Trapezoidal Cavity Research Articles

Heat loss analysis from a trapezoidal cavity receiver in LFR system using conduction-radiation model

Linear Fresnel Reflector systems are medium temperature (100–400 °C) application systems where heat flux from the sun is concentrated on absorber tubes housed in a trapezoidal cavity by an array of mirrors. The absorber tubes carry working fluid inside them. Several earlier works have considered convective and radiative heat transfer from these trapezoidal cavities in LFR systems. It has also been shown that the convective heat transfer constitutes up to 15% of the total heat losses which is significant. On the other hand, it is seen that the flow velocities are negligible due to stratification of isotherms with hot air trapped on top of the cavity which suggests that convection should be negligible. In the present work, it is shown that the heat transfer which is considered as convective is actually, only conduction through (almost) static air inside the cavity. Due to the abovementioned reason, in the present work, only conduction-radiation problem is considered in the cavity which is far easier to solve due to the absence of complex Navier-Stokes equations. The comparison of heat transfer results obtained using conduction-radiation model and those obtained using convection-radiation model show that the difference between the two results is negligible. Moreover, new correlations are developed with fewer parameters to capture the underlying physics of the heat loss mechanism in such cavities.

MHD heat transfer and entropy generation in inclined trapezoidal cavity filled with nanofluid

PurposeThe main purpose of this paper is to define 2D numerical study and a sensitivity analysis of natural convection heat transfer and entropy generation of Al2O3-water nanofluid in a trapezoidal cavity, with considering of the presence of a constant axial magnetic field.Design/methodology/approachThe effects of the three effective parameters, the Rayleigh number, Hartmann number (Ha) and also inclination angle on the heat transfer performance and entropy generation, are investigated using a finite volume approach. The sensitivity analysis of the effective parameters is done utilizing the response surface methodology.FindingsThe results obtained showed that the mean Nusselt number and total entropy generation increase with the Rayleigh number. Also, increasing the inclination angle reduces the mean Nusselt number (regardless of the magnetic field). In addition, it is found that the mean Nusselt number increases until Ha = 10 and then decreases by increasing of Ha number, regardless of the inclination angle. The sensitivity of the mean Nusselt number to the Ha number and inclination angle α is negative. It is concluded that to maximize the mean Nusselt number and minimize the entropy generation, simultaneously, the Ha and inclination angle must be 50° and 0°, respectively.Originality/valueThere is no published research in the literature about sensitivity analysis of magneto-hydrodynamic heat transfer and entropy generation in inclined trapezoidal cavity filled with nanofluid.

High-output piezoelectric energy harvester using tapered beam with cavity

Energy harvesting using cantilever-based piezoelectric structure is most popular for harvesting electrical energy from ambient vibrations. Efforts are also made to maximize the harvester power by means of tailoring the structural parameters of the cantilever beam. This article proposes a method to maximize the harvester voltage from the cantilever-based piezoelectric energy harvester by means of tailoring the structure of the cantilever, to have a tapering in width, thickness and in both width and thickness (double taper). It is also proposed to introduce rectangular and trapezoidal cavities in the tapered energy harvesters to further maximize the harvester voltage. The analytical model of the proposed harvesters is developed using Euler–Bernoulli beam theory, and its free vibration solution is analysed using Bessel functions. The energy harvesters are fabricated and experimentally evaluated for its performance. It is concluded from the results of analytical model and experimentation that width, thickness and double-tapered beam increases the harvester voltage by 35.6%, 84.8% and 126.6%, respectively, as compared to the energy harvester designed with uniform cantilever beam. Among all the energy harvesters proposed in this article, the maximum voltage is generated from the double-tapered beam with trapezoidal cavity. The experimental results are in close agreement with the results obtained from the analytical model.

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.

