Turbulent natural convection in a vertical parallel-plate channel with asymmetric heating

Turbulent natural convection in a vertical parallel plate channel has been investigated both experimentally and numerically. The experimental channel is formed of a uniform temperature heater wall and an opposing glass wall. A fibre flow laser doppler anemometer (LDA) is used to measure velocity profiles along the channel. Simultaneous velocity and temperature profile measurements are made at the channel outlet. A commercial computational fluid dynamics (CFD) code is used to simulate heat transfer and fluid flow in the channel numerically. The code is customised building in some low Reynolds number (LRN) k–ε turbulence models. The numerical method used in this study is found to predict heat transfer and flow rate fairly accurately. It is also capable of capturing velocity and temperature profiles with some accuracy. Experimental and numerical data are presented comparatively in the form of velocity, temperature, and turbulent kinetic energy profiles along the channel for a case. Correlating equations are obtained from the numerical results for heat transfer and induced flow rate and, are presented graphically comparing with other studies available in the literature.     

Turbulent natural convection cooling of electronic components mounted on a vertical channel

The paper presents a numerical simulation of conjugate, turbulent natural-convection air cooling of three heated ceramic components, which are identical and mounted on a vertical adiabatic channel. A two-dimensional, conjugate heat transfer model and the standard k–ϵ turbulence model were used to obtain the dynamic and thermal fields. The finite-volume method has been used to solve the model equations throughout the entire physical domain (solid and fluid). After validation of the method with available measurements for a single source, it was applied to investigate the effects on cooling of spacing between the heated electronic components and of the removal of heat input in one of the components. The former modification led to better cooling while the latter can be partially advantageous only when the non-powered components are mounted between the powered ones: this reduces the temperature of the powered components situated downstream from the non-powered component.     

Turbulent heat transfer of natural convection between two vertical parallel plates

We measure heat transfer coefficients of natural convection between two vertical smooth parallel plates heated uniformly in the laminar, transition, and turbulent regions. The heat transfer characteristics are experimentally investigated with changing width, δ, between the vertical parallel plates, wall heat flux, q_w, overall watercourse length, L,of the vertical parallel plate and heating conditions. For natural convection between the vertical parallel plates, in the turbulent region of , the heat transfer is strongly suppressed owing to the effect of combined convection. On the contrary, the heat transfer in the laminar region is enhanced due to the tunnel effect. These tendencies become pronounced with decreasing δ and increasing L.The location of the heat transfer reduction shifts downstream with increasing q_w under a fixed δ. Furthermore, under smaller δ, we cannot clearly distinguish the transition process in accordance with both the heat transfer enhancement in the laminar region and the heat transfer reduction in the turbulent region. © 2001 Scripta Technica, Heat Trans Asian Res, 31(1): 56–67, 2002     

Turbulent plumes evolving in a vertical flow under a mixed convection regime

Turbulent asymmetric thermal plume evolves in a uniform upward flowing fluid in the region of mixed convection, where the far field velocity has a magnitude comparable to the velocities generated by the plume, are examined. In the process, a first order solution of the governing equation about the far stream velocity is obtained. The analytical results are compared with experimental data available in the literature as well as to simulations obtained using computational fluid dynamics. It is shown that in both cases the agreement is good.     

Flow visualization of natural convection in a vertical channel with asymmetric heating

A dynamical study of the flow in an asymmetrically heated vertical plane channel has been conducted experimentally. Experiments were carried out in water for three aspect ratios and for a range of modified Rayleigh numbers corresponding to the boundary layer flow regime. The flow dynamics were characterized by means of visualization techniques based on laser tomography using discrete and continuous tracers. Flow visualizations were carried out in the plane of symmetry of the channel along its entire height. The investigations focused more specifically on the influence of the aspect ratio and the modified Rayleigh number on the flow structure both in steady-state regime and during the transitional phase occurring just after the start of the heating. An upward boundary layer flow is found near the heated wall, accompanied by a reverse flow developing on the opposite side from the top open-end of the channel. In steady state, the reverse flow takes the form of an elongated eight-shaped structure with two main recirculation cells. The length of the upper cell of the eight-shape structure decreases with increasing aspect ratio. For a fixed aspect ratio, the increase in modified Rayleigh number results in a decrease in the penetration of the reverse flow. During the transient the flow structure is shown to evolve from a single cell to a final eight-shaped structure.     

Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel

In this study numerical predictions of local and global entropy generation rates in natural convection in air in a vertical channel symmetrically heated at uniform heat flux are reported. Results of entropy generation analysis are obtained by solving the entropy generation equation based on the velocity and temperature data. The analyzed regime is two-dimensional, laminar and steady state. The numerical procedure expands an existing computer code on natural convection in vertical channels. Results in terms of fields and profiles of local entropy generation, for various Rayleigh number, Ra, and aspect ratio values, L/b, are given. The distributions of local values show different behaviours for the different Ra values. A correlation between global entropy generation rates, Rayleigh number and aspect ratio is proposed in the ranges 10³ ⩽ Ra ⩽ 10⁶ and 5 ⩽ L/b ⩽ 20.     

Natural convection flow due to a heat source in a vertical channel

An analysis is presented of the laminar natural convection flow due to a localized heat source on the centerline of a long vertical channel or pipe whose walls are kept at a constant temperature. Stationary solutions are obtained for infinitely long and finite length channels, the asymptotic limit of infinite Rayleigh numbers is discussed, and an optimal height of the channel is found leading to maximum mass flux and minimum temperature for a given heat release rate.     

Fully developed mixed convection flow in a vertical channel filled with nanofluids

In this paper, the fully developed mixed convection flow in a vertical channel filled with nanofluids is investigated. Analytical solutions for both the buoyancy-assisted and -opposed flow are obtained. Further analysis shows that the analytical solution for the opposing flow is only valid for a certain region of the Rayleigh number Ra in physical sense. Besides, the effects of the nanoparticle volume fraction φ on the temperature and the velocity distributions are then exhibited. It is confirmed that the nanoparticle volume fraction φ plays a key role for improving the heat and mass transfer characteristics of the fluids.     

Large-eddy simulation of combined forced and natural convection in a vertical plane channel

A combined forced and natural convective flow between two vertical plates with different temperatures is studied using large eddy simulation. The numerical simulations were performed with a Grashof number of Gr = 9.6 × 10⁵ and Reynolds number of Re_τ = 150 (based on the wall friction velocity and half channel width). Two sets of dynamic subgrid-scale (SGS) models were tested in the simulation; namely, the set of linear SGS models consisting of the dynamic Smagorinsky SGS stress model (DM) and dynamic eddy diffusivity SGS heat flux model (DEDM-HF), and the set of nonlinear SGS models consisting of the dynamic nonlinear SGS stress model (DNM) and dynamic tensor diffusivity SGS heat flux model (DTDM-HF). The numerical results are compared with the reported direct numerical simulation data. It is found that the resolved and SGS quantities related to the temperature field are noticeably influenced by the choice of SGS models. In general, the set of dynamic nonlinear SGS models yields better prediction of the flow than the set of dynamic linear SGS models.     

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.     

Turbulent flow in a composite channel

Numerical solutions for turbulent flow in a composite channel are presented. Here, a channel with a centered porous material is considered. The interface between the porous medium and the clear flow was assumed to have different transversal positions and the porous matrix was simulated with distinct permeabilities. Governing equations were discretized and solved for both domains making use of one unique numerical methodology. Increasing the size of the porous material pushes the flow outwards, increasing the levels of turbulent kinetic energy at the macroscopic interface. For high permeability media, a large amount of mechanical energy is converted into turbulence inside the porous structure.     

Time-dependent natural convection fluid flow of stably stratified fluid in an asymmetrically heated vertical channel filled with an anisotropic porous material

This paper presents a theoretical analysis of the combined effects of anisotropic porous material and thermal stratification on the transient natural convection fluid flow in an asymmetrically heated vertical parallel channel. The solutions of the governing equations for the temperature and velocity fields are obtained using Laplace transform technique, Riemann sum approximation, and the D'Alembert method. The choice of the D'Alembert method is to provide a simple decoupling procedure for the coupled governing equations while still retaining their original orders. The research established that owing to the layering effect induced by the thermal stratification $(S)$, the temperature and the velocity distributions of the fluid are found to be attenuated with an increase in thermal stratification. It is also observed that the inclusion of anisotropic parameters in the transport equations aids in regulating the fluid velocity, temperature, Nusselt number, skin friction, and mass flow rate. In addition, by neglecting the anisotropic parameter and taking into account the adiabatic stratification of the fluid, the numerical values for the mass flow rate of the present research favorably compared with the numerical results obtained by Singh et al.     

