Numerical simulation of a trapezoidal cavity receiver for a linear Fresnel solar collector concentrator

A new trapezoidal cavity receiver for a linear Fresnel solar collector is analysed and optimized via ray-trace and CFD simulations. The number of receiver absorber tubes and the inclination of lateral walls in the cavity are checked with simplified ray-trace simulation. The CFD simulation makes possible to optimize cavity depth and rock wool insulation thickness. The simulated global heat transfer coefficient, based on primary mirror area, is correlated with a power-law fit instead of a parabolic fit. The correlation results are compared with heat transfer coefficients available for linear Fresnel collector prototypes.     

Analysis of heat losses from a trapezoidal cavity used for Linear Fresnel Reflector system

A Computational study to investigate the heat loss due to radiation and steady laminar natural convection flow in a trapezoidal cavity having eight absorber tubes for a Linear Fresnel Reflector (LFR) solar thermal system with uniformly heated tubes and adiabatic top wall and side walls has been performed. The losses due to convection and radiation were considered from the bottom glass cover. The results are validated with experimental data. Radiative component of losses from the cavity was found to be dominant which contributes around 80–90%. Heat loss characteristics have been studied for cavities of different depths. Simulations have been carried out for various values of heat transfer coefficient based on the wind speed below the glass surface. Effect of emissivities of the tubes on the heat loss has also been simulated. Flow pattern and isotherms inside the cavity for various depths have been analyzed. Finally, the correlation between the total average Nusselt number and its influencing parameters has been obtained for the proposed cavity.     

Natural convection in a rectangular cavity with partially active side walls

A numerical study is performed to investigate the effect of aspect ratio on the natural convection of a fluid contained in a rectangular cavity with partially thermally active side walls. The active part of the left side wall is at a higher temperature than that of the right side wall. The top and bottom of the cavity and inactive part of the side walls are thermally insulated. Nine different relative positions of the active zones are considered. The equations are discretized by the control volume method with power law scheme and are solved numerically by iterative method together with a successive over relaxation (SOR) technique. The results are obtained for Grashof numbers between 10³ and 10⁵ and the effects of the aspect ratio on the flow and temperature fields and the rate of heat transfer from the walls of the enclosure are presented. The heat transfer rate is high for the bottom–top thermally active location while the heat transfer rate is poor in the top–bottom thermally active location. The heat transfer rate is found to increase with an increase in the aspect ratio.     

Natural Convection in a Trapezoidal Enclosure Heated from the Side with a Baffle Mounted on Its Upper Inclined Surface

A numerical investigation examined the effects on heat transfer of mounting baffles to the upper inclined surfaces of trapezoidal cavities. Two thermal boundary conditions are considered. In the first, the left, short vertical wall is heated while the right, long vertical wall is cooled (buoyancy assisting mode along the upper inclined surface of the cavity). In the second, the right, long vertical wall is heated while the left, short vertical wall is cooled (buoyancy opposing mode along the upper inclined surface of the cavity). For each boundary condition, computations are performed for three baffle heights, two baffle locations, four Rayleigh number values, and three Prandtl number values. Results are displayed in terms of streamlines, isotherms, and local and average Nusselt number values. For both boundary conditions, predictions reveal a decrease in heat transfer in the presence of baffles, with its rate generally increasing with increasing baffle height and Prandtl number. For a given baffle height, a higher decrease in heat transfer is generally obtained with baffles located close to the short vertical wall. Average Nusselt number correlations for both boundary conditions are presented.     

Numerical simulation of double-diffusive mixed convection and entropy generation in a lid-driven trapezoidal enclosure with a heat source

In this study, entropy generation of double-diffusive mixed convection is investigated inside a right-angled trapezoidal cavity with a partially heated and salted bottom wall. Similar to the approach that assigns color to streamlines, a new coloring scheme is employed to visualize heatlines and masslines in a more meaningful manner. In addition, various consequential parameters, namely the Lewis and Richardson numbers, the buoyancy ratio, the direction of lid movement, and the heat source location, have been analyzed. According to the results, as the Lewis number increases, the average Nusselt number declines, while the total entropy generation augments. Furthermore, for Le?=?0.1, the conduction mass transfer dominates the mass transfer field; hence, the masslines are virtually perpendicular to the isoconcentration lines.     

