synchronous heat transfer regime is characterized by a single heat wake that envelopes all cylinders while quasiperiodic heat transfer regime is characterized by the formation of thermal blobs in the gap between cylinders. A chaotic heat transfer regime is characterized by the shedding of thermal blobs and interference of thermal blobs by downstream cylinders. Regardless of spacing, the average Nusselt number encountered by cylinders is smaller than that for the isolated cylinder. The novelty of the work is that transitions occurring in the flow of heat are considered for an understanding of heat flow from bluff bodies.     

Variation of Nusselt number with flow regimes behind a circular cylinder for Reynolds numbers from 70 to 30 000

The dependence of the Nusselt number in the separated flow behind a circular cylinder to the cross-flow varies greatly with Reynolds number according to the flow regimes, i.e., laminar shedding, wake transition, and shear-layer transition regimes. The Nusselt number at the rear stagnation point, Nu_r/Re^0.5, increases with Reynolds number in the laminar shedding regime (Re < 150) and the shear-layer transition regime (3000 < Re < 15 000), corresponding to the shortening of the vortex formation region. On the contrary, the Nusselt number, Nu_r/Re^0.5, decreases with Reynolds number in the regime in which the wake develops to a complex three-dimensional flow (300 < Re < 1500), corresponding to the lengthening of the vortex formation region. This distinctive change affects the correlation of the overall Nusselt number with Reynolds number, i.e., the exponent of the Reynolds number has a lower value for 200 < Re < 2000 than that for 70 < Re < 200 and Re > 2000.     

Numerical study on natural convection in a square enclosure containing a rectangular heated cylinder

In this paper, the natural convection in a square enclosure with a rectangular heated cylinder is investigated via the lattice Boltzmann method. A detailed study is conducted on the effect of the cylinder width and the Rayleigh number on the fluid flow and heat transfer. The flow structures and heat transfer patterns are classified into eight buoyant regimes, i.e., four steady regimes, two periodic regimes, one multiple periodic regime, and one chaos regime, two of which are reported for the first time.     

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.     

Wall–bounded flow and heat transfer around a circular cylinder at low Reynolds and Hartmann numbers

A two–dimensional numerical simulation is performed following a finite volume approach to analyze the forced convection heat transfer for the hydromagnetic flow around a circular cylinder at low Reynolds numbers. The cylinder is placed within a rectangular channel subjected to externally applied magnetic fields and acted upon by the magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conductive fluid. The magnetic field is applied either along the streamwise or transverse directions. The simulation is carried out for the range of Reynolds number 10 ≤ Re ≤ 80 with Hartmann number 0 ≤ Ha ≤ 10 and for different Prandtl numbers, Pr = 0.02 (liquid metal), 0.71 (air), and 7 (water) for a blockage ratio β = 0.25. The flow is steady for the above range of conditions. Apart from the channel wall, the magnetic field provides additional stability to the flow as a result of which the recirculation region behind the obstacle reduces with increasing magnetic field strength for a particular Reynolds number. The rate of heat transfer is found almost invariant at low Re whereas it increases slightly for higher Re with the applied magnetic field. The heat transfer increases as usual with the Reynolds number for all Hartmann numbers. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21025     

Heat transfer around a circular cylinder in separated air flow

An experimental study has been conducted to determine the heat transfer characteristics around a circular cylinder attached to the separated flow of air shed from a fence. The fence was located vertically to the flow with a height of H = 40 mm. d/H was constant at 0.638, where d is the cylinder diameter of 25.5 mm. X/H were 0.50 and 0.775 and Y/H ranged from 0.525 to 1.50, where X and Y are, respectively, the distances between the axis of the cylinder and the front face of the fence, and the bottom wall of the test section. The Reynolds number based on the cylinder diameter and the velocity of the undisturbed flow ranged from 1.9 × 10⁴ to 6.0 × 10⁴. It was found that the maximum local Nusselt number changes drastically in the vicinity of Y/H = 1.0–1.11 and that the maximum mean Nusselt number occurs in the neighborhood of Y/H = 1.24–1.43 for X/H = 0.50 and 1.3–1.4 for X/H = 0.775. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 211–226, 1999     

