Free-convection effects inside tubes of flat-plate solar collectors

An experimental and theoretical study of the effects of free convection superimposed on forced flow in inclined tubes is made. The theoretical analysis considered fully developed laminar flow under uniform heat flux and constant pressure gradient. Solutions for velocity and temperature equations have been obtained by perturbation analysis, in terms of power series of Rayleigh number. Nusselt number has been evaluated on bulk temperature difference basis and a maximum value of it appears to lie between 20 deg and 60 deg of tube inclination. An experimental study was done for 45 deg tube inclination and also for vertical position.     

ANALYSIS OF COMBINED NATURAL AND FORCED CONVECTION IN VERTICAL SEMICIRCULAR DUCTS WITH RADIAL INTERNAL FINS

A numerical analysis of combined natural and forced convection is conducted for the fully developed laminar flow and heat transfer in a vertical semicircular duct with radial, internal longitudinal fins. Accurate solutions for heating upward flow are obtained by the finite difference method based on a fine grid, while the hydraulic and thermal conditions of the fins are ascertained. The results represent a range of Rayleigh numbers and various values of fin lengths and number of fins. The fully developed f Re and Nu values for pure forced convection in the finned semicircular duct are also documented. It is found that both the friction factor and the Nusselt number in the finned tube increase as the Rayleigh number increases. The effect of buoyancy is significant in semicircular ducts with short fins. By comparing the results of finless ducts with those of finned ducts, it was concluded that heat transfer in combined natural and forced convection in the semicircular duct is dramatically enhanced by using radial internal fins.     

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on Rayleigh number and solid volume fraction.     

Buoyancy Induced Heat Transfer Flow Inside a Tilted Square Enclosure Filled with Nanofluids in the Presence of Oriented Magnetic Field

This paper analyzes heat transfer and fluid flow of natural convection in an inclined square enclosure filled with different types of nanofluids having various shapes of nanoparticles in the presence of oriented magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing non-dimensional partial differential equations. In the numerical simulations, water, ethylene glycol, and engine oil containing copper, alumina, titanium dioxide nanoparticles are considered. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, magnetic field inclination angle, geometry inclination angle on the fluid flow and heat transfer are investigated. The results indicate that increment of the Rayleigh number and nanoparticle volume fraction increase the heat transfer rate in a significant way, whereas, increment of the Hartmann number decreases the overall heat transfer rate. It is also observed that a blade shape nanoparticle gives higher heat transfer rate compared to other shapes of nanoparticles. The critical geometry inclination angle at which the maximum heat transfer rate is achieved depends on the nanoparticle volume fraction as well as on the magnetic field orientation. These results are new and have direct applications in solar thermal collectors and thermal insulator of buildings.     

Laminar natural convection in an inclined cavity with a wavy wall

In the present work, a numerical study of the effect of a hot wavy wall of a laminar natural convection in an inclined square cavity, differentially heated, was carried out. This problem is solved by using the partial differential equations, which are the vorticity transport, heat transfer and stream function in curvilinear co-ordinates. The tests were performed for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. Two geometrical configurations were used namely one and three undulations.The results obtained show that the hot wall undulation affects the flow and the heat transfer rate in the cavity. The mean Nusselt number decreases comparing with the square cavity. The trend of the local heat transfer is wavy. The frequency of the latter is different from the undulated wall frequency.     

Heat transfer by mixed convection in a vertical flow undergoing transition

Heat transfer, for aiding mixed convection from vertical, uniform flux surfaces and for small forced convection effects, is considered here. Simple relations have been proposed to correlate the new experimental data which were obtained in a flow undergoing transition from a laminar regime toward turbulence. Experiments were performed in air at pressures ranging from 4.4 to about 8 bar. The correlation based on experimental data for laminar flow for Pr = 0.7 has been extended to other Prandtl numbers through numerical integration of the transport equations. It is shown that, for both laminar and turbulent mixed convection, the Nusselt number may be successfully correlated, employing suitable combinations of the corresponding heat transfer correlations for forced and for natural convection. The parameter characterizing the mixed convection effect was found to be different in laminar and turbulent flow. However, in each of these regions, the relevant parameter is proportional to the ratio of the applicable characteristic forced and natural convection velocity scales.     