Maximum density effects on buoyancy-driven convection in a porous trapezoidal cavity

A numerical study of the steady buoyancy-induced flow and heat transfer in a trapezoidal cavity filled with a porous medium saturated with cold water at a temperature around 4 °C has been performed. The analysis has been done for a cavity with different aspect ratios ranging from 0.25 to 0.75 and Rayleigh numbers ranging from 100 to 1000 using a finite-difference method. It is found that four cells are formed inside the cavity independent of the Rayleigh number and aspect ratio. The existence of buoyancy force reversal resulting from the maximum density effect, leads to a reduction in the strength of the convective flow and also the average Nusselt number.     

Entropy generation due to mixed convection in an enclosure with heated corners

Entropy generation due to steady state heat transfer and the motion of the vertical boundaries in a two-dimensional square cavity is numerically studied, using the value of the velocity and temperature obtained by solving the Navier–Stokes equation coupled with the energy equation with the finite element method and an operator splitting scheme. Increasing the Richardson number, the entropy generation by fluid friction is intensified inside the cavity due to the vortex formation at the central part of the cavity. The entropy generation by heat transfer becomes more intense at the vertical walls and the central low part of the cavity due to the stronger temperature gradients at this region.     

模拟井筒耦合传热大涡模拟的建模与数值求解

模拟井筒加温系统是研究油田井下高温高压环境的特种实验装置,其主体部分模拟井筒为耐高温高压的厚壁圆柱形封闭腔体,模拟井筒温度场是其加温系统设计与工作参数确定的基本依据。分析加热过程中腔体内流体与厚壁腔体之间的动态耦合传热,通过合理简化建立了井筒加热物理模型,给出了其基于大涡模拟方法的数学模型,采用有限差分法和应用投影法求解模型。研究结果表明：模型和求解方法可以用于高温高压模拟井筒流固耦合传热研究,其实验误差低于16%;通过模拟计算得到了井筒及其腔体内流体的动态耦合传热过程温度场分布规律,为模拟井筒加温系统设计与工作参数确定提供理论依据。     

Channel cross section effect on heat transfer performance of oblique finned microchannel heat sink

In the present work, the effect of channel cross section on the heat transfer performance of an oblique finned micro-channel heat sink was investigated. Water and Al₂O₃/water nanofluid of volume fraction 0.25% were used as a coolant. The oblique finned microchannels are designed with three channel cross-sections namely square, semicircle and trapezoidal. The primary work of this paper is to study the heat transfer and hydrodynamic characteristics in the oblique finned microchannel. The experimental setup and procedure are validated using water as coolant in a micro-channel heat sink. Heat transfer and flow characteristics are examined for three cross-sections of varying mass flux. The trapezoidal channel cross-section increases the considerable heat transfer rate improvement for both water and nanofluid by 3.133% and 5.878% compared to square and semicircle cross section. Also, the pressure drop is higher in the trapezoidal cross-section over the square and semicircle cross section. This is due to increase in friction loss of trapezoidal cross section. The results indicate that trapezoidal cross-section oblique finned micro-channel is more suitable for heat transfer in the electronic cooling application.     

A novel heat dissipation fin design applicable for natural convection augmentation

In this study, a comparative study of heat sink having various fin assembly under natural convection is investigated. The fin pattern includes a rectangular, a trapezoidal and an inverted trapezoidal configuration. Tests were performed in a well controlled environmental chamber having a heat load ranging from 3 to 20 W. From the test results, the heat transfer coefficient of the conventional rectangular fins is higher than that of the trapezoidal fins while the heat transfer coefficient of the inverted trapezoidal fins is higher than the trapezoidal one by approximately 25%, and it exceeds that of convectional rectangular fin by about 10%. The heat transfer improvements of the inverted trapezoidal fin are mainly associated with a larger temperature difference and inducing more air flow into the heat sink.     

Flow structure and heat transfer induced by embedded vorticity

Several vortex generator shapes are used to increase heat and mass transfer in open and internal flows. Here we report a three-dimensional numerical study investigating the effects of longitudinal and transverse vortices on the heat and mass transfer mechanisms generated by rows of trapezoidal vortex generators. The turbulent macrostructures of these streamwise vortices appear greatly to enhance radial convective transfer. Due to Kelvin–Helmholtz instability, the shear layer shed from the tab’s edge becomes unstable and generates periodic transverse vortices that enhance fluid mixing and heat transfer. A global performance analysis of the high-efficiency vortex (HEV) heat exchanger designed to exploit these embedded vortices, shows that the HEV is very competitive with other multifunctional heat exchangers/reactors, especially due to its very low energy consumption.     