A robust higher order compact scheme for solving general second order partial differential equation with derivative source terms on nonuniform curvilinear meshes

A fourth order compact finite difference scheme is proposed for solving general second order steady partial differential equation (PDE) in two-dimension (2D) on geometries having nonuniform curvilinear grids. In this work, the main efforts are focused not only on nonorthogonal curvilinear grids but also on the presence of mixed derivative term and nonhomogeneous derivative source terms in the governing equation. This is in turn suitable for solving fluid flow and heat transfer problems governed by Navier–Stokes(N–S) equations on geometries having nonuniform and nonorthogonal curvilinear grids. The newly proposed scheme has been applied to solve general second order partial differential equation having analytical solution and some pertinent fluid flow problems, namely, viscous flows in a lid driven cavity such as trapezoidal cavity using nonorthogonal grid, square cavity using distorted grid, complicated enclosures using curvilinear grid, and mixed convection flow in a bottom wavy wall cavity. It is seen to efficiently capture steady-state solutions of the N–S equations with Dirichlet as well as Neumann boundary conditions. Detailed comparison data produced by the proposed scheme for all the test cases are provided and compared with existing analytical as well as established numerical results available in the literature. Excellent comparison is obtained in all the cases.

Magneto-convection of nanofluids in a lid-driven trapezoidal cavity with internal heat generation and discrete heating

ABSTRACTThe present work investigates numerically the effect of an inclined magnetic field on the mixed convection flow in a trapezoidal enclosure in the presence of internal heat generation or absorption. The trapezoidal enclosure is filled with water-based nanofluid containing copper nanoparticles. Both the inclined left and right walls are adiabatic. A heat source with constant heat flux placed on the bottom wall of the enclosure and the remaining portions are thermally insulated. The top wall of the enclosure is maintained at a constant low temperature and is moving with a constant speed in its own plane from left to right. The governing equations are discretized by the control volume method and are solved numerically by the SIMPLE algorithm. A parametric study is performed and a set of graphical results is presented and discussed to demonstrate the interesting features of the solution.

Darcian Natural Convection in an Inclined Trapezoidal Cavity Partly Filled with a Porous Layer and Partly with a Nanofluid Layer

The problem of Darcian natural convection in a trapezoidal cavity partly filled with porous layer and partly with nanofluid layer is studied numerically using finite difference method. The left slopping wall is maintained at a constant hot temperature and the right slopping wall is maintained at a constant cold temperature, while the horizontal walls are adiabatic. Water-based nanofluids with Ag or Cu or TiO2 nanoparticles are chosen for the investigation. The governing parameters of this study are the Rayleigh number (104 ≤ Ra ≤ 107), Darcy number (10–5 ≤ Da ≤ 10–3), nanoparticle volume fraction (0 ≤ φ ≤ 0.2), porous layer thickness (0.3 ≤ S ≤ 0,7), the side wall inclination angle (0° ≤ ϕ ≤ 21.8°) and the inclination angle of the cavity (0° ≤ ϖ ≤ 90°). Explanation for the influence of various above-mentioned parameters on streamlines, isotherms and overall heat transfer is provided on the basis of thermal conductivities of nanoparticles, water and porous medium. It is shown that convection increases remarkably by the addition of silver-water nanofluid and the heat transfer rate is affected by the inclination angle of the cavity variation. The results have possible applications in heat-removal and heat-storage fluid-saturated porous systems.

Study of heat transfer in water-Cu nanofluid saturated porous medium through two entrapped trapezoidal cavities under the influence of magnetic field