Mixed convection flow from a vertical flat plate with temperature dependent viscosity

A two-dimensional mixed convection flow of a viscous incompressible fluid of temperature dependent viscosity past a vertical impermeable fluid is considered. The governing equations for the flow are transformed for the regions appropriate to the forced convection, free convection and forced-free convection regimes. Solutions of the reduced equation appropriate in the forced convection and free convection regime are obtained using the perturbation technique treating ξ, the buoyancy parameter, as the perturbation parameter and those for the forced-free convection regime are obtained by the implicit finite difference method. Numerical results thus obtained are presented in terms of the local shear stress and local surface heat-flux. Effect of the viscosity variation parameter, ε, on the surface shear stress and the surface heat-flux for the fluid appropriate for Prandtl number ranging from 0.02 to 100 is shown. The perturbation solutions obtained for small and large values of ξ are found in excellent agreement with the finite difference solutions for the entire ξ regime.     

Transition of nanofluids flow in an inclined heated pipe

A numerical investigation is carried out to investigate the transitional flow behaviour of nanofluids flow in an inclined pipe using both single and multi-phase models. Two different nanofluids are considered, and these are Al₂O₃–water and TiO₂–water nanofluids. Moreover, SST κ − ω transitional model is implemented to study the nanofluids flow in inclined pipe. Gravitational force is also adopted by considering Boussinesq approximation in the momentum equation. Results reveal that Buoyancy force play a significant role on the degeneration of heat transfer rate with the increase of Reynolds number for different inclination angles. It indicates that mixed convection has opposite effect on the inclined pipe than the forced convection on the horizontal pipe. Moreover, some deformation of the flow and temperature fields near the upstream region is observed with the increase of inclination angle due to Buoyancy force.     

Routes to chaos of natural convection flows in vertical channels

The aim of the present study is the analysis of the transition to turbulence of natural convection flows between two infinite vertical plates. For the study of the problem, a number of Direct Numerical Simulations (DNSs) have been performed. The continuity, momentum and energy equations, cast under the Boussinesq assumption, are tackled numerically by means of a pseudospectral method, through which the three-dimensional domain is decomposed with Chebychev polynomials in the wall-normal direction and with Fourier modes in the wall-parallel directions. For low Rayleigh number values, the predictions of the flow regimes are consistent with the classical analytical results and linear stability analyses. In particular, the first bifurcation (Ra ≈ 5800) from the so-called laminar conduction regime to steady convection is correctly captured. By increasing the Rayleigh number beyond a second critical value (Ra ≈ 10200), the flow regime becomes chaotic. This transition to chaos is found to be related with the amplification of spanwise instabilities occurring at scales larger than the channel gap, H. The study of the return of the system from the chaotic regime to the laminar base flow reveals a phenomenon of hysteresis, i.e. the chaotic regime persists even at Ra-values lower than the second critical value. From a numerical point of view, the predicted flow regimes appear to be extremely sensitive to the domain size, grid resolution and perturbation amplitude. These aspects are shown to be of crucial importance for the prediction of the heat transfer performance, and, hence, should be taken into consideration when numerical methods are used for the simulation of real-world problems.     

Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom

Laminar mixed convective heat transfer in two-dimensional shallow rectangular driven cavities of aspect ratio 10 is studied numerically. The top moving lid of the cavity is at a higher temperature than the bottom wall. Computations are performed for Rayleigh numbers ranging from 10⁵ to 10⁷ keeping the Reynolds number fixed at 408.21, thus encompassing the dominating forced convection, mixed convection, and dominating natural convection flow regimes. The fluid Prandtl number is taken as 6 representing water. The effects of inclination of the cavity on the flow and thermal fields are investigated for inclination angles ranging from 0° to 30°. Interesting behaviours of the flow and thermal fields with increasing inclination are observed. The streamline and isotherm plots and the variation of the local and average Nusselt numbers at the hot and cold walls are presented. The average Nusselt number is found to increase with cavity inclination. The rate of increase of the average Nusselt number with cavity inclination is mild for dominating forced convection case while it is much steeper in dominating natural convection case.     

Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition

The aim of the present numerical study is to understand the natural convection flow and heat transfer in an inclined rectangular enclosure with sinusoidal temperature profile on the left wall. The top and bottom walls of the enclosure are kept to be adiabatic. The finite difference method is used to solve the governing equations with a range of inclination angles, aspect ratios and Rayleigh numbers. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first then decreases with increasing the inclination of the enclosure for all aspect ratio and Rayleigh number. Increasing the aspect ratio shows a decreasing trend of the heat transfer for all Rayleigh numbers considered. A correlation equation is also introduced for the heat transfer analysis in this study.     

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 10⁸, Darcy number = 10^?4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.     

Natural convection heat transfer in partially open inclined square cavities

A numerical study has been carried out on inclined partially open square cavities, which are formed by adiabatic walls and a partial opening. The surface of the wall inside the cavity facing the partial opening is isothermal. Steady-state heat transfer by laminar natural convection in a two dimensional partially open cavity is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10³ to 10⁶, dimensionless aperture size from 0.25 to 0.75, aperture position at high, center and low, and inclination of the opening from 0° (facing upward) to 120° (facing 30° downward). It is found that the volume flow rate and Nusselt number are an increasing function of Rayleigh number, aperture size and generally aperture position. Other parameters being constant, Nusselt number is a non-linear function of the inclination angle. Depending on the application, heat transfer can be maximized or minimized by selecting appropriate parameters, namely aperture size, aperture position and inclination angle at a given operation Rayleigh number.     

定壁温水平传热管外降膜对流显热换热特性理论研究

采用层流模型对定壁温边界条件时水平管外垂降液膜的强制对流显热换热性能进行了数值计算。计算中对管顶部的冲击滞止区和管侧部的自由绕流区分别采用不同的坐标变换方法进行微分方程组筒化。根据滞止区计算结果确定自由烧流区的初始边界条件。计算结果证明管径对平均换热系数的影响不容忽视。定壁温条件时的平均换热系数比定热通量时约高12％到20％左右。     

Large eddy simulation of transition of free convection flow over an inclined upward facing heated plate

Transition of free convection flow of air over an inclined heated surface is investigated numerically by using a large eddy simulation method. In particular, we focus on how inclination angle of an upward-facing heated plate affects flow transition. Special attention is paid to the development of the thermal boundary layer and the transition from the laminar to turbulent stage. Results show that the transition occurs early when the plate is moved from its vertical position due to the rapid growth of both the velocity and thermal boundary layers. As a consequence, the critical Grashof number drops. Effects of the inclination of plate on the turbulent velocity fluctuations are also investigated, and the predicted results are in very good agreement with various experimental data available in the literature.     

A numerical investigation of conjugated-natural convection heat transfer enhancement of a nanofluid in an annular tube driven by inner heat generating solid cylinder

Laminar conjugate heat transfer by natural convection and conduction in a vertical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal cylindrical boundary has been studied by a numerical method. It is assumed that the two sealed ends of the tube to be adiabatic. Governing equations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. Results are presented for the flow and temperature distributions and Nusselt numbers on different cross sectional planes and longitudinal sections for Rayleigh number ranging from 10⁵ to 10⁸, solid volume fraction of 0‹φ‹0.05 with copper-water nanofluid as the working medium. Considering that the driven flow in the annular tube is strongly influenced by orientation of tube, study has been carried out for different inclination angles.     

