Trapezoidal Cavity Research Articles

Erratum to: MHD natural convection and thermal radiation of diamond–water nanofluid around rotating elliptical baffle inside inclined trapezoidal cavity

In this work, we study the natural convection and thermal radiation heat transfer of diamond–water nanofluid around rotating elliptical baffle inside inclined trapezoidal cavity under Lorentz forces effect in the presence of uniform heat generation/absorption. The trapezoidal cavity lateral walls are uniformly cooled, and the top and bottom walls are kept adiabatic. The interior rotating elliptical baffle is uniformly heated. Our numerical study is realized by the software Comsol Multiphysics based on the on the finite element method. The results extracted show that an increment on the convection heat transfer is reached by increasing Rayleigh number, the radiation parameter and the elliptical baffle horizontal radius; however, the increment of Hartmann number reduces it. The effect of cavity inclination on the convection heat transfer depends on the baffle position. The presence of uniform heat generation increases the temperature field inside cavity and improves the convection flow, but the presence of uniform heat absorption reduces it. Using nanoparticles with higher shape factor improves more the convection heat transfer.

Finite element analysis of mixed convection flow in a trapezoidal cavity with non-uniform temperature

A two dimensional flow analysis in a cavity shaped isosceles trapezium is carried out. Non-parallel sides of a trapezium are adiabatic. A varying sinusoidal temperature is applied to the lower wall while the upper wall is at constant temperature. Upper wall of the cavity moves with a velocity η0 in the positive x-direction. Also, B0 is constant magnetic field of strength aligned in the same x-direction and Newtonian fluid is considered. The values of magnetic field parameter used are Ha=0,50, the Richardson number is Ri=0.1,1,10, Re=100 is Reynolds number used for the analysis, the amplitude of sinusoidal temperature is m=0.25,0.5,1. The impacts of different leading parameters are analyzed by plotting streamlines for flow fields and isotherm contours for temperature of the flow dynamics. The graphs that signify the variation of average Nusselt number and local Nusselt number are sketched for both lower and upper walls of the cavity. Result indicated that with constant temperature the top wall of the boundary layer thickness decreases as Richardson number Ri increases and for bottom wall with variable temperature. The Nusselt number gets higher with an increment in the amplitude of the oscillation of temperature function. Furthermore, the study revealed that the average Nusselt number gets reduced as the intensity of magnetic field is enhanced. The variation in transit of heat at the bottom wall is similar but the maximum value of heat transfer at the bottom wall shows a variation from 3.8 to 20 when Ha=0 and from 3 to 18 when Ha=50. The accuracy of the present numerical algorithms is also established.

Numerical Analysis of Labyrinth Seal Performance for the Impeller Backface Cavity of a Supercritical CO2 Radial Inflow Turbine

For a radial inflow turbine (RIT), leakage flow in impeller backface cavity has critical impacts on aerodynamic performance of the RIT and axial force acting on the RIT impeller. In order to control this leakage flow, different types of labyrinth seals are numerically studied in this paper based on a supercritical carbon dioxide (S-CO2) RIT. The effects of seal clearance and cavity outlet pressure are first analyzed, and the impacts of seal design parameters, including height, number and shape of seal teeth, are evaluated. Results indicate that adding labyrinth seal can improve cavity pressure and hence adequately inhibits leakage flow. Decreasing the seal clearance and increasing the height of seal teeth are beneficial to improve sealing performance, and the same effect can be obtained by increasing the number of seal teeth. Meanwhile, employing seals can reduce leakage loss and improve RIT efficiency under a specific range of cavity outlet pressure. Finally, the influences of seal types on the flow field in seal cavity are numerically analyzed, and results demonstrate that isosceles trapezoidal type of seal cavity has better sealing performance than triangular, rectangular and right-angled trapezoidal seal cavities.