This manuscript contains numerical investigation of heat transfer by free convection through an enclosure of two trapezoidal cavities full of water-copper nanofluid saturated porous medium when horizontal upper and lower sides are provided uniform heat, inclined boundaries are assumed cold and central horizontal wall is considered insulated perfectly. The momentum equations governing the flow problem are first simplified by using penalty method to eliminate pressure terms using continuity equation and then the reduced momentum equations along with energy equation are solved by the Galerkin weighted residual technique of finite element method. Numerical computations are performed in terms of streamlines, isotherms, Nusselt number and average Nusselt number for various values of pertinent parameters governing the flow like Darcy number, Hartman number, Rayleigh number, Prandtl number, Porosity parameter and solid volume fraction.It has been noticed that the stream line circulations gets stronger in the enclosure with increase in Rayleigh number and it appears more significantly in lower enclosure in comparison to top enclosure. Whereas isotherms are observed to be broken and distorted for large Rayleigh numbers showing the convection dominant effects in the enclosure. Isotherms deform largely for large value of Darcy number and strength of streamline circulations is noted to increase with increase in Darcy number. Furthermore, local Nusselt numbers for horizontal walls are seen to be maximum at edges and decreases while moving towards center of the side from corners. Average Nusselt numbers are noted to be increasing function of porosity parameter however it increases along bottom wall and decreases along top wall with increase in Darcy number.

Thermal management of water based SWCNTs enclosed in a partially heated trapezoidal cavity via FEM

Present study, examines the phenomena of natural convection flow in a partially heated trapezoidal cavity loaded with the nanofluid in the presence of Single Wall Carbon Nanotubes (SWCNTs). A modified model for effective thermal conductivity of carbon nanotube is used to develop the governing partial differential equations. Thermal management within the cavity is controlled via two simultaneous features: one is to use the partially heated bottom wall and other is to use conductivity of Carbon particles. Most significant and physical conditions are adjusted at the inclined walls of the trapezoidal cavity to obtain the behavior of stream lines and heat management. The Gelerkin finite element method is implemented to solve the dimensionless form of PDEs. Simulations are performed for the different lengths of the heated portion (0.3⩽L⩽0.7), various choices of Raleigh number (104⩽Ra⩽107) and volume fraction (0.0⩽ϕ⩽0.2). Flow field and thermal field are visualized through streamlines and isotherms. Moreover, results are obtained for Nusselt number over partially heated wall, temperature and velocity distribution over the mean position of the cavity. It is found that, by reducing the length of heated portion, flow filed is getting stronger but thermal depicts the opposite trend inside the cavity. Variation of Raleigh number also has significant influence on flow and thermal field. Conduction was dominant at low Ra but later on convection was found to be dominant for large choice. Fluid circulation was stronger and heat transfer rate was very slow at low viscous effects. From the graph it is clear that greater heat transfer will be occurred in the presence of nanofluid as compared to the based fluid water. Similarly velocity distribution of water is dominant as compare to the nanofluid.

Natural Convection in a Trapezoidal Cavity with an Inner Conductive Object of Different Shapes and Filled with Nanofluids of Different Nanoparticle Shapes

Natural convection in a trapezoidal cavity having different conductive obstacles which are portions of a full circular object and filled with different shaped nanoparticles (spherical, blade and cylindrical) was numerically investigated. The side walls of the trapezoidal cavity are kept at constant hot and cold temperatures, while the top and bottom walls are assumed to be adiabatic. The governing equations are solved with finite element method. The effects of the Rayleigh number (between 104 and 106), inclination angle of the side walls (between 0° and 20°), thermal conductivity ratio (between 0.01 and 100), solid volume fraction of the nanoparticles (between 0 and 0.04) and nanoparticle shape (spherical, blade and cylindrical) on the fluid flow and heat transfer characteristics were studied in detail. It was observed that the shape of the obstacle is very effective to change the heat transfer characteristic for lower values of Rayleigh number. Thermal conductivity ratio influences the heat transfer characteristics slightly. Averaged Nusselt number increases linearly with nanoparticle volume fraction and the slope of the curves is highest for the cylindrical nanoparticle and it is not affected by the obstacle types. Averaged Nusselt number enhancements are in the range of 13 and 16% when cylindrical nanoparticles are used instead of spherical ones with different obstacle shapes for thermal conductivity ratio of 0.01 and 100.

