Buoyancy driven vortex flow and its stability in mixed convection of air through a blocked horizontal flat duct heated from below

Experimental flow visualization combined with transient temperature measurement are carried out here to explore the possible stabilization of the buoyancy drive vortex flow in mixed convection of air in a bottom heated horizontal flat duct by placing a rectangular solid block on the duct bottom. Two acrylic blocks having dimensions 40 × 20 × 5 mm³ (block A) and 40 × 20 × 10 mm³ (block B) are tested. The blocks are placed on the longitudinal centerline of the duct bottom at selected locations. How the location and orientation of the rectangular block affect the stability of the regular vortex flow is investigated in detail. Experiments are conducted for the Reynolds number varying from 3 to 30 and Rayleigh number from 3000 to 6000, covering a wide range of the buoyancy-to-inertia ratio. For longitudinal vortex flow, the presence of either block near the duct entry causes the onset points of the longitudinal rolls to move significantly upstream especially for the roll pair directly behind the block. Besides, the longitudinal vortex flow in the exit portion of the duct is destabilized by the block. The transverse vortex flow is found to be only slightly affected by the block when it is placed in the exit half of the duct. Significant deformation of the transverse rolls is noted as they pass over the block. However, they restore to their regular shape in a short distance. Substantial decay in the transient flow oscillation results in the region right behind the block. Elsewhere the flow oscillates at nearly the same frequency and amplitude as that in the unblocked duct. When the block is placed near the duct entry, stabilization of the vortex flow behind the block is more pronounced. This flow stabilization is more prominent for block B with its height being twice of block A. Placing the block with its long sides normal to the forced flow direction can also enhance the flow stabilization. For the mixed longitudinal and transverse vortex flow, placing the block near the duct inlet causes the transverse rolls to change to regular or deformed longitudinal rolls in the duct depending on the buoyancy-to-inertia ratio and orientation of the block. The flow stabilization by the block is substantial. Again the stabilization of the mixed vortex flow can be enhanced by increasing the block height and length and by placing the block with its long sides normal to the forced flow direction.     

Stationary transverse rolls and U-rolls in limiting low Reynolds number mixed convective air flow near the convective threshold in a horizontal flat duct

Combined experimental flow visualization and temperature measurement are carried out in the present study to explore the buoyancy driven vortex flow patterns in a limiting low Reynolds number mixed convective air flow through a bottom heated horizontal flat duct. In Particular, attention is paid to the flow approaching the natural convection limit (Re=0) for Re=1.0 and 2.0 with the Rayleigh number near the critical level for the onset of convection for 1200?Ra?4000. Results from the flow visualization have revealed two unfamiliar vortex flow patterns which were not seen in our earlier study [Int. J. Heat Mass Transfer 44 (4) (2001) 705]. One is characterized by the stable stationary transverse rolls in the duct entry and stable longitudinal rolls in the downstream. Another is in the form of U-rolls. The relations of these two patterns with those reported in the literature from analytical, numerical and experimental studies are discussed. Moreover, stable longitudinal rolls along with nonperiodic traversing waves, and mixed longitudinal and transverse rolls as well as irregular cells which appear in the higher Reynolds number for 3.0?Re?5.0 are also noted here. The temporal and spatial characteristics of the unfamiliar vortex flows are inspected in detail. In addition, the flow formation processes leading to the two unfamiliar vortex flow structures are also examined carefully. During the flow formation we noted merging of longitudinal and transverse rolls to form U-rolls, splitting of rolls into cells and the reverse process of cell integration into rolls, aside from the generation of the longitudinal and transverse rolls. Finally, a flow regime map is provided to delineate various vortex flow structures observed in this study and in the previous study (cf. the above-mentioned reference) driven by the slightly supercritical and subcritical buoyancies for 1.0?Re?5.0.     

Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate

The fluid flow and heat transfer induced by the combined effects of the mechanically driven lid and the buoyancy force within rectangular enclosures were investigated in this work. The fluid filled enclosures are heated and lid-driven either on the upper or on the lower horizontal wall, thermally isolated on the right vertical wall, and cooled on the other walls. The basis of the investigation was the numerical solutions of the equations for the conservation of mass, momentum, and energy transport using the finite difference method. The effects of the flow governing parameters including the Richardson and the Prandtl numbers, and the length-to-height aspect ratio, respectively, in the range 10⁻²  Ri  10², 10⁻³  Pr  10, and 1  AR  4 for a fixed Reynolds number, Re = 100, were studied. The results are presented in the form of the hydrodynamic and thermal fields, and the profiles for vertical and horizontal components of velocity, temperature, and the local heat flux. The fluid flow and energy distributions within the enclosures and heat flux on the heated wall are enhanced by the increase in the Richardson number. While an increase in the Prandtl number improves the heat flux on the heated wall, an increase in aspect ratio suppresses it. The results can be used as base line data in the design of systems in which mixed convection heat transfer in rectangular enclosures occurs.     

