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.     

Mixed convective flow in a bottom heated lid‐driven cubical cavity: Energy streamlines and field synergy

Analysis of three dimensional natural convective lid‐driven cavity flow is carried out numerically. The top wall is assumed to slide in its own plane at a constant speed. Isothermal temperature is maintained at horizontal walls in which the bottom wall is assumed to be at a higher temperature than the top wall. Governing equations of this problem, expressed in dimensionless form are solved by using the finite volume method. Numerical results are computed for the control parameters arising in the system, namely, the Reynolds number (Re) and Richardson number (Ri) in the range of 100 ≤ Re ≤ 1000 and 0.001 ≤ Ri ≤ 10. The contours of isotherms, streamlines, Vortex corelines, energy pathlines, and field synergy are used to visualize the flow and thermal characteristics. The simulated results are corroborated with those available in the literature. When Re = 100 and 400 with growth of Ri there are "free" energy streamlines and they exhibited symmetric nature near the boundaries. The participation of convective thermal energy and kinetic energy is insignificant compared to conductive thermal energy, where the velocity components are modest. When Re = 1000 with increase of Ri, "trapped" energy streamlines are detected. Energy streamlines occupy substantial part. This is due to the result of high Re, with increasing Ri, kinetic energy and convective thermal energy get dominated and hence "trapped" streamlines formed. As Re increases, synergy angle increases for distinct Ri values. So the synergy between temperature and velocity gets worse. The synergy angle of buoyant‐aiding flow is high while the buoyant‐opposing flow is significantly less than that of forced convection flow when Ri = 1. This gives the relation between temperature field and velocity at buoyant‐aiding flow, which is at the worst situation leading to increasing average Nusselt number.     

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.     

Unstable vortex flow and new inertia-driven vortex rolls resulting from an air jet impinging onto a confined heated horizontal disk

An experiment combining flow visualization and temperature measurement is carried out here to investigate the possible presence of new inertia-driven vortex rolls and some unique characteristics of the time-dependent mixed convective vortex flow in a high-speed round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. How the jet Reynolds and Rayleigh numbers and jet-to-disk separation distance affect the unique vortex flow characteristics is examined in detail. Specifically, the experiment is conducted for the jet Reynolds number varying from 0 to 1623 and Rayleigh number from 0 to 63,420 for the jet-to-disk separation distance fixed at 10.0, 20.0 and 30.0 mm. The results indicate that at sufficiently high Re_j the inertia-driven tertiary and quaternary rolls can be induced aside from the primary and secondary rolls. At an even higher Re_j the vortex flow becomes unstable due to the inertia-driven flow instability. Only for H = 20.0 mm the flow is also subjected to the buoyancy-driven instability for the ranges of the parameters covered here. Because of the simultaneous presence of the inertia- and buoyancy-driven flow instabilities, a reverse flow transition can take place in the chamber with H = 20.0 mm. At the large H of 30.0 mm the flow unsteadiness results from the mutual pushing and squeezing of the inertia- and buoyancy-driven rolls since they are relatively large and contact with each other. It is also noted that the critical Re_j for the onset of unsteady flow increases with ΔT for H = 10.0 and 20.0 mm. But for H = 30.0 mm the opposite is true and raising ΔT can destabilize the vortex flow. Based on the present data, flow regime maps delineating the temporal state of the flow are provided and correlating equations for the boundaries separating various flow regimes are proposed.     

On the mixed convective carbon nanotube flow over a convectively heated curved surface

In this article, mixed convective boundary layer stream of nanofluid flow with carbon nanotube as nanoparticles and transmission of heat over a coiled stretched surface are studied. The influence of magnetic orientation and velocity slip is also encountered in this problem. Two classes of carbon nanotubes, SWCNT and MWCNT, are considered as nanoparticles and water as a pure liquid. The foremost leading partial differential equations (PDEs) are formulated through curvilinear coordinate system subjected to proper boundary conditions. To simplify this nonlinear PDE‐associated model, we have employed a compatible similarity conversion and acquired the nonlinear dimensionless ordinary differential equations (ODEs). To determine the requisite numerical solution of the transformed problem, a shooting procedure embedded with RK‐4 technique has been applied. Various pictorial attempts have been initiated against different parametric inputs to reveal the hydrothermal scenario. Some physical quantities like skin friction and Nusselt numbers are calculated to investigate flow distribution inside the preferred system. A comparison with earlier research depicts parallel outcomes. Results assured that velocity is a cumulative function with positive increment of curvature parameter, but an opposite scenario is shown for temperature for both type of nanofluids. The amount of heat transition has been declined against the improvement of the magnetic parameter.     

Laser schlieren measurement of vertical flow past a heated horizontal circular cylinder

Flow past a heated horizontal circular cylinder in the vertically upward direction has been experimentally studied using a monochrome schlieren technique. Both free convection ((Gr)^1/3Re)=0 and mixed convection ((Gr)^1/3Re)=1011, 1055, 1095 and 1133 cases have been studied. The Reynolds number based on the cylinder diameter is set at 102 for the mixed convection, and four heating levels have been utilized with Grashof numbers of Gr=975, 1105, 1240 and 1370. The temperature distribution of the plume, the Strouhal number and the schlieren images have been reported. The vortex shedding frequency decreases with increasing Grashof number and a complete suppression of vortex shedding takes place at Grashof number of 1370. The wake is seen to become visibly narrow during the suppression of vortex shedding. The nondimensional temperature profile inside the plume is a strong function of Grashof number for free convection in comparison to that of mixed convection.     

Conjugate free convection above a cooled finite horizontal flat plate embedded in a porous medium

We investigate conjugate free convection in a semi-infinite porous medium above a cold finite plate. Numerical solutions of the coupled governing equations for the fluid and the plate regions are obtained, and an analytical method is developed to predict the average temperature of the conjugate boundary and the Nusselt number.     

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.     

Laminar natural convection of power‐law fluids over a horizontal heated flat plate

Natural convection of power‐law fluids over a horizontal flat plate with constant heat flux is studied. The stretching transformations relating the similarity forms of the boundary layer velocity, pressure, and temperature profiles are applied to the governing boundary layer equations. The resultant set of coupled ordinary differential equations are solved analytically and numerically using the integral method and the finite difference method, respectively. The results are presented for the details of the velocity and temperature fields for various values of the non‐Newtonian power‐law viscosity index (n) and the generalized Prandtl number (Pr*). At a fixed value of the viscosity index, increasing the Prandtl number increases the skin friction and wall temperature. For Pr* > 1, a lower viscosity index results in larger wall skin friction, temperature scale, and thermal boundary layer thickness, and thus lower Nusselt number. The reverse trend is observed for Pr* < 1. By using an integral solution and the numerical results, a semi‐analytical correlation for the Nusselt number is obtained, valid for and .     

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.     

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.     

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.     

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.