Effect of spatial side-wall temperature variation on transient natural convection of a nanofluid in a trapezoidal cavity

PurposeThis paper aims to study analytically and numerically the problem of transient natural convection heat transfer in a trapezoidal cavity with spatial side-wall temperature variation.Design/methodology/approachThe governing equations subject to the initial and boundary conditions are solved numerically by the finite difference scheme consisting of the alternating direction implicit method and the tri-diagonal matrix algorithm. The left sloping wall of the cavity is heated to non-uniform temperature, and the right sloping wall is maintained at a constant cold temperature, while the horizontal walls are kept adiabatic.FindingsIt is shown that the heat transfer rate increases in non-uniform heating increments, whereby low wave number values are more affected by the convection. The best heat transfer enhancement results from larger side wall inclination angle; however, trapezoidal cavities require longer time compared to that of square to reach steady state.Originality/valueThe study of natural convection heat transfer in a trapezoidal cavity filled with nanofluid and heated by spatial side-wall temperature has not yet been undertaken. Thus, the authors of the present study believe that this work is valuable.

MHD-mixed convection flow in a lid-driven trapezoidal cavity under uniformly/non-uniformly heated bottom wall

PurposeThe purpose of this paper is to analyze numerical results for heat transfer through mixed convection in an incompressible steady lid-driven fluid flow inside a trapezoidal cavity in the presence of a uniform magnetic field.Design/methodology/approachIn this study, the authors have considered three different cases, in which left and right walls of the cavity are tilted at different angles of 0, 30 and 45 degrees, respectively. Both left and right side walls of the cavity are taken cold and the upper wall is insulated and assumed moving with constant speed, whereas the bottom wall is considered to be heated uniformly/non-uniformly. To eliminate pressure term, penalty method is applied to governing Navier–Stokes’ equations. The reduced equations are solved by Galerkin weighted residual technique of finite element method. Grid-independent results are obtained and shown in terms of plots for streamlines, isotherms, Nusselt number and average Nusselt number for a wide range of flow parameters, including Rayleigh numbers Ra, Prandtl number Pr and Hartman number Ha.FindingsIt has been observed that the effects of moving lid become negligible for Ra = 100,000, whereas increasing Rayleigh number results in stronger streamline circulation and convection dominant effects inside the enclosure. Local Nusselt number Nu along the bottom wall is observed to be maximum at edges and it reduces while moving toward the center from edges, and attains minimum value at the center of the bottom wall.Research limitations/implicationsThe problem is modeled for laminar and incompressible flow, induced magnetic field has been considered negligibly small and local thermal equilibrium has been assumed.Originality/valueIn this investigation, the authors have presented new and original results for mixed convection flow inside a lid-driven trapezoidal cavity under the influence of a magnetic field. Hence, this study would be important for the researchers working in the area of heat transfer in cavity flows involving magnetic effects to become familiar with the flow behavior and properties.

Numerical Investigation on Trapezoidal Cavity Receiver Used In LFR with Water Flow in Absorber Tubes

In the present study, numerical three dimensional model of trapezoidal cavity used in LFR was analysed. Results are presented in the form of Thermal losses occurring from the receiver operating with an absorber tube temperature from 350-550 K in step of 50 K and emissivity varied from 0.5-1.0. Effect of wind blowing below lower glass plate (cavity aperture) were also analysed considering the heat transfer coefficient from 5 to 25 W/m2K. At lower absorber temperature (350 K) convective losses is found to be 43% of the total heat loss whereas radiative losses accounted 57%. For higher absorber temperature radiative losses are dominant (77%) and convective losses are reduced to 23%. The air temperature gradient in the horizontal direction (parallel to lower glass plate) is found to be negligible whereas it is varied significantly in vertical direction (normal to lower glass plate). The average cavity air temperature is observed to be 480 K for low wind flow (h=5 W/m2K) and it reduces to 360 K for h=25 W/m2K. This has resulted in increased convective losses (27% higher).