Numerical Study of Mixed Convection in an Isosceles Trapezoidal Cavity for the Optimization of ASUTO Charcoal Stove

Numerical Study of Mixed Convection in an Isosceles Trapezoidal Cavity for the Optimization of ASUTO Charcoal Stove

Nanofluid thermal performance inside an absorber tube of LFR unit equipped with helical T-shape tape

Entropy generation and thermal treatment of nanofluid through a solar unit with turbulent regime was examined in current investigation. To create the solar system, mirrors, trapezoidal cavity and tube have been utilized. The mirrors were situated above the ground with certain angles and tube was equipped with turbulator. Working fluid is homogeneous mixture of H2O-Al2O3 and temperature dependent variables were incorporated. Verification based on empirical correlation depicts the high accuracy of FVM simulation. Irreversibility components and friction resistance as well as Nu and thermal efficiency have been reported in outputs. The active variables are Twist ratio (TR), V·, Width ratio (WR), Tin. Each factor which can augment the secondary flow makes the stronger impingement of fluid with wall and lower Tw appears. Such disruption of boundary layer causes cooling rate to augment. As V·, TR and WR augment, wall temperature reduces about 1.01%, 0.063% and 0.0217%. With rise of TR and WR, pressure drop augments about 25.87% and 10.85%, respectively. Revolution number has greater impact on resistance of fluid than width of the tape. Augment of WR and TR makes friction resistance to augment about 7.46% and 29.68%. Considering greater WR and TR can able to more disturb the boundary layer and Nu can be augmented about 1.5% and 4.54%, respectively. Augmenting TR, WR and Re can reduce the irreversibility which is a pleasant result to obtain more available work. Augment of TR makes Sgen,h to decline by 3.29% while Sgen,f rises about 15.24%. Thermal performance decreases about 23.68% with rise of Tin while it augments about 0.027% and 0.11% with growth of WR and TR, respectively.

Numerical Simulation of MHD Natural Convection Flow Within Porous Trapezoidal Cavity With Heated Triangular Obstacle

A steady laminar two-dimensional finite element based Galerkin weighted residual numerical approach (GWRNA) has been adopted to solve magnetohydrodynamic (MHD) natural convective flow filled with porous medium in a trapezoidal cavity with various aspect ratio of heated triangular obstacle $$ (1/3 \le AR \le 1) $$ . The boundary location of the cavity consists of non-uniform heating of bottom wall whilst the two vertical walls are maintained at a cold temperature and the top wall is thermal insulated. For the simulation purpose, wide range of parameters, such as, Hartmann number (Ha = 50), Prandtl number (0.026 ≤ Pr ≤ 1000), Rayleigh number (103 ≤ Ra ≤ 106) and Darcy number (10−5 ≤ Da ≤ 10−1) are used in the cavity with various AR. The study demonstrated that the aforementioned parameters have strong influence on the stream functions and isotherms for different AR. A stronger flow circulation is observed for higher Ra and Da. Besides these, a symmetry for fluid flow simulations and isotherm contours are viewed. The result too unveils that the heat transfer rates as well as local and average Nusselt numbers strongly depend on various AR and abovementioned parameters.

MHD natural convection and thermal radiation of diamond–water nanofluid around rotating elliptical baffle inside inclined trapezoidal cavity

In this work, we study the natural convection and thermal radiation heat transfer of diamond–water nanofluid around rotating elliptical baffle inside inclined trapezoidal cavity under Lorentz forces effect in the presence of uniform heat generation/absorption. The trapezoidal cavity lateral walls are uniformly cooled, and the top and bottom walls are kept adiabatic. The interior rotating elliptical baffle is uniformly heated. Our numerical study is realized by the software Comsol Multiphysics based on the on the finite element method. The results extracted show that an increment on the convection heat transfer is reached by increasing Rayleigh number, the radiation parameter and the elliptical baffle horizontal radius; however, the increment of Hartmann number reduces it. The effect of cavity inclination on the convection heat transfer depends on the baffle position. The presence of uniform heat generation increases the temperature field inside cavity and improves the convection flow, but the presence of uniform heat absorption reduces it. Using nanoparticles with higher shape factor improves more the convection heat transfer.