Lattice Boltzmann simulation of MHD mixed convection in a two‐sided lid‐driven square cavity

In this paper the effects of a magnetic field on mixed convection flow in a two‐sided lid‐driven cavity have been analyzed by the lattice Boltzmann method (LBM). The Hartmann number varied from Ha = 0 to 100. The study has been conducted for different Richardson numbers (Ri) from 0.01 to 100 while the direction of the magnetic field was investigated in the x‐direction. Consequences demonstrate that the heat transfer augments with an increment of the Richardson number for different Hartmann numbers for two cases. The heat transfer declines with the growth of the magnetic field for various Richardson numbers for two cases. The difference between the values of heat transfer for the two cases at variant parameters is negligible but the trend of fluid flow for the two cases is multifarious. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20402     

Melting of a vertical ice cylinder inside a rotating cylindrical cavity filled with binary aqueous solution

The melting of a vertical ice cylinder into a homogeneous calcium chloride aqueous solution inside a rotating cylindrical cavity with several rotating speeds is considered experimentally. The melting mass and temperature are measured on four initial conditions of the solution and four rotating speeds of the cavity. The temperature of the liquid layer becomes uniform by the mixing effect resulting from cavity rotation and it enhances the melting rate of the ice cylinder. As the cavity‐rotating speed increases, the melting rate increases. The dimensionless melting mass is related to the Fourier number and the rotating Reynolds number in each initial condition, therefore an experimental equation that is able to quantitatively calculate the dimensionless melting mass is presented. It is seen that the melting Nusselt numbers increase again in the middle of the melting process. The ice cylinder continues to melt in spite of the small temperature difference between the ice cylinder and the solution. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 359–373, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20211     

LBM simulation of forced convective channel flow containing multiple obstacles: Effects of obstacles height and position

We examine the effects of the obstacles, height, and position on the forced convective flow in a channel having three obstacles on the lower wall of the channel. All the walls of the channel and obstacles are retained at a constant temperature while the fluid with temperature more than the walls are entered into the channel. The flow governing equations, vorticity equation, and energy equation are solved numerically by using the lattice Boltzmann method (LBM) together with the finite difference successive over relaxation method (SOR). The effects of obstacles height, h, and distance, d, between the obstacles on the streamlines and isotherms are presented. To investigate the heat transfer rate for changing the height and position of the obstacles, local Nusselt number distribution and the mean Nusselt number distribution are also presented. It is observed that vortices, produced backward to each obstacle, increase axially with increasing the height of each obstacle. Also vortices, produced between obstacles, change its shape with decreasing the distance between obstacles. It is asserted that heat transfer rate can be increased by extending only the height of first obstacle.     

Heat transfer on a horizontal rotating cylinder near a flat plate in a cross‐flow

An experimental study of heat transfer on a horizontal rotating cylinder near a flat plate was performed. The cylinder and plate were set in a cross‐flow. Temperature distribution and coefficients of local heat transfer were measured by a Mach–Zehnder interferometer. Flow visualization was made using smoke. Rotating Reynolds numbers (Re_r) and cross‐flow Reynolds numbers (Re_d) were varied from 0 to 2000. The spaces between cylinder and plate were varied from 1 × 10^?3 m to 5 × 10^?3 m. The rotating direction of cylinder was changed clockwise or counterclockwise. The following results are obtained: When the space between the rotating cylinder and flat plate is the same as the displacement thickness on the plate, the heat transfer on the cylinder near the plate has the best performance. We have procured the empirical equation of heat transfer from a rotating cylinder near the flat plate in the cross‐flow. 8 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20329     

Effects of wall confinement and rheology of non‐Newtonian nanofluids on mixed convection phenomenon of a square cylinder in a vertical channel

