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.     

Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 10⁵ to 10⁸ with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed except for the density where Boussinesq’s approximation has been considered. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh number with corrugation amplitude and frequency.     

竖直圆环形通道内充分发展自然对流的分析解

对于均匀加热的竖直圆环形通道内的充分发展自然对流换热问题，发现了前人分析解不完善的地方，通过运用能量守衡原理得到了封闭形式的分析解并给出了其计算实例。在一个壁面恒热流、另一个壁面绝热的两类热边界条件下，分析解所计算得到的充分发展段的发热壁面温度与实验结果都符合得较好。最后，筒述了此分析解存在的误差以及可能产生此误差的原因。     

G-jitter fully developed combined heat and mass transfer by mixed convection flow in a vertical channel

The effect of g-jitter induced combined heat and mass transfer by mixed convection flow in microgravity for a simple system consisting of two heated vertical parallel infinite flat plates held at constant but different temperatures and concentrations. The governing equations are solved analytically for the induced velocity, temperature and concentration distributions. Graphical results for the velocity profile of the oscillating flow in the channel are presented and discussed for various parametric physical conditions. Despite the simplicity of the problem, it does display some features, which have also been observed in real mixed convection flows, such as flow reversal and flow dependence on the buoyancy parameter ratio.     

Numerical analysis of natural convection in air in a vertical convergent channel with uniformly heated conductive walls

Natural convection in air in a convergent channel with the two principal flat plates at uniform heat flux with finite thickness and thermal conductivity was numerically investigated. Laminar, two-dimensional steady-state conditions were assumed. An extended computational domain was adopted, which allows to take into account the diffusion by both momentum and energy outside the channel. A comparison with experimental data was carried out. Stream function and temperature fields are presented. Average Nusselt numbers were evaluated and presented.Temperature profiles are strongly affected by the convergence angle at low Rayleigh numbers. At the lower minimum gap, streamlines and isotherms show a low pressure region in the channel due to a choked flow in its upper end. Numerical values of the Nusselt number are in good agreement with experimental results.     

Combined boundary and inertia effects for fully developed mixed convection in a vertical channel embedded in porous media

The fully developed laminar mixed convection in a vertical channel embedded in porous media has been solved by using non-Darcy flow model. Through proper manipulation of nondimensional variables and parameters, the governing equations are derived and the thermal boundary conditions on the left and right walls can be prescribed as isothermal-isothermal, isothermal-isoflux, or isoflux-isothermal, respectively. Including the Darcian force, buoyancy force and boundary effect, the exact solutions for temperature and velocity profiles are obtained. Meanwhile, parametric zones for the occurrence of flow reversal based on the analytical solutions are presented. Finally, the numerical solution is also provided to investigate their further influence due to the existence of inertia effect.     

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.     

Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

Thermal transport analysis for natural convection in a porous corrugated rhombic enclosure

A numerical study of fluid flow and heat transfer, applying natural convection is carried out in a porous corrugated rhombic enclosure. A uniform heating source is applied from the bottom boundary wall while the inclined side walls are maintained to a constant cold temperature and the top corrugated wall is retained at insulated condition inside the enclosure. The heat transfer and flow features are presented for a wide spectrum of Rayleigh numbers (Ra), 10⁴ ≤ Ra ≤ 10⁶, and Darcy numbers (Da), 10^?3 ≤ Da ≤ 10^?2. The number of undulations (n) for the top and bottom walls have been varied from 1 to 13 keeping the amplitude of undulation fixed. It is revealed that the characteristics of heat transfer are conceivably modulated by changing the parameter of the undulation number on the enclosure walls, specifically at the bottom and top. The influencing control of n in altering the heat transfer rate is felt maximum on the left wall and minimum for the right wall, and there is a strong interplay between Ra and Da together with n on dictating the heat transfer characteristics. The critical value, where heat transfer rate is observed as maximum is at n = 11 and thereafter the values decrease.     

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.     

