Enhanced natural convection in an isosceles triangular enclosure filled with a nanofluid

Natural convection is studied in an isosceles triangular enclosure with a heat source located at its bottom wall and filled with an Ethylene Glycol–Copper nanofluid. This paper examines the effects of pertinent parameters such as the Rayleigh number, the solid volume fraction, the heat source location, and the enclosure apex angle on the thermal performance of the enclosure. The thermal performance of the enclosure is improved with an increase in the Rayleigh number and solid volume fraction. The results also show that the variation of heat transfer rate with respect to the enclosure apex angle and heat source position and dimensions is different at low and high Rayleigh numbers. A comparison is also presented between the results obtained from the modified and original Maxwell models. The results show that the heat transfer is generally higher based on the modified Maxwell model.     

Phase change process with free convection in a circular enclosure: numerical simulations

A numerical study of unsteady natural convection flow during freezing of water in a circular enclosure is presented. Mathematical model for phase change is based on apparent capacity method formulation and the governing equations are discretized on a fixed grid by means of finite element method. Water’s temperature is initially higher than its freezing temperature. Then, the temperature of the enclosure’s boundary is dropped to a temperature lower than freezing temperature. Ice forms at the enclosure boundary while natural convection flow is induced in the liquid region. Calculations have been made for the rate of change of solid fraction and temperature distributions, for conduction and conduction plus convection modes of heat transfer, and density inversion near freezing temperature phenomenon of water is considered. High resolution capturing of solid/liquid moving boundary as well as the details of flow structure is presented. The results indicate that the effect of natural convection is dominant over conduction if the Rayleigh number is higher than 5 × 10⁶ and relatively insignificant if the Rayleigh number is less than 1 × 10⁶.     

Simulation of natural convection heat transfer in an enclosure by the lattice-Boltzmann method

This paper presents the simulation of natural heat convection in an enclosure using Cubic-Interpolated-Pseudo-Particle (CIP) lattice-Boltzmann method. A D2Q9 lattice model was coupled with the simplest D2Q4 lattice model to represent density and internal energy distribution function, respectively. The effects of the Rayleigh number on the flow pattern were studied. The enclosure is filled with air heated by a small localized source of heat at two different positions on the bottom wall. The results explain the mechanism of natural convection rate increasing due to the Rayleigh number and heat source position changing. The comparison of the results was in excellent agreement with results from the literature.     

MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM

Magnetohydrodynamic flow in a nanofluid filled inclined enclosure is investigated numerically using the Control Volume based Finite Element Method. The cold wall of cavity is assumed to mimic a sinusoidal profile with different dimensionless amplitude, and the fluid in the enclosure is a water-based nanofluid containing Cu nanoparticles. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts and Brinkman models, respectively. Numerical simulations were performed for different governing parameters namely the Hartmann number, Rayleigh number, nanoparticle volume fraction and inclination angle of enclosure. The results show that in presence of magnetic field, velocity field retarded, and hence, convection and Nusselt number decreases. At Ra = 10³, maximum value of enhancement for low Hartmann number is obtained at γ = 0°, but for higher values of Hartmann number, maximum values of E occurs at γ = 90°. Also, it can be found that for all values of Hartmann number, at Ra = 10⁴ and 10⁵, maximum value of E is obtained at γ = 60° and γ = 0°, respectively.     

A two-dimensional study on natural convection and heat transfer in the enclosure with heat transfer and radiation coupled in natural convection

Numerical investigation using SIMPLE algorithm with QUICK scheme for natural convection and heat transfer in the enclosure bounded by a solid wall and with heat transfer and radiation coupled in natural convection has been conducted.The various parameters are:Rayleigh number(from 103 to 105),dimensionless conductivity of bounding wall(from 0 to 100),dimensionless wall thickness(from 0 to 0.6) and radiation emissivity of all surfaces(from 0 to 1).The results suggest that flow and heat transfer are influenced...     

Natural convection in a porous trapezoidal enclosure with an inclined magnetic field

The effect of a magnetic field on steady convection in a trapezoidal enclosure filled with a fluid-saturated porous medium is studied numerically by the finite difference method. The inclined sloping boundaries is treated by adopting staircase-like zigzag lines. The sloping walls are maintained isothermally at different temperatures. The top and bottom horizontal straight walls are kept adiabatic. The results indicate that the heat transfer performance decreases by decreasing the angle of sloping wall. Optimum reducing of the heat transfer rate was obtained for an acute trapezoidal enclosure and large magnetic field in the horizontal direction.     