Chebyshev collocation spectral lattice Boltzmann method in generalized curvilinear coordinates

Abstract In this work, the Chebyshev collocation spectral lattice Boltzmann method is implemented in the generalized curvilinear coordinates to provide an accurate and efficient low-speed LB-based flow solver to be capable of handling curved geometries with non-uniform grids. The low-speed form of the D2Q9 and D3Q19 lattice Boltzmann equations is transformed into the generalized curvilinear coordinates and then the spatial derivatives in the resulting equations are discretized by using the Chebyshev collocation spectral method and the temporal term is discretized with the fourth-order Runge–Kutta scheme to provide an accurate and efficient low-speed flow solver. All boundary conditions are implemented based on the solution of the governing equations in the generalized curvilinear coordinates. The accuracy and robustness of the solution methodology presented are demonstrated by computing different benchmark and practical low-speed flow problems that are 2D Couette flow between concentric moving cylinders, 2D flow in a gradual expansion duct, 2D regularized trapezoidal cavity flow, and 3D flow in curved ducts of rectangular cross-sections. Results obtained for these test cases are in good agreement with the existing analytical and numerical results. The computational efficiency of the proposed solution methodology based on the Chebyshev collocation spectral lattice Boltzmann method implemented in the generalized curvilinear coordinates is also examined by comparison with the developed second-order finite-difference lattice Boltzmann method that indicates the proposed method provides more accurate and efficient solutions in terms of the CPU time and memory usage. The study shows the present solution methodology is robust and accurate for solving 2D and 3D low-speed flows over practical geometries. Indications are that the solution algorithm based on the CCSLBM in the generalized curvilinear coordinates does not need any filtering or numerical dissipation for stability considerations and thus high accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the evaluation of other LBM-based flow solvers.

Influence of Heat Sources and Thermal Boundary Conditions on Natural Convective Currents in a Trapezoidal Porous Cavity

This paper deals with steady laminar natural convective Darcian flow of a viscous incompressible fluid in a finite trapezoidal cavity filled with isotropic permeable material of low permeability. The vertical side walls of the cavity are assumed to be adiabatic, whereas the lower horizontal and the sloping upper walls are isothermal but with different temperatures. It is further assumed that the flow domain is subject to heat sources/sinks of uniform strength, resulting in the internal generation or absorption of heat. The governing non-dimensional partial differential equations, together with an appropriate set of thermal conditions and subject to Boussinesq approximation, have been solved numerically. The effects of a number of important non-dimensional quantities, namely Rayleigh–Darcy number, aspect ratio, internal heating parameter and inclination parameter have been discussed in relation to the isotherms and streamlines.

Mixed convection heat transfer of nanofluids in a trapezoidal cavity having an adiabatic square body at its center

Mixed convection heat transfer of nanofluids in a trapezoidal cavity having an adiabatic square body at its center

Fabrication and testing of silicon-based microchannel heat exchanger inspired by leaf venation pattern for electronic cooling

Microchannel heat sinks (MCHS) provide an efficient means to dissipate large heat flux. The task of fabricating MCHS becomes challenging due to availability of large number of newer materials and processes. In this work, tetra methyl ammonium hydroxide (TMAH) etching and LASER machining methods for fabricating the microchannels are compared with respect to dimensional accuracy, the profile of channel, surface roughness, aspect ratio, material compatibility, cost and thermal performance. TMAH etching results in trapezoidal cavity instead of the rectangular cavity, finest surface finish (8 nm), and is suited for batch fabrication. While, LASER machining results in small taper profile (10o to vertical surface), rough surface (2.83 μm), and better dimensional accuracy and is suited for job production. Experimental results show that both MCHS exhibit similar thermal performance at lower flow rates. At higher flow rates, however, LASER fabricated MCHS have 25% higher thermal performance than TMAH etched channels.