Solar energy application for LFR unit with trapezoidal cavity receiver considering radiative mode

In current article, influence of radiation and convection modes on behavior of air inside an absorber in trapezoidal shape has been investigated. Such cavity is part of Linear Fresnel Reflector (LFR) unit and it is important to analyze such geometry to reach higher performance. Properties of carrier fluid were assumed as function of temperature. To involve radiation effect, discrete ordinates model was implemented. Influences of external convective factor (hext), Angle of adiabatic wall (θ), temperature ratio (Tr) on irreversibility and heat transfer were depicted in outputs. Augment of Tr, θ and hext cause incident radiation to decline about 85.95%, 20.97% and 20.68% with assuming lowest values of other factors. Strength of eddy, temperature difference augments about 180% and 9.77% when θ enhances at Tr = 0.8. With considering highest level of other factors, as values of wind speed and θ intensify, Nu enhances 9.28% and 17.36% while it declines about 52.2% with rise of Tr. Given minimum values of other parameters, irreversibility intensifies about 45.45% and 8.3% with augment of hext and θ but it declines about 84.44% with augment of Tr.

Effects of cavity shapes and rounded corners of mold on polymer filling process in nanoimprint lithography

The effects of cavity shapes and rounded corners on polymer filling and mold stress distributions of nanoimprint lithography are investigated using a numerical simulation approach. Three types of mold cavities including a rectangular cavity with vertical sidewalls, a trapezoidal cavity with inclined sidewalls, and a semicircular cavity with curved sidewalls are used to study the polymer flow and the filling situation in the embossing stage. Stress distributions of three types of molds are compared to evaluate the mold durability under different imprint pressures. To further optimize filling ratios and the stress concentration, three molds with round corners are proposed. Simulation results show that the mold with a semicircular cavity can achieve complete filling under the lowest pressure, but the maximum von Mises stress is greater than that of others. The filling ratio of the trapezoidal cavity is better than that of the rectangular cavity, and the maximum von Mises stress is the smallest among three types of molds. With the increase in the radius of round corners for three molds, filling ratios are improved and the maximum stresses decrease apparently, which not only improve the pattern transferring fidelity but also prolong the service life of the mold effectively.

Numerical Simulation of Natural Convection in A Cavity Filled with A Nanofluid Who’s Wall Containing the Heat Source Is Inclined

In this work, we study by numerical simulation the natural convection in a trapezoidal cavity filled with a nanofluid whose wall containing the heat source is successively inclined at an angle varying from 0 to 60 ° at the most (in order to maintain a valid model straight vertical wall) with respect to the horizontal. The upper and lower walls on either side of the heat source are adiabatic while the other walls are subjected to a constant cold temperature. The hydrodynamic and thermal phenomena are described by the equations of Navier-Stockes and energy. The models Brinkman and Wasp are used to describe the thermo-physical properties of the nanofluid (water- ).The finite element method; based on the Galerkin principle; is used to solve the system of partial differential equations. We consider the effect of the solid volume fraction for different values ??of the Rayleigh number on the results obtained, in the form of isotherms and local, modified Nusselt numbers.

Impinging jet into an open trapezoidal cavity partially filled with a porous layer

A confined slot jet impinging into an open trapezoidal cavity containing a porous layer is investigated. To make the study accounts for a practical problem, constant heat flux is applied at the bottom of the cavity which is covered by a thin porous layer subjected to a cold impingement air jet. Darcy-Forchheimer model is used for the porous layer and its porosity range was taken to ensure thermal equilibrium between the fluid and the porous matrix. Finite element method is adopted for the numerical solution. Results show that the best thickness of the porous layer should be as minimal as possible, where increasing the porous layer thickness from 0.1 to 0.3 reduces the average Nusselt number by 17% when Darcy number is 10−3. It is found also that the trapezoidal cavity serves in attaining the fully developed condition early.

