Laminar fully developed forced-convection flow within an asymmetrically heated horizontal double-passage channel

The present analytical study is concerned with the thermal characteristics of hydrodynamically and thermally fully developed flow in an asymmetrically heated horizontal channel, which is divided into two passages (by means of a baffe) for two separate flow streams. Each stream will have its own pressure gradient and hence its own individual velocity profile. Based upon bulk mean temperature of the whole flow in the channel, Nusselt numbers and the generalized temperature profiles in the fully developed regions are determined by means of integration of the momentum and energy equations. Three possible combinations of the thermal boundary conditions on the two wall plates of the channel are considered: isothermal-isothermal, isothermal-isoflux, and isoflux-isoflux. Results show that the thermal characteristics of the fully developed flow could be significantly affected by the position of the baffle, the pressure-gradient ratio by the two separate streams, and thermal boundary conditions on the channel walls.     

Direct numerical simulation of heated vertical air flows in fully developed turbulent mixed convection

Turbulent mixed convection associated with upward and downward flows in heated vertical tubes is investigated using the direct numerical simulation technique. With increasing heat flux, the skin friction first decreases and then increases in upward heated flow, while it changes little in downward heated flow. The heat transfer coefficient exhibits a similar trend in upward heated flow, but it monotonically increases in downward heated flow. The log laws of the mean-velocity and temperature profiles are valid for downward heated flow but not for upward heated flow. Finally, the influence of buoyancy on turbulent transport of momentum and heat is elucidated by the ‘external’ and ‘structural’ effects.     

A study on un‐fully developed slug flow in a vertical tube

Gas‐liquid co‐current vertical slug flow was studied in a vertical Plexiglas tube. Taylor bubbles and liquid slug lengths and their rising velocities were measured by means of a pair of conductivity probes under un‐fully developed flow conditions. The influences of the superficial velocity of gas and liquid on slug flow parameters were examined. Using statistical analysis on the length of Taylor bubbles, the probability distribution of the length of the Taylor bubbles was obtained, which obeyed a normal distribution under a significance level of α = 0.05. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 235–242, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20063     

Large eddy simulation of heated vertical annular pipe flow in fully developed turbulent mixed convection

The goal of the present study was to perform a large eddy simulation of vertical turbulent annular pipe flow under conditions in which fluid properties vary significantly, and to investigate the effects of buoyancy on the turbulent structures and transport. Isoflux wall boundary conditions with low and high heating are imposed. The compressible filtered Navier-Stokes equations are solved using a second order accurate finite volume method. Low Mach number preconditioning is used to enable the compressible code to work efficiently at low Mach numbers. A dynamic subgrid-scale stress model accounts for the subgrid-scale turbulence. Comparisons were made with available experimental data. The results showed that the strong heating and buoyant force caused distortions of the flow structure resulting in reduction of turbulent intensities, shear stress, and turbulent heat flux, particularly near the wall.     

On the transition from partial to fully developed subcooled flow boiling

The subject of the present study is to relate the boiling heat transfer process with experimentally observed bubble behaviour during subcooled flow boiling of water in a vertical heated annulus. It presents an attempt to explain the transition from partial to fully developed flow boiling with regard to bubble growth rates and to the time that individual bubbles spend attached to the heater surface.Within the partial nucleate boiling region bubbles barely change in size and shape while sliding a long distance on the heater surface. Such behaviour indicates an important contribution of the microlayer evaporation mechanism in the overall heat transfer rate. With increasing heat flux, or reducing flow rate at constant heat flux, bubble growth rates increase significantly. Bubbles grow while sliding, detach from the heater, and subsequently collapse in the bulk fluid within a distance of 1-2 diameters parallel to the heater surface. This confirms that bubble agitation becomes a leading heat transfer mode with increasing heat flux. There is however, a sharp transition between the two observed bubble behaviours that can be taken as the transition from partial to fully developed boiling. Hence, this information is used to develop a new model for the transition from partial to fully developed subcooled flow boiling.     