Investigations on the effect of non-uniform temperature on fluid flow and heat transfer in a trapezoidal cavity filled with porous media

Simulations were carried out for natural convection in a trapezoidal cavity filled with porous media to investigate the effect of uniformly and non-uniformly heated bottom wall using finite element computational procedure. The enclosure used for flow and heat transfer analysis has hot bottom wall, constant temperature cold top wall and adiabatic side walls. The bottom wall is subjected to uniform/linear/sinusoidally varying temperatures. Results are presented in the form of stream lines, isotherms, heatline plots, local and average Nusselt numbers. Heatline visualization technique is a useful method that gives information on heat transport from the heated to cold region inside the porous trapezoidal enclosure with varying temperature boundary conditions. Nusselt numbers are computed for Darcy-modified Rayleigh numbers or Rayleigh number (Ra) ranging from 100 to 2000 for an aspect ratio (H/L) of 0.5. It is observed from this study that the uniform temperature at the bottom wall of the enclosure gives higher Nusselt number as compared to the linear and sinusoidally varying temperature cases. The average Nusselt numbers increases monotonically with Rayleigh number for bottom wall and top walls. The power law correlations between average Nusselt number and Rayleigh numbers are presented for convection dominated regions.

Transient natural convective heat transfer in a trapezoidal cavity filled with non-Newtonian nanofluid with sinusoidal boundary conditions on both sidewalls

Transient, laminar natural convection in a trapezoidal cavity filled with a non-Newtonian nanofluid with sinusoidal boundary conditions on both sidewalls is studied numerically by using the finite element method. The sloping walls of the cavity are heated by sinusoidal temperature distributions, while the horizontal walls allow no heat transfer to the surrounding. Water-based nanofluids with Ag or Cu or Al2O3 or TiO2 nanoparticles are chosen for investigation. The governing parameters of this study are the Rayleigh number (104 ≤Ra ≤ 106), phase deviation (0 ≤ γ ≤ π), amplitude ratio (0 ≤ ε ≤ 1), power-law index (0.6 ≤ n ≤ 1.4), sidewall inclination angle (0°≤ φ ≤ 21.8°), nanoparticle volume fraction (0 ≤ ϕ ≤ 0.2), and dimensionless time (0 ≤ τ ≤ 0.2). The results show that the heat transfer rate increases significantly by the addition of phase deviation. Strong heat transfer enhancements are obtained by higher sidewall inclination angles. However, for a square cavity, the heat transfer approaches the steady-state condition with the increment of the dimensionless time.

Sound Transmission Through a Double-Wall Structure Coupled with Two Trapezoidal Acoustic Cavities

This paper aims at investigating the sound transmission mechanism of a flexibly-linked finite length double-wall structure. The problem stems from the modeling of sound transmission through corrugated core sandwich panels for predicting its transmission loss. The spatial segmentation of the acoustic gap and fully structure-acoustic coupling effect between the flexural vibration of the inclined mechanical link and the two adjacent trapezoidal acoustic cavities are considered. The theoretical model of the considered vibro-acoustic system is developed by using the modal superposition method in conjunction with envelope rectangular technique. Based on the developed theoretical model, the general vibro-acoustics characteristics of the system is presented. Particularly by using the [Formula: see text] mode of the acoustic cavity and the first structural modal frequency, the ratio between the aerostatic stiffness and the structural stiffness is formulated, and a criterion is proposed to determine whether the sound insulation performance of the vibro-acoustic system is controlled mainly by the structure or the acoustic cavity. Numerical investigations reveal that with different stiffness ratio, the acoustic cavity affects the sound transmission through both the added stiffness and added mass following different mechanisms. Besides, the influence of the inclined angle of the connecting beam on sound insulation performance of the double-wall structure is also studied. The obtained results are believed to be helpful in the optimal design of corrugated core sandwich panels for sound insulation.