Visualization of mixed convective vortex rolls in an impinging jet flow of air through a cylindrical chamber

In this study a combined buoyancy and inertia driven vortex flow in an air jet impinging onto a heated circular plate confined in a cylindrical chamber simulating that in a vertical single-wafer rapid thermal processor for semiconductor manufacturing is investigated experimentally by flow visualization. A copper plate is used here to simulate the wafer for its better uniformity of the surface temperature and air is used to replace the inert gases. We concentrate on how the inlet gas flow rate, temperature difference between the wafer and air jet, and chamber pressure affect the vortex flow. The results show that typically the flow in the chamber is in the form of two-roll structure characterized by a circular vortex roll around the air jet along with another circular roll near the side wall of the chamber. Both rolls are somewhat deformed. The rolls are generated by the reflection of the jet from the wafer and by the deflection of the wall boundary layer flow along the wafer surface by the upward buoyancy due to the heated wafer. At low buoyancy and inertia the vortex rolls are steady and axisymmetric. At increasing buoyancy associated with the higher temperature difference and chamber pressure, the inner roll becomes slightly smaller and the outer roll becomes correspondingly bigger. Moreover, at a higher gas flow rate the inner roll is substantially bigger. Based on the present data, a correlation equation is provided to predict the location where the two rolls contact each other, providing the approximate size of the rolls. Moreover, at high buoyancy and inertia the flow becomes time dependent and does not evolve to a steady state.     

Unsteady mass transfer in mixed convective heat flow from a vertical plate embedded in a liquid-saturated porous medium with melting effect

This paper numerically studies the transient mass transfer in mixed convective heat flow with melting effect from a vertical plate in a liquid saturated porous medium in the presence of aiding external flow. The governing equations are transformed into the non-dimensional form by using pseudo similarity coordinate (ζ) and dimensionless time (ξ). The resulting two dimensional boundary value problem (BVP) is then solved by the method of lines (MOLs) with the central finite difference and Newton's iteration to obtain the entire numerical solutions for all transient process from the initial stage (ξ = 0) to the final state (ξ = 1). The results show the rate of dynamic mass transfer at the solid–liquid interface is reduced with increasing the melting strength. In addition, the response time and the rate of the dynamic mass transfer for aiding buoyancy are respectively shorter and faster than those for opposing buoyancy from the transient molecular diffusion to the steady mixed convection in a porous medium with melting effect.     

Non-Darcy mixed convection from a horizontal plate embedded in a nanofluid saturated porous media

The problem of steady mixed convection boundary-layer flow over an impermeable horizontal flat plate embedded in a porous medium saturated by a nanofluid is numerically studied. The model used for the nanofluid incorporates only the effect of the volume fraction parameter. The surface of the plate is maintained at a constant temperature and a constant nano-particle volume fraction. The resulting governing partial differential equations are transformed into a set of two ordinary (similar) equations, which are solved using the bvp4c function from Matlab. A comparison is made with the available results in the literature, and the present results are in very good agreement with the known results. A representative set of numerical results for the reduced heat transfer from the plate, dimensionless velocity and temperature profiles is graphically and tabularly presented. Also, the salient features of the results are analyzed and discussed.     

Laminar-turbulent transition behavior of fully developed air flow in a heated horizontal tube

I have experimentally studied the influence of the buoyancy force and inlet flow conditions on the laminar-turbulent transition process of fully developed air flow in a heated horizontal tube with uniform wall heat flux at modified Rayleigh number 3.1×10⁶. Eight time-series of the air temperature were simultaneously obtained using eight thermocouples positioned within the tube along a vertical line passing through the tube's axis. I have studied the time and space dependence of the transition behavior by analyzing these instantaneous time-series. By calculating a set of Lyapunov exponents and the correlation dimension of the time-series of a single thermocouple, these transitional flows are found to be chaotic.     