Thermally fully developed electroosmotic flow through a rectangular microchannel

This study investigates the velocity and temperature distributions of the thermally fully developed electroosmotic flow through a rectangular microchannel. Based on linearized Poisson–Boltzmann (PB) equation, Navier–Stokes equation and thermally fully developed energy equation, analytical solutions of normalized velocity, temperature and Nusselt number are derived. They greatly depend on the ratio K of characteristic scale of the rectangular microchannel to Debye length, width to height ratio α and Joule heating to heat flux ratio S. By numerical computation, we found that for prescribed electrokinetic width K, increased S yields greater temperature. For small K, the variations of the temperature θ are larger than those of large K. The dependence of temperature on S is more significant for a small K, while at a larger K the temperature profiles are almost identical. In addition, we illustrate the Nusselt number Nu variations with S, α and K.     

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     

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     

Velocity measurements in the free convection flow above a heated horizontal cylinder

The fluid dynamics of the free convection water flow above a heated horizontal cylinder were investigated using particle image velocimetry. Velocity measurements were obtained in three orthogonal planes, with each plane acquired independently in time. The experiment was performed for a Rayleigh number of 1.33 × 10⁶ and for water heights above the cylinder surface of H/D = 1, 2, 4, 6, 8, and 12. The top water surface was open to room air, and the height of the free surface introduced different effects of vertical confinement. For all water heights studied, the plume above the cylinder and its interaction with the free surface were observed. For water heights of H/D = 4 and 6, the appearance of a swaying motion was captured in the plane perpendicular to the cylinder axis, and a meandering motion was detected in the other two orthogonal planes. A vortex was observed to form alongside of the plume and rise to the free surface, where it detached from the plume structure and moved along the free surface. Vortex dynamics and the physical characteristics of the swaying and meandering motions appeared to be interdependent, providing a possible relation between vortex formation, swaying, and meandering. Comparisons with previous analytical and experimental results highlight the complicated three-dimensional flow structure that governs heat transfer from the cylinder.     

Scaling heat transfer in fully developed turbulent channel flow

An analysis is given for fully developed thermal transport through a wall-bounded turbulent fluid flow with constant heat flux supplied at the boundary. The analysis proceeds from the averaged heat equation and utilizes, as principal tools, various scaling considerations. The paper first provides an accounting of the relative dominance of the three terms in that averaged equation, based on existing DNS data. The results show a clear decomposition of the turbulent layer into zones, each with its characteristic transport mechanisms. There follows a theoretical treatment based on the concept of a scaling patch that justifies and greatly extends these empirical results. The primary hypothesis in this development is the monotone and limiting Peclet number dependence (at fixed Reynolds number) of the difference between the specially scaled centerline and wall temperatures. This fact is well corroborated by DNS data. A fairly complete qualitative and order-of-magnitude quantitative picture emerges for a complete range in Peclet numbers. It agrees with known empirical information. In a manner similar to previous analyses of turbulent fluid flow in a channel, conditions for the existence or nonexistence of logarithmic-like mean temperature profiles are established. Throughout the paper, the classical arguments based on an assumed overlapping of regions where the inner and outer scalings are valid are avoided.     

Analytical study of two-phase flow pressure-drop oscillations in a vertical heated tube

This paper focuses on an analytical investigation of two-phase flow pressure-drop oscillations in a vertical heated tube with the two-fluid model employed in the computer code MINI-TRAC. Pressure-drop oscillation is an important phenomenon appearing in a two-phase flow channel with compressible volume existing in the upstream region. In a previous investigation, pressure-drop oscillations with superimposed density-wave oscillations were observed. In this work, numerical calculations have been carried out to predict the characteristics of pressure-drop oscillations and the range of instabilities. We also offer an application of the two-fluid model to the analysis of pressure-drop oscillations at low pressure in a heated channel with a small inner diameter. Good agreement between the simulations and experiments was obtained. © 1999 Scripta Technica, Heat Trans Jpn Res, 27(8): 597–608, 1998     

Surfactant effects on passive scalar transport in a fully developed turbulent flow

Direct numerical simulations of fully developed turbulence in an open channel were performed. Effects of surfactants on heat transfer and the underlying turbulent structures were investigated. As surface elasticity is increased turbulent fluctuations are damped and the mean surface temperature is decreased. A surface strain model is introduced to explain this behavior in a heuristic manner. A nondimensional parameter representing the ratio of surface elastic forces to local inertial forces is introduced. It is concluded that for values of the parameter of order one, surfactants have strong effects on surface turbulence, whereas an effectively clean surface can be obtained for parameter values less than O(10⁻³).     