Buoyant Marangoni convection of nanofluids in right-angled trapezoidal cavity

The phenomena of buoyant Marangoni natural convection in a right-angled trapezoidal enclosure filled with water-based nanofluids have been studied numerically. The left vertical wall of the trapezoidal cavity is heated uniformly, the right inclined wall is cooled, and the top and bottom walls are insulated (adiabatic). The finite element method (FEM) is implemented to solve the non-dimensional governing equations. The investigation has been done for different values of parameters: the aspect ratio of the enclosure, Ar the nanoparticles volume fraction, the Marangoni numbers, Ma bf and the Rayleigh numbers, Ra bf

Cross flow on transient double‐diffusive natural convection in inclined porous trapezoidal enclosures

AbstractThis paper investigates the cross‐diffusion effects subject to exponential variable boundary conditions on transient double‐diffusive natural convection flow in an enclosure. The flow domain is a two‐dimensional inclined trapezoidal cavity filled with a porous medium. The top wall is assumed to be insulated and permeable, while the enclosure's bottom wall is subject to exponential varying temperature and concentration. The prescribed temperature and concentration are different at the vertical walls. Conservation equations are used as the governing equations. The finite element Galerkin weighted residual method, in association with the Newton‐Raphson scheme is employed to solve the system of coupled nondimensional equations. The numerical tests are confirmed with existing literature and are found to be in excellent agreement. The simulations results for stream functions, isotherms, and isoconcentrations are discussed for the various flow parameters. A sensitivity analysis using the response surface method suggests that the average Nusselt and Sherwood numbers are more sensitive to the cross‐diffusion effects. It is further observed that the cross‐diffusion terms stabilize the sensitivity to the angle of inclination.

Minimization of entropy generation due to MHD double diffusive mixed convection in a lid driven trapezoidal cavity with various aspect ratios

Entropy generation minimization has significant importance in fluid flow, heat and mass transfer in an enclosure to get the maximum efficiency of a system and to reduce the loss of energy. In the present study, the analysis of mixed convection fluid flow, heat and mass transfer with heat line and mass line concept and entropy generation due to the effects of fluid flow, heat flow, mass flow and magnetic field in a trapezoidal enclosure with linearly heated and diffusive left wall, uniformly heated and diffusive lower wall, cold and nondiffusive right wall, adiabatic and zero diffusion gradient top wall have been reported. Parametric studies for the wide range of Prandtl number (Pr = 0.7 for air cooling system and Pr = 1000 for the engines filled with olive or engine oils), Rayleigh number (Ra = 103–105), aspect ratio (A = 0.5–1.5) and inclination angle of the cavity (ϕ = 45°–90°) have been performed, which help to construct the perfect shape of cavity in many engineering and physical applications so that the entropy is minimum to get the maximum efficiency of any system. The finite-difference approximation has been used to find out the numerical solutions. Biconjugate Gradient Stabilized (BiCGStab) method is used to solve the discretized nonhomogeneous system of linear equations.

Effect of Driven Sidewalls on Mixed Convection in an Open Trapezoidal Cavity With a Channel

Abstract The mixed convection in an open trapezoidal lid-driven cavity connected with a channel is investigated in the present paper. Four different cases were considered depending on the movement of the cavity sidewalls. For case I, the left sidewall moves downward; for case II, the left sidewall moves downward and the right one moves upward; while for case III, only the right sidewall moves upward. A comparative case (case 0) is accounted when both sidewalls are assumed stationary. The base of the cavity is subjected to a localized heat source of constant temperature Th. The effects of Richardson number Ri and Reynolds number ratio Rer on the flow and thermal fields have been investigated. The results indicated that for cases I and II, the average Nusselt number increases with the increase of the Richardson number and Reynolds number ratio. Moreover, it was found that the maximum average Nusselt number occurs with case I. When the lid-driven speed is three times that of the inlet airflow velocity, the augmentations of the average Nusselt number compared with stationary walls are 163%, 158%, and 96% for cases I, II, and III, respectively.