The mixed convective momentum and heat transfer phenomena of confined square cylinders in non‐Newtonian nanofluids are numerically investigated. The experimental thermophysical properties of alumina‐water‐based nanofluids are adopted from literature and these nanofluids obey shear‐thinning power‐law type non‐Newtonian behavior. The square cylinder is confined in a vertical channel with a confinement ratio of 0.1333. The flow is assumed to be two‐dimensional and the fluid is allowed to flow in upward direction across the confined square cylinder in the vertical channel. The aiding/opposing buoyancy in the flow is incorporated in terms of Richardson number (Ri ) in the range of –2 to 2. The ranges of other dimensionless parameters considered are: Reynolds number, Re : 1 to 40; and volume fraction of nanoparticles, ?: 0.005 to 0.045. This range of volume fraction of nanoparticles (i.e., ? = 0.005 to 0.045) corresponds to the power‐law index (n ) of a non‐Newtonian nanofluid in the range of n = 0.88 to 0.5, respectively. Prior to obtaining new results, the solution methodology is validated with existing literature counterparts. Finally, effects of the Reynolds number, Richardson number, and the rheology of non‐Newtonian nanofluids on streamline patterns, surface pressure, surface vorticity, drag coefficients, isotherm contours, local and average Nusselt numbers are delineated.     

Natural-convection heat transfer around a horizontal array of heated cylinders in air

An experimental study was performed to determine the natural-convection heat transfer characteristics of horizontal cylinders placed in a horizontal line in air. Local heat transfer coefficients were measured for three- and nine-cylinder arrays in various cylinder-spacing arrangements. As a result, it was found that there were no major differences in heat transfer coefficient among cylinders, other than for the array-edge cylinders. The mean value of all cylinders was clearly different from that of the array-edge cylinders. Based on a simple consideration for the effect of cylinder-spacing on heat transfer coefficient, correlation equations were proposed for each kind of heat transfer coefficient mentioned above. All the experimental heat transfer coefficients were expressed well by these equations. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(6): 410–419, 1996     

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.     

Flow and heat transfer around a single row of circular cylinders

A numerical investigation of flow and heat transfer around a single row of circular cylinders was conducted using a boundary-fitted coordinate system. Numerical calculations for center-to-center distance between cylinders L/d=2.0, 2.5, 3.3, and ∞ were made of water flows in the Reynolds number range from 75 to 500. Numerical values of average Nusselt number for uniformly heated cylinders are in relatively good agreement with those obtained from experiments in water (Prandtl number Pr ≒ 8). The interaction of wake flows behind cylinders, observed in the experiments, was also found to occur with decreasing cylinder spacing L/d. © 1997 Scripta Technica, Inc. 25(3): 192–200, 1996     

Wall‐Confined Flow and Heat Transfer Around a Square Cylinder at Low Reynolds and Hartmann Numbers

This article discusses the results obtained through a two‐dimensional numerical simulation following a finite volume approach on the forced convection heat transfer for the hydromagnetic flow around a square cylinder at low Reynolds and Hartmann numbers. The magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conducting fluid is assumed to take place in a rectangular channel subjected to externally imposed magnetic fields and the cylinder is fixed within the channel. The magnetic fields may be applied either along the streamwise or transverse directions. Simulations are performed for the range of kinetic Reynolds number 10 ≤ Re ≤ 60 with Hartmann number 0 ≤ Ha ≤ 15 and for different thermal Prandtl numbers, Pr = 0.02 (liquid metal), 0.71 (air), and 7 (water) for a blockage ratio β = 0.25. A steady flow can be expected for the above range of conditions. Besides the channel wall, the magnetic field imparts additional stability to the flow as a consequence of which the recirculation region behind the obstacle reduces with increasing magnetic field strength for a particular Re. The critical Hartmann numbers for the complete suppression of flow separation in the case of a transversely applied magnetic field are computed. The rate of heat transfer is found almost invariant at low Re whereas it increases moderately for higher Re with the applied magnetic field. The heat transfer increases in general with the Reynolds number for all Hartmann numbers. Finally, the influence of obstacle shape on the thermohydrodynamic quantities is noted. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 459–475, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21091     