Numerical modelling and optimisation of natural convection heat loss suppression in a solar cavity receiver with plate fins

This study details the numerical modelling and optimization of natural convection heat suppression in a solar cavity receiver with plate fins. The use of plate fins attached to the inner aperture surface is presented as a possible low cost means of suppressing natural convection heat loss in a cavity receiver. In the first part of the study a three-dimensional numerical model that captures the heat transfer and flow processes in the cavity receiver is analyzed, and the possibilities of optimization were then established. The model is laminar in the range of Rayleigh number, inclination angle, plate height and thickness considered. In the second part of the study, the geometric parameters considered were optimized using optimization programme with search algorithm. The results indicate that significant reduction on the natural convection heat loss can be achieved from cavity receivers by using plate fins, and an optimal plate fins configuration exit for minimal natural convection heat loss for a given range of Rayleigh number. Reduction of up to a maximum of 20% at 0° receiver inclination was observed. The results obtained provide a novel approach for improving design of cavity receiver for optimal performance.     

Laminar free convection underneath a downward facing inclined hot fin array

A combined theoretical, experimental and numerical study was conducted to investigate the problem of laminar free convection underneath a hot isothermal and inclined fin array. The influence of inclination on the location where the flow stagnates, and splits, was examined. Heat transfer rates were calculated for different fin array geometries and temperatures. The results show that for small inclination angles the cooling rate is essentially constant. Beyond a certain angle, the tilting of the fin array enhances substantially the heat transfer rate. Sensitivity analyses indicate that the heat transfer coefficient increases at higher fin temperatures and larger fin spacing, but is of a lesser sensitivity to fin height changes. Additionally, it was discovered that the array optimal fin spacing do not depend on the inclination angle. In the theoretical part, a semi empirical model was developed for the heat transfer coefficient of horizontal and slightly inclined arrays that have large fin spacing. In effect it constitutes the necessary modeling addition to the previously developed model for moderately and tightly spaced fins of slightly tilted arrays. Together, they provide analytical expressions for the heat transfer coefficient of slightly inclined arrays, for any fin spacing.     

Contribution Analysis of Dimensionless Variables for Laminar and Turbulent Flow Convection Heat Transfer in a Horizontal Tube Using Artificial Neural Network

The artificial neural network (ANN) method has shown its superior predictive power compared to the conventional approaches in many studies. However, it has always been treated as a “black box” because it provides little explanation on the relative influence of the independent variables in the prediction process. In this study, the ANN method was used to develop empirical correlations for laminar and turbulent heat transfer in a horizontal tube under the uniform wall heat flux boundary condition and three inlet configurations (re-entrant, square-edged, and bell-mouth). The contribution analysis for the dimensionless variables was conducted using the index of contribution defined in this study. The relative importance of the independent variables appearing in the correlations was examined using the index of contribution based on the coefficient matrices of the ANN correlations. For the turbulent heat transfer data, the Reynolds and Prandtl numbers were observed as the most important parameters, and the length-to-diameter and bulk-to-wall viscosity ratios were found to be the least important parameters. The method was extended to analyze the more complicated forced and mixed convection data in developing laminar flow. The dimensionless parameters influencing the heat transfer in this region were the Rayleigh number and the Graetz number. The contribution analysis clearly showed that the Rayleigh number has a significant influence on the mixed convection heat transfer data, and the forced convection heat transfer data is more influenced by the Graetz number. The results of this study clearly indicated that the contribution analysis method can be used to provide correct physical insight into the influence of different variables or a combination of them on complicated heat transfer problems.     

Inlet conditions effects on vertical wall jets in forced and mixed convection regimes

In this paper a numerical investigation of a laminar isothermal or nonisothermal two dimensional plane wall jet is carried out. Special attention has been paid to the effect of the inlet conditions at the nozzle exit on the hydrodynamic and thermal characteristics of the flow, in both convection regimes: forced and mixed. Two velocities profiles at the nozzle exit are used: uniform profile and parabolic profile. The Prandtl number effect on the jet flow characteristics is also analyzed in the case of forced convection regime.The system of governing equations is solved with an implicit finite difference scheme. For numerical stability we use a staggered non-uniform grid. The obtained results show, for the two convection modes, that the inlet conditions affect the flow in the immediate neighbourhood of the nozzle (core region) in which the flow is governed mainly by the inertia forces. In the established region the results become independent of the flow inlet conditions. Secondly, the effect of the Prandtl number is significant in the plume region in which the jet flow is governed by buoyant forces.