Effects of volume fraction on water-based carbon nanotubes flow in a right-angle trapezoidal cavity: FEM based analysis

The purpose of the current study is to investigate the effects of water-based single-walled carbon nanotubes on free convection in a partially heated right trapezoidal cavity. The bottom wall of the cavity is heated while the side walls are kept cold, and the top wall is adiabatic. The governing dimensionless partial differential equations are solved with selected dimensionless boundary conditions via finite element scheme. The effects of the heating domain, the volume fraction of carbon nanotubes, Rayleigh and Hartmann numbers on the streamlines, isotherms, dimensionless horizontal and vertical velocities, dimensionless temperature and the local Nusselt number along the heating element are investigated numerically. The strength of streamlines decreases with increasing values of volume fraction of CNTs and Hartmann number while an enhanced behavior is noted for higher values of Rayleigh number and increasing the length of the heating element. The isotherms confirm the transfer of heat from bottom to side cold walls. It is demonstrated that the local Nusselt number attains the maximum values around the edges of the heating element and then decreases. Furthermore, the heating domain and the carbon nanotubes enhance the local Nusselt number along the heated surface.

Mixed convection of hybrid nanofluid in a porous trapezoidal chamber

A new class of nanofluids, called «hybrid nanofluids» is being used recently to enhance the heat transfer rate. The problem of mixed convection in a porous trapezoidal cavity filled with a hybrid nanofluid (Cu-Al2O3/water), is presented and the numerical results are obtained and discussed. Governing equations, transformed in terms of the dimensionless variables, have been worked out by the developed numerical algorithm based on the finite difference technique. The numerical results of streamlines and isotherms are investigated and the effect of different important parameters, such as: Reynolds number, Darcy number and the nanoparticles volume fraction is discussed. The variation of the average Nusselt number and fluid flow rate is obtained and observed that, by choosing different and appropriate nanoparticle combinations in hybrid nanofluid, the desired heat transfer rate can be obtained. The results are compared and successfully validated with previous reported results of the literature.

A comparative study of different optimised mirrors layouts of Linear Fresnel concentrators on annual energy and exergy efficiencies

This paper is aimed at investigating optimised mirror layout effects of Linear Fresnel Concentrators (LFC) by evaluating the annual energy and exergy efficiencies. Subsequently, a north–south central receiver LFC with cylindrical mirror profile and Trapezoidal Cavity Receiver (TCR) were considered. Two distinct mirrors reference configurations such as the sun and specific references and four different layouts such as the constant width and shift, constant width and variable shift, variable width and constant shift and variable width and variable shift studied separately and for each of them, the widths and shifts of mirrors optimised through an analytic method. A TCR was designed for every layout, and its heat loss was estimated from numerical modelling to derive the annual energy and exergy values. It was concluded that considered mirrors reference configurations and mirrors layouts play an important role in energy and exergy efficiencies. Furthermore, variable width layouts have a higher impact on energy and exergy amounts than variable shift layouts due to their effects on the receiver dimension and its heat loss. Finally, besides the highest efficiency of variable width and shift layout in specific reference, the constant and variable width layouts demonstrate superior performance in sun and specific references, respectively.

Numerical Study of the Turbulent Natural Convection in a Trapezoidal Cavity: Influence of the Inclination of the Lateral Walls

In this paper, we study the heat transfer in turbulent natural convection in a two- dimensional cavity with a trapezoidal section and isoscales filled out of air with as height H =2.5 m. In these conditions, the side walls are differentially heated while the horizontal walls are adiabatic. The k-ε turbulence model with a small Reynolds number was integrated in our calculation code. The governing equations of the problem were solved numerically by the commercial CFD code Fluent; which is based on the finite volume method and the Boussinesq approximation. The elaborated model is validated from the experimental results in the case of the turbulent flow in a square cavity. Then, the study was related primarily to the influence of the slope of the side walls of the cavity on the dynamic behavior and the heat transfer within the cavity.

Numerical simulation on MHD mixed convection of Cu-water nanofluid in a trapezoidal lid-driven cavity

Numerical simulation on MHD mixed convection of Cu-water nanofluid in a trapezoidal lid-driven cavity