Natural convection from a confined horizontal cylinder: the optimum distance between the confining walls

The laminar natural convection from an isothermal horizontal cylinder confined between vertical walls, at low Rayleigh numbers, is investigated by theoretical, experimental and numerical methods. The height of the walls is kept constant, however, their distance is changed to study its effect on the rate of the heat transfer. Results are incorporated into a single equation which gives the Nusselt number as a function of the ratio of the wall distance to cylinder diameter, t/D, and the Rayleigh number. There is an optimum distance between the walls for which heat transfer is maximum.     

Fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations

This work examines the effects of the vortex viscosity parameter and the buoyancy ratio on the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. The closed-form analytic solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived. Increasing the vortex viscosity parameter tends to increase the magnitude of microrotation and thus decreases the fluid velocity in the vertical channel. Moreover, the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid for micropolar fluids are lower than those of Newtonian fluids.     

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.     

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.     

Non-darcy mixed convection in a vertical porous channel with discrete heat sources at the walls

A numerical study of mixed convection in a parallel-plate vertical channel filled with a fluid-saturated porous medium and containing discrete heat sources at the walls is performed using the Brinkman-Forchheimer-extended Darcy model. The evolution of buoyancy-assisted mixed convection is examined for both the Darcy and the non-Darcy regimes. The results indicate that as the Darcy number is decreased, the location of flow separation from the cold wall did not change while reattachment moved further downstream. The Nusselt number increased with decreasing Darcy number and the effect of Darcy number is more pronounced over the first heat source and in the non-Darcy regime.     

Entropy generation and thermodynamic optimization of fully developed laminar convection in a helical coil

The present paper analyses the entropy generation of the fully developed laminar convection in a helical coil with constant wall heat flux and presents the optimal design based on the minimum entropy generation principal. The important design parameters, including Reynolds number (Re), coil-to-tube radius ratio (δ) and nondimensional coil pitch (λ) are varied to investigate their influences on the entropy generation. The results presented in this paper cover Re range of 100–10,000, δ and λ range from 0.01 to 0.3. Compared with Re and δ, the coil pitch λ is found to have minor influence on the entropy generation. For a demonstrated case, the minimum entropy generation occurs in the range bounded by Re from 2271 to 4277 and δ from 0.17 to 0.3, within which the irreversibility of the system is lowest and the system performance would be optimum. The details show that there is an optimal Re for a helical coil with a fixed δ; meanwhile for a helical coil flow with a specified Re, the smaller δ should be selected when the Re is larger than 5000, and the larger δ should be selected when the Re is less than 5000. These results provide worthwhile information for heat exchanger designers to find the optimal helical coil design from the viewpoint of the thermodynamic second law.     

Effects of temperature-dependent viscosity on fully developed laminar forced convection in a curved duct

For most liquids the specific heat and thermal conductivity are almost independent from temperature, but the viscosity decreases significantly. A fully developed laminar water flow in a curved duct with temperature-dependent viscosity is analyzed in this work. The mass, momentum and energy conservation equations are numerically solved by the finite element method. Both heating and cooling of the water flow is studied. The secondary flow induced by the curvature effects increases the heat transfer rate in comparison with the straight ducts but the velocity and temperature profiles are distorted when the effects of temperature-varying viscosity are included. The Nusselt number obtained when the fluid is cooled with variable viscosity assumption are lower than the constant properties results due to the increase of the viscosity values at the inner points of the curved tube that reduces the secondary flow effect. The friction factor results also show a marked dependence on the viscosity variations in the coil tube cross-section.     

Laminar natural convection in differentially heated rectangular enclosures with vertical diffusive walls

Real enclosures have diffusive walls. A procedure is developed to evaluate the natural convection effective global Nusselt number for rectangular enclosures with vertical diffusive walls. The effective Nusselt number is evaluated using the temperature difference imposed over the exterior faces of the enclosure, the usual correlations for rectangular enclosures without diffusive walls, and the diffusive properties of the solid vertical walls, which are concentrated on a single dimensionless parameter. The proposed procedure is tested by comparing the obtained results with those achieved from the complete two-dimensional numerical simulation of the conjugated heat transfer problem occurring in the complete enclosure, with diffusive walls. The result is a helpful tool that promptly helps the thermal engineer when dealing with enclosures with diffusive walls.