Natural convective flow in an inclined lid-driven enclosure with a heated thin plate in the middle

Natural convection heat transfer from a heated thin plate located in the middle of a lid-driven inclined square enclosure has been analyzed numerically. Left and right of the cavity are adiabatic, the two horizontal walls have constant temperature lower than the plate’s temperature. The study is formulated in terms of the vorticity-stream function procedure and numerical solution was performed using a fully higher-order compact (FHOC) finite difference scheme on the 9-point 2D stencil. Air was chosen as a working fluid (Pr = 0.71). Two cases are considered depending on the position of heated thin plate (Case I, horizontal position; Case II, vertical position). Governing parameters, which are effective on flow field and temperature distribution, are Rayleigh number values (Ra) ranging from 10³ to 10⁵ and inclination angles γ (0° ? γ < 360°). The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and Nusselt number (Nu). It is found that fluid flow and temperature fields strongly depend on Rayleigh numbers and inclination angles. Further, for the vertical located position of thin plate heat transfer becomes more enhanced with lower γ at various Rayleigh numbers.     

Fluid flow and heat transfer of mixed convection adjacent to vertical heated plates placed in uniform horizontal flow of air

Experiments have been carried out for mixed convective flows of air adjacent to the vertical heated plates in uniform horizontal forced flows to investigate relationships between the flow and the heat transfer. The experiments cover the ranges of the Reynolds and modified Rayleigh numbers: Re_L = 160 to 2300 and Ra_L^* = 4.3 × 10⁵ to 2.0 × 10⁸. The flow fields over the plates are visualized with particles and smoke. The results show that a stagnation point moves downward away from the center of the plate when the surface heat flux is beyond a critical value. The condition where the stagnation point begins to move is expressed with non‐dimensional parameters as: Gr_L^*/Re_L^2.5 = 0.15. Profiles of measured local heat transfer coefficients are smooth even at the stagnation points in all the cases examined. When buoyancy effect is sufficiently weak, the coefficients agree well with those of the wedge flow. With increasing the surface heat flux, the coefficients are augmented to approach asymptotically the boundary layer solution of natural convection along a vertical heated plate. Finally, forced, mixed, and natural convection regimes are classified by the non‐dimensional parameter (Gr_L^*/Re_L^2.5). © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20256     

Heat transfer characteristics of a boundary-layer flow driven by a power-law shear over a semi-infinite flat plate

The hydrodynamic and thermal boundary layer similarity flows driven past a semi-infinite impermeable flat plate by a power-law shear with asymptotic velocity profile U_∞(y)=βy^−1/2 (y→∞,β>0) is considered (y denotes the coordinate normal to the plate). Assuming that the buoyancy and viscous dissipation effects may be neglected, the special cases of an isothermal and of an adiabatic flat plate are examined both analytically and numerically.     

MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition

A numerical approach has been used to study the heat and mass transfer from a vertical plate embedded in a porous medium experiencing a first-order chemical reaction and exposed to a transverse magnetic field. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The momentum, energy, and concentration equations derived as coupled second-order, ordinary differential equations are solved numerically using a highly accurate and thoroughly tested finite difference algorithm. The effects of Biot number, thermal Grashof number, mass transfer Grashof number, permeability parameter, Hartmann number, Eckert number, Sherwood number and Schmidt number on the velocity, temperature, and concentration profiles are illustrated graphically. A table containing the numerical data for the plate surface temperature, the wall shear stress, and the local Nusselt and Sherwood numbers is also provided. The discussion focuses on the physical interpretation of the results as well their comparison with the results of previous studies.     

Free convection boundary layer flow over vertical and horizontal flat plates embedded in a porous medium under mixed thermal boundary conditions

A similarity analysis of the steady free convection boundary layer over vertical and horizontal surfaces embedded in a fluid-saturated porous medium with mixed thermal boundary conditions is performed in this paper. New variables relating the similarity solutions of the Darcian velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter have been obtained. Boundary layer velocity and temperature profiles have been determined numerically for some values of the mixed thermal boundary condition parameter ε and the similarity exponent m.     