Natural convection in a periodically finned vertical channel

This paper presents the experimental results of natural convection in a rectangular cross-sectional vertical channel. Along the channel fins connected to both plates are placed, periodically. The channel walls are maintained at uniform heat flux. Rayleight number and Nusselt number are obtained based on channel width. The ratio of the channel length to the channel width, L/b, is 66. The experiments are performed for modified Rayleigh number, (b/L)RA, ranges from 20 to 90. Results shows that Nusselt number for finned channel are less than those of the smooth channel.     

Dual mixed convection flows in a vertical channel

The classical problem of the fully developed mixed convection flow with frictional heat generation in a vertical channel bounded by isothermal plane walls having the same temperature is revisited in this paper. The existence of dual solutions of the local balance equations is pointed out. They are either columnar upflows or cellular down–up–down flows. Below a maximum value Ξ_max of the governing parameter Ξ = Ge Pr Re (the product of the Gebhart, Prandtl and Reynolds numbers), for any given Ξ a pair of different solutions occurs. The value Ξ_max corresponds to a maximum value of the Reynolds number above which no laminar solution can be found. At this maximum value, the two solution branches bifurcate from each other. In the neighborhood of the bifurcation point Ξ_max even small perturbations can cause transitions from one flow regime to the other. In the paper, the mechanical and thermal characteristics of the dual flow regimes are discussed in detail both analytically and numerically.     

Effects of flow inertia on vertical,natural convection in saturated,porous media

An analytical study is made for the effect of flow inertia on vertical, natural convection in saturated, porous media. Within the framework of boundary-layer approximations, Forchheimer's model was transformed into a set of non-similar equations. Effects of flow inertia are measured and examined in terms of the dimensionless inertia parameter ξ = Gr_xFo_x where Gr_x is the local Grashof number of determined by the bulk properties of saturated porous media, and Fo_x is a new dimensionless parameter governed by the microstructure of porous matrix. The non-similar solutions are presented and discussed for two types of flow: (1) the uniform heat flux surface; and (2) plane plume flows. Results show that thermal boundary layer in the non-Darcy regime is thicker than the corresponding pure-Darcy flow. In addition, the local wall heat fluxes for the first case and the maximum temperature gradient for the second case decrease with increasing ξ.     

Investigation of natural convection in convergent vertical channels

Using air as the working fluid, natural convection heat transfer in a uniform wall temperature convergent vertical channel has been investigated numerically. The investigation encompassed half angles of convergence between 0° (parallel-walled channel) and 10° and the solutions were performed for (S/L) Ra_s range of 1 to 2 × 10⁴. In order to find a correlation format which will merge the convergent channel results for low Rayleigh number ranges (Ra′ < 10²) with those for the parallel-walled channel ones, the minimum (S_min), mean (S_avg), and maximum (S_max) interval spacing between channel walls were used as characteristic dimensions. It was found that merging was best achieved by the use of maximum interval spacing (S_max) as the characteristic dimension. These numerical findings agree with those for high Rayleigh number ranges (RA′ > 10²) reported in the literature.     

Turbulent natural convection heat transfer from a vertical plate to the power-law fluid at high prandtl numbers

A simple analytical technique for turbulent natural convection heat transfer from an isothermal vertical plate to a power-law fluid is developed. The model is based on the assumption that the turbulent heat transfer rate is controlled by the flow characteristic near the surface in the limit of large Prandtl numbers. The formulation proposed in this work agrees well with the correlations available in the literature.     

Numerical simulation for natural convection in vertical channels

The investigation of laminar natural convection in vertical obstructed channels is conducted using an h-adaptive finite element algorithm. The adaptive model uses an L₂ norm based a-posteriori error estimator with a semi-implicit, time-stepping projection technique. The advection terms are treated using an explicit Adams Bashforth method while the diffusion terms are advanced by an implicit Euler scheme. By using the adaptive algorithm, mesh independent studies can be avoided. Results are obtained for thermal and flow patterns including average Nusselt numbers for different parameters (Rayleigh number, aspect ratio and locations of obstructions) in both smooth and obstructed channels.     

On fully-developed mixed convection and flow reversal of a power-law fluid in a vertical channel

The fully-developed mixed convection of power-law fluids is investigated for laminar flow in a parallel-plate vertical channel. The boundary condition of uniform and unequal temperatures prescribed at the channel walls is considered. The velocity field, the viscous stress field and the temperature field are obtained by solving analytically the momentum and energy balance equations as well as the stress-strain constitutive equation. An expression which allows the evaluation of the friction factors is presented. The condition for the occurrence of flow reversal is obtained.