Heat transfer in micro-channels: Comparison of experiments with theory and numerical results

This paper considers experimental and theoretical investigations on single-phase heat transfer in micro-channels. It is the second part of general exploration “Flow and heat transfer in micro-channels”. The first part discussed several aspects of flow in micro-channels, as pressure drop, transition from laminar to turbulent flow, etc. [G. Hetsroni, A. Mosyak, E. Pogrebnyak, L.P. Yarin, Fluid flow in micro-channels, Int. J. Heat Mass Transfer 48 (2005) 1982–1998]. In this paper, the problem of heat transfer is considered in the frame of a continuum model, corresponding to small Knudsen number. The data of heat transfer in circular, triangular, rectangular, and trapezoidal micro-channels with hydraulic diameters ranging from 60 μm to 2000 μm are analyzed. The effects of geometry, axial heat flux due to thermal conduction through the working fluid and channel walls, as well as the energy dissipation are discussed. We focus on comparing experimental data, obtained by number of investigators, to conventional theory on heat transfer. The analysis was performed on possible sources of unexpected effects reported in some experimental investigations.     

Numerical Studies on Natural Convection in a Trapezoidal Enclosure With Discrete Heating

Abstract

A steady state laminar natural convection flow in a trapezoidal enclosure with discretely heated bottom wall, adiabatic top wall, and constant temperature cold inclined walls is performed. The finite volume based commercial code “ANSYS-FLUENT” is used to investigate the influence of discrete heating on natural convection flows in a trapezoidal cavity. The numerical solution of the problem covers various Rayleigh numbers ranging from 10³ to 10⁶, non-dimensional heating length ranging from 0.2 to 0.8 and Prandtl number is 0.7. The performance of the present numerical approach is represented in the form of streamfunction, temperature profile and Nusselt number. Heat transfer increases with increase of Rayleigh numbers at the corners of the cavity for same heating length from center of the bottom wall. However, the heat transfer rate is less and almost constant for the Rayleigh numbers considered. It is found that the average Nusselt number monotonically increases with increase of Rayleigh number and length of heat source. The variation of local and average Nusselt numbers is more significant for larger length of heating than smaller one. The heat transfer correlations useful for practical design problems have been predicted.     

The importance of rib shape effects on the local heat transfer and flow friction characteristics of square ducts with ribbed internal surfaces

Accurate prediction of ribbed duct flow and heat transfer is of importance to the gas turbine industry. In the present work, a computer code has been developed to study the turbulent heat transfer and friction in a square duct with various-shaped ribs mounted on one wall. The simulations were performed for four rib shapes, i.e., square, triangular, trapezoidal with decreasing height in the flow direction, and trapezoidal with increasing height in the flow direction. The prepared algorithm and the computer code are applied to demonstrate distribution of the heat transfer coefficient between a pair of ribs. The results show that features of the inter-rib distribution of the heat transfer coefficient are strongly affected by the rib shape and trapezoidal ribs with decreasing height in the flow direction provide higher heat transfer enhancement and pressure drop than other shapes.     

Analysis of mixed convection of nanofluid in a 3D lid-driven trapezoidal cavity with flexible side surfaces and inner cylinder

Numerical study of mixed convection in a lid-driven 3D flexible walled trapezoidal cavity with nanofluids was performed by using Galerkin weighted residual finite element method. Effects of various pertinent parameters such as Richardson number (between 0.05 and 50), elastic modulus of the side surfaces (between 1000 and 10⁵), side wall inclination angle (between 0° and 20°) and solid particle volume fraction (between 0 and 0.04) on the fluid flow and heat transfer characteristics in a 3D lid-driven-trapezoidal cavity were numerically examined. It was observed that these characteristics are influenced when the pertinent parameters change. Flexible side surface can be used as control element for heat transfer rate. Increment and reduction in the space which are provided by the flexible side walls result in heat transfer enhancement and deterioration for side wall inclination angle of 0° and 10°. Average Nusselt number enhances by about 9.80% when the value of the elastic modulus is increased from 1000 to 10⁵ for side wall inclination angles of θ = 0°. Adding nanoparticles to the base fluid results in linear increment of heat transfer and at the highest volume fraction, 25.30% of heat transfer enhancement is obtained. A polynomial type correlation for the average Nusselt number along the hot wall was proposed and it has a fourth order polynomial dependence upon the Richardson number and first order dependence upon the solid particle volume fraction.     