Extended Oberbeck-Boussinesq approximation study of convective instabilities in a porous layer with horizontal flow and bottom heating

A study of the onset of convective instabilities in a porous layer with a horizontal basic flow is performed by including the effects of viscous dissipation and pressure work in the energy balance. Firstly, the so-called extended Oberbeck-Boussinesq approximation, i.e. the model based on the enthalpy formulation of the energy balance, is adopted. Then, the results for the marginal stability condition are compared with those obtained by the so-called Chandrasekhar approximation, i.e. the model based on the internal-energy formulation of the energy balance. It is shown that a marked discrepancy occurs between the two approaches, that becomes specially evident for high values of the Gebhart number. According to the extended Oberbeck-Boussinesq approximation, the effects of the viscous dissipation and of the pressure work result in a stabilization of the basic flow. On the contrary, the Chandrasekhar approximation predicts a destabilization of the basic flow induced by the viscous dissipation. The destabilization can be so intense that the onset of convective rolls may occur even in the absence of a boundary temperature difference, i.e. with a vanishing Darcy-Rayleigh number.     

A further investigation of effects of jet-disk separation distance on steady mixed convective vortex flow resulting from a confined impinging air jet

We extend our previous study [J.C. Hsieh, T.F. Lin, Effects of jet-to-disk separation distance on the characteristics of mixed convective vortex flow in an impinging air jet confined in a cylindrical chamber, Int. J. Heat Mass Transfer 48 (2005) 511–525] here to further investigate how the jet-disk separation distance H affects the mixed convective vortex flow resulting from a round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. The experiment is conducted for the jet-disk separation distance varying from 40.0 to 60.0 mm and the jet flow rate is varied from 0 to 12.0 slpm (standard liter per minute) for the jet Reynolds number Re_j ranging from 0 to 1623. The temperature difference between the disk and the air injected into the chamber is varied from 0 to 25.0 °C for the Rayleigh number Ra ranging from 0 to 507,348. The data from the present study for the ratio H/D_j = 4–6 are compared with our previous study for H/D_j = 1–3. The results indicate that the critical jet Reynolds numbers for the onsets of the secondary and tertiary inertia-driven rolls and for the onset of the buoyancy-driven roll vary nonmonotonically with the jet-disk separation distance due to the complicate changes of the vortex flow structure with H. In the steady vortex flow, both the primary inertia-driven roll and the buoyancy-driven roll get larger at increasing jet-disk separation distance before they contact with each other for H/D_j = 1 and 2. But for H/D_j ≧ 3 the primary roll and buoyancy roll do not always grow at increasing H. Finally, empirical correlations are proposed for the critical conditions leading to the onsets of the inertia- and buoyancy-driven vortex rolls.     

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.     

Transient natural convective heat transfer of a low-Prandtl-number fluid from a heated horizontal circular cylinder to its coaxial triangular enclosure

Transient natural convective heat transfer of liquid gallium, which has a Prandtl number of 0.023 at 310 K, from a heated horizontal circular cylinder to its coaxial triangular enclosure is studied numerically by employing the control volume method. Two orientations of the triangular cylinder are investigated and the Grashof number is varied from 10⁴ to 10⁷. Development of natural convection is presented by means of the evolutions of the average Nusselt number over the outer triangular wall. Temporal stages during the course of development are identified and demonstrated through representative snapshots of streamlines and isotherms. The time-averaged Nusselt number is scaled with Grashof number for both conduction- and convection-dominated regimes. It is found that by placing horizontally the top side of the triangular cylinder, the convective flow becomes more stable and the overall heat transfer is enhanced. In addition, pitchfork bifurcation is explored quantitatively and its onset times are predicted as well.     

Effects of aspect ratio on mixed convection in a horizontal rectangular duct with heated and cooled side walls

This paper describes the effect of aspect ratio on mixed convection in a horizontal rectangular duct with heated and cooled side walls numerically and experimentally. In the numerical analysis, fluid flow and temperature distributions for Ri=1.61, Pr=6.99, Re=100 and aspect ratio, Ar=0.2–10, were obtained by solving dimensionless governing equations using the SIMPLE procedure. The QUICK scheme was applied to the convective term of these equations. In the experimental analysis, the flow behavior for A_r=0.5–2 was visualized by the dye‐injection method. Numerical results showed that the swirl flow was generated along the flow direction, and its pitch length was influenced by A_r. The pitch length was the shortest when A_r=0.5–1, and this tendency was the same in numerical results and experimental results. The heat transfer behavior was also discussed corresponding to the flow, and the heat transfer ratio was highest at A_r=1 in 0.2 ≤ A_r ≤ 10. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20391