Numerical determination of boundary heat fluxes in an enclosure dynamically with natural convection through Fletcher-Reeves gradient method

An iterative Fletcher-Reeves conjugate gradient method (CGM) is adopted to estimate the boundary heat fluxes in a fluid-saturated enclosure, where the fluid flow is dynamically coupled with the heat convection. The sets of direct, sensitivity and adjoint equations required for the solution of the inverse problem are formulated in terms of an arbitrary domain in two dimensions. The methodology of conjugate gradient method solves the inverse natural convection problem satisfactorily without any a priori information about the unknown heat fluxes. The pressure-correction method is utilized to solve the continuum direct, sensitivity and adjoint problems by enforcing global mass and energy conservations. Effects of boundary heat flux profile and thermal Rayleigh number on the convective heat transport are investigated. The effects of position and number of temperature sensors on the inverse problem solution are also addressed in this paper. Inverse solutions of noise data are regularized with the Discrepancy Principle of Alifanov; otherwise, the high frequency components of the random noise were reproduced.     

The Rayleigh-Benard convection in an enclosure with walls of finite thickness

Mathematical simulation of transient natural convection in an enclosure having walls of a finite thickness at the presence of a heat source located at the bottom of the cavity has been carried out. Special attention was given to the analysis of the Grashov number (Gr) effect, describing the intensity of a heat source; of the transient factor, defining the formation and development of thermodynamic structures; and also of the heat conductivity ratio. Typical distributions of streamlines and temperature fields have been received. Scales of key parameters (the Grashov number, dimensionless time, the heat conductivity ratio), affecting both local characteristics (streamlines, isotherms) and integral characteristics (the average Nusselt number) of the analyzed process, have been determined.     

Effect of aspect ratio on convection in a porous enclosure with partially active thermal walls

The aim of the present numerical investigation is to understand the effect of aspect ratio and partially thermally active zones on convective flow and heat transfer in a rectangular porous enclosure. Five different heating and cooling zones are considered along the vertical walls while the remaining portions of the sidewalls and top and bottom of the enclosure are adiabatic. The Brinkman-Forchheimer extended Darcy model is used in the study. The governing equations are solved by the finite volume method with the SIMPLE algorithm. The computations are carried out for a wide range of parameters and the results are presented graphically. The results reveal that the location of heating and cooling zones has a significant influence on the flow pattern and the corresponding heat transfer in the enclosure. The rate of heat transfer approaches to a constant value for very low values of the Darcy number. The heat transfer rate is decreased on increasing the aspect ratio.     

A finite element numerical solution of natural convection in enclosed cavities

Steady state free convective flow enclosed within a cavity and subjected to a temperature gradient is predicted using the finite element method. The matrix equations resulting from the finite element discretisation and formulation are solved using both an iterative and a modified Newton-Raphson scheme. An assessment of the variation in the characteristics of the flow regime is made in association with the dimensionless Prandtl and Rayleigh numbers. A further parameter of interest in such problems is the cavity aspect ratio. The upper limit for the Rayleigh number (based on cavity width) presented in the present paper is 10⁷. The flow patterns are obtained for Prandtl numbers in the range 10^?2 ? Pr ? 10³ and for aspect ratios 1, 10, 20. Where possible the results are compared with existing solutions obtained using the finite difference method. A satisfactory correlation exists where such comparisons can be made. The results complement and extend those obtained during previous theoretical and numerical investigations.     

A numerical method for predicting natural convection in horizontal cylinders with asymmetric boundary conditions

A numerical technique is developed to predict the two-dimensional transient natural convection heat transfer within a horizontal cylinder. Finite difference analogs of the Navier-Stokes and thermal energy equations are solved in the stream function-vorticity framework. The solution method, which is a modification of an alternating-direction implicit (ADI) scheme wherein the convective terms are evaluated explicitly, is found to be computationally more efficient than either an ADI or an explicit method. Unlike previous work, the present technique will accommodate completely arbitrary temperature boundary conditions. Thus, rather than considering an annular space or half of a symmetric cylinder, the solutions are determined for a full cylinder. A Cartesian form of the governing equations is employed at the point $\text{r= 0}$ where the polar coordinate equations become singular. The computed results are found to be in good agreement with previously published experimental data.     