Thermal and hydrodynamic analysis of gaseous flow in trapezoidal silicon microchannels

Thermal and hydrodynamic character of a hydrodynamically developed and thermally developing flow in trapezoidal silicon microchannels is analyzed. The continuum momentum and energy equations, with the velocity slip and temperature jump condition at the solid walls, are solved numerically in a square computational domain obtained by transformation of the trapezoidal geometry. The effects of rarefaction, aspect ratio and a parameter representing the fluid/wall interaction on thermal and hydrodynamic character of flow in trapezoidal microchannels are explored. It is found that the friction factor decreases if rarefaction and/or aspect ratio increase. It is also found that at low rarefactions the very high heat transfer rate at the entrance diminishes rapidly as the thermally developing flow approaches fully developed flow. At high rarefactions, heat transfer rate does not exhibit considerable changes along the microchannel, no matter the flow is developing or not.     

The effect of geometrical parameters on heat transfer characteristics of microchannels heat sink with different shapes

The effect of geometrical parameters on water flow and heat transfer characteristics in microchannels is numerically investigated for Reynolds number range of 100–1000. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using finite volume method. The computational domain is taken as the entire heat sink including the inlet/outlet ports, wall plenums, and microchannels. Three different shapes of microchannel heat sinks are investigated in this study which are rectangular, trapezoidal, and triangular. The water flow field and heat transfer phenomena inside each shape of heated microchannels are examined with three different geometrical dimensions. Using the averaged fluid temperature and heat transfer coefficient in each shape of the heat sink to quantify the fluid flow and temperature distributions, it is found that better uniformities in heat transfer coefficient and temperature can be obtained in heat sinks having the smallest hydraulic diameter. It is also inferred that the heat sink having the smallest hydraulic diameter has better performance in terms of pressure drop and friction factor among other heat sinks studied.     

Influence of various base nanofluids and substrate materials on heat transfer in trapezoidal microchannel heat sinks

Numerical investigations are performed to investigate the laminar flow and heat transfer characteristics of trapezoidal MCHS using various types of base nanofluids and various MCHS substrate materials on MCHS performance. This study considered four types of base fluids including water, ethylene glycol (EG), oil, and glycerin with 2% volume fraction of diamond nanoparticle, and four types of MCHS substrate materials including copper, aluminium, steel, and titanium. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using the finite volume method. It is found that the best uniformities in heat transfer coefficient and temperature among the four mixture flows can be obtained using glycerin-base nanofluid followed by oil-base nanofluid, EG-base nanofluid, and water-base nanofluid heat sinks. However, the heat transfer performance of water-base nanofluid can be greatly enhanced in steel made substrate heat sink.     

Numerical Study on Double Diffusive Mixed Convection with a Soret Effect in a Two-Sided Lid-Driven Cavity

In the present study, a numerical analysis is performed to understand the mixed convection flow, and heat and mass transfer with Soret effect in a two-sided lid-driven square cavity. The horizontal walls of the cavity are adiabatic and impermeable, while vertical walls are kept at constant but different temperatures and concentrations. The vertical walls move in a constant velocity. According to the direction of the movement of walls, three cases have been studied for different combinations of parameters involved in the study. The governing unsteady equations are solved numerically by the finite volume method with the SIMPLE algorithm. The results are presented graphically in the form of streamlines, isotherms, and velocity profiles. Heat and mass transfer rates are reduced if both walls are moving the in same direction, while heat and mass transfer rates are enhanced if the walls are moving in the opposite direction.     

Laminar Momentum and Heat Transfer in a Channel with a Built‐In Tapered Trapezoidal Bluff Body

Effects of wall confinements on the laminar flow and heat transfer around a heated tapered trapezoidal bluff body are investigated numerically in the confined domain (Reynolds number, Re = 1 to 40; blockage ratio = 0.125 to 0.5; and Prandtl number, Pr = 0.71). The onset of flow separation is found between Re = 4 and 5 for the blockage ratio of 0.125 and between Re = 5 and 6 for the blockage ratios of 0.25 and 0.5. If compared with a long circular obstacle on the basis of equal projected area, the total drag coefficient of the trapezoidal cylinder is found to be larger than the circular one, but an opposite trend is observed for the heat transfer. The augmentation in heat transfer for trapezoidal and circular cylinders is found to be approximately 46, 72, 74, and 65 percent for Re = 1, 5, 10, and 40, respectively for the blockage ratio of 0.25. The maximum enhancement in heat transfer for a tapered trapezoidal bluff body with respect to a square bluff body is found to be approximately 104 percent and 101 percent for blockage ratios of 0.25 and 0.5, respectively. Finally, simple correlations of wake length, drag, and average cylinder Nusselt number are established.