Structure of a two-dimensional vortex behind a highly heated cylinder

The two-dimensional vortex structure behind a highly heated cylinder has been studied experimentally. The air velocity was set at 1.0 m/s. The surface temperature of the heated cylinder was varied up to 600 °C. Particle image velocimetry (PIV) was used to measure the two-dimensional instantaneous and average velocities. Just downstream of the heated cylinder, the vortex was intensified by increasing the wall temperature of the heated cylinder. The vortex frequency decreased when the wall temperature increased. This indicates that the local kinematic viscosity plays a key role in the vortex structure. As a result, the vortex frequency of the heated cylinder can be expressed as a function of the Strouhal and Reynolds numbers, when the local kinematic viscosity is reasonably estimated by taking into account the effect of the wall heating. © 1999 Scripta Technica, Heat Trans Asian Res, 28(8): 706-718, 1999     

Lattice Boltzmann simulation of natural convection and heat transfer from multiple heated blocks

This study is aimed to investigate the natural convection heat transfer from discrete heat sources (similar to heated microchips) using Bhatnagar‐Gross‐Krook lattice Boltzmann method via graphics process unit computing. The simulation is carried out separately for three and six heated blocks model for different Rayleigh numbers and fixed Prandtl number, $Pr=0.71$ (air). The uniformly heated blocks are placed at the bottom wall inside a rectangular enclosure. The enclosure is maintained by the cold temperature at its left and right walls. The top and bottom surface is maintained by adiabatic conditions apart from the regions where blocks are attached to the bottom wall. The numerical code is validated with the benchmark heat transfer problem of side‐heated square cavity as well as with an experimental study for one discrete heat source. The rate of heat transfer is presented in terms of the local Nusselt and average Nusselt number for each block. It is found that the heat transfer rate becomes maximized in the leftmost and rightmost blocks due to the adjacent cold walls. It is found that the number of blocks and their positions play a substantial role in determining their collective performance on the heat transfer rate.     

Heat transfer for flow boiling of water and critical heat flux in a half‐heated round tube under low‐pressure conditions

Heat transfer for flow boiling of water and critical heat flux (CHF) experiments in a half‐circumferentially heated round tube under low‐pressure conditions were carried out. To clarify the flow patterns in the heated section, experiments in the round tube under the same conditions were also carried out, and their results were compared. The experiments were conducted with atmospheric‐pressure water in test sections with inner diameter D = 6 mm, heated length L = 360 mm, inlet water subcooling ΔT_in = 80 K, and mass velocity G from 0 to 2000 kg/(m²·s) for the half‐circumferentially heated round tube and from 0 to 7000 kg/(m²·s) for the full‐circumferentially heated tube. The experimental data demonstrated that the wall temperature near the outlet of the half‐circumferentially heated tube remained almost the same until CHF. It was found that burnout occurred when the flow regime changed from churn flow to annular flow, and the liquid film on the heated wall dried out although liquid film on the unheated wall remained. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(3): 149–164, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10022     

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.     

Experimental study of heat transfer coefficient with rectangular baffle fin of solar air heater

This paper presents an experimental analysis of a single pass solar air collector with, and without using baffle fin. The heat transfer coefficient between the absorber plate and air can be considerably increased by using artificial roughness on the bottom plate and under the absorber plate of a solar air heater duct. An experimental study has been conducted to investigate the effect of roughness and operating parameters on heat transfer. The investigation has covered the range of Reynolds number Re from 1259 to 2517 depending on types of the configuration of the solar collectors. Based on the experimental data, values of Nusselt number Nu have been determined for different values of configurations and operating parameters. To determine the enhancement in heat transfer and increment in thermal efficiency, the values of Nusselt have been compared with those of smooth duct under similar flow conditions.