An analytical method for solving exact solutions of the convective heat transfer in fully developed laminar flow through a circular tube

This paper proposes an exact solution to the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions, and one initial condition. The mathematical derivation utilized the separation of variables method where several stages were completed to reach the solution to the Graetz problem.     

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.     

Prediction of turbulent flow structure in a fully developed rib-roughened narrow rectangular channel

Fully developed turbulent water-flow structure over one-side repeated-ribs in narrow two-dimensional rectangular channels was investigated experimentally by Particle Image Velocimetry (PIV) and analytically by the standard κ-ɛ and nonlinear κ-ɛ turbulent models. Two rib-pitch to height ratios (p/k) of 10 and 20 were investigated while the rib height was held constant at 4 mm. The rib height-to-channel equivalent diameter ratio (k/De) was 0.1. The streamwise mean velocity and turbulent kinetic energy distributions at six selected axial stations from the center rib for the two Reynolds number (Re) of 7,000 and 20,000 were obtained and compared with the predicted one. The performance ability in predicting separating and reattaching turbulent water-flow between the standard κ-ɛ and nonlinear κ-ɛ models had yielded no clear conclusion. A large-scale turbulent eddy was generated by the rib promoter and then propagated into the mainstream flow, which led to the deformation of the velocity profile. The turbulent kinetic energy was increased about two times higher at p/k = 20 than that at p/k =10 under the two Reynolds numbers. The effect of the p/k value and the Reynolds number (Re) on reattachment length (XR) was investigated and showed that the p/k and Re had no significant effect on the reattachment length beyond a critical value of Re = 15,000 where XR was found to be approximately 4 times of the rib height under water-flow condition.     

Visualization of heat flow in a vertical channel with fully developed mixed convection

A study on visualization of heat flow in three channels with laminar fully developed mixed convection heat transfer is performed. The first channel is filled with completely pure fluid; the second one is completely filled with fluid saturated porous medium. A porous layer exists in the half of the third channel while another half is filled with pure fluid. The velocity, temperature and heat transport fields are obtained both by using analytical and numerical methods. Analytical expression for heat transport field is obtained and presented. The heatline patterns are plotted for different values of Gr/Re, thermal conductivity ratio, Peclet and Darcy numbers. It is found that the path of heat flow in the channel strongly depends on Peclet number. For low Peclet numbers (i.e., Pe = 0.01), the path of heat flow is independent of Gr/Re and Darcy numbers. However, for high Peclet numbers (i.e., Pe = 5), the ratio of Gr/Re, Darcy number and thermal conductivity ratio influence heatline patterns, considerably. For the channels with high Peclet number (i.e., Pe = 5), a downward heat flow is observed when a reverse flow exits.     

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.     

DNS of fully developed turbulent heat transfer of a viscoelastic drag-reducing flow

A direct numerical simulation (DNS) of turbulent heat transfer in a channel flow with a Giesekus model was carried out to investigate turbulent heat transfer mechanism of a viscoelastic drag-reducing flow by additives. The configuration was a fully-developed turbulent channel flow with uniform heat flux imposed on both the walls. The temperature was considered as a passive scalar with the effect of buoyancy force neglected. The Reynolds number based on the friction velocity and half the channel height was 150. Statistical quantities such as root-mean-square temperature fluctuations, turbulent heat fluxes and turbulent Prandtl number were obtained and compared with those of a Newtonian fluid flow. Budget terms of the temperature variance and turbulent heat fluxes were also presented.