Performance of a bend-diffuser system: Experimental and numerical studies

The turbulent flow inside a combined bend-diffuser configuration with a rectangular cross section is experimentally and numerically studied. The experimental study includes the outer and inner-wall-pressure measurements and the overall system/diffuser loss determination. Simulation is performed using the high-Reynolds number k-ε turbulence model improved by the low-Reynolds number k-ε turbulence model near the walls, because of its success to predict the flow with strong adverse pressure gradient. So the present paper provides a numerical procedure for the calculation of turbulent flow in a sequence curved, expanding passages, with emphasis on the bend-diffuser configuration system consisting of a 90° bend followed by a diffuser with different expanding angles ranges from 2θ = 6-30° at different inflow Reynolds numbers. Satisfied comparisons with reported experimental data in the literature as well as that carried out by the present authors at the heat engine laboratory of Menoufiya university show that the numerical method with the utilized closure turbulence model reproduces the essential features of upstream curved flow effects on the diffuser performance. The effect of spacer length (between the bend and diffuser) is also experimentally and numerically included. The results show that there is an optimum diffuser angle which depends on the inflow Reynolds number and produces the minimum pressure loss and hence good performance of such complex geometry is obtained.     

Analysis of radiation-natural convection in a divided enclosure using the lattice Boltzmann method

A numerical hybrid lattice-Boltzmann equation finite-difference is used to study the radiation-natural convection phenomena in a square cavity, differentially heated, with partition of finite thickness and varying height located vertically at the center of the cavity. The results obtained show that the radiation exchange produces a rise in the heat transfer. The average Nusselt number and the throughflow strength increase when the gap width (w), maximal difference temperature (ΔT) and cavity width (L) get larger. Effects of different parameters on streamlines, temperature fields, average Nusselt number and throughflow strength are discussed.     

Modeling nonlinear waves in a numerical wave tank with localized meshless RBF method

This paper presents the numerical simulation of free surface waves in a 2D domain which represents a wave tank, using a localized approach of the meshless radial basis function (RBF) method. Instead of global collocation, the local approach breaks down the problem domain into subdomains, leading to a sparse global system matrix which is particularly advantageous in tackling the time consuming simulation process. Mixed Eulerian–Lagrangian approach is adopted for free surface tracking and fourth order Adams–Bashforth–Moulton scheme (ABM4) is used for time stepping. Both linear and nonlinear Stokes waves are simulated and compared to analytical solutions.     

A numerical analysis of freezing and melting with convection

An explicit finite element algorithm is presented for the solution of the basic equations describing combined conductive and convective transfer of heat in materials which may undergo a liquid/solid change of phase. The method is used to analyse the influence of natural convection on the process of freezing and melting in a cylindrical thermal cavity. The results produced in the case of freezing are shown to agree qualitatively with experimental observations.     

具有非均匀内热源的多孔介质中自然对流传热的数值研究

采用数值方法分析了填充多孔介质的竖直同心套管内,非均匀分布的内热源和内外壁面温差对自然对流的影响。考察了高宽比A、内热源分布系数m以及内外Rayleigh数之比Rai/Ra对流场、温度场和内外壁面Nusselt数的影响。结果表明：Rai/Ra较大时流场中部形成逆向环流,并出现θ＞1的高温区;内壁面Nusselt数呈现先增大后减小的趋势,大约在Z=0．8处出现转折。外壁面Nusselt数在Z＞0．8处变化加剧,表明外壁面对流传热主要集中在管上部区域。m增大流体中心逆向环流随之减小并最终消失。     

重力场及微重力场下Marangoni对流的实验测定与数值模拟

研究了在重力场及微重力场下,由温度梯度引起的Marangoni对流。实验在NASA的KC-135飞机中进行,通过飞机作俯冲飞行而产生微重力场。应用激光辐照激发染料变色技术,使流体流动可视化。研究了在不同粘度的硅油与水的液-液相界面上的流体流动,借助于二维正交曲线坐标中的Navier-Stokes方程进行数值模拟,并对比了计算与实验结果。     

Effect of heating location and size on mixed convection in lid-driven cavities

A numerical study is performed to analyze the mixed convection heat transfer and fluid flow in lid-driven cavities with different lengths of the heating portion and different locations of it. The left wall has been heated fully or partially to a higher temperature, whereas the right wall is maintained at a lower temperature. Three different lengths of the heating portion and three different locations of it are used along the hot wall. The remaining portions of the left wall, and the top and the bottom walls of the cavity are insulated. The finite volume method is used to discretize the governing equations which are then solved iteratively. The velocities and pressure are coupled by the SIMPLE algorithm. Results are presented graphically in the form of streamlines, isotherms and velocity profiles. It is concluded that the heat transfer rate is enhanced on reducing the heating portion and when the portion is at middle or top of the hot wall of the cavity.     

A numerical study of a 3D bioheat transfer problem with different spatial heating

We develop numerical methods for the computer simulation and modeling of a three dimensional heat transfer problem in biological bodies. The technique is intended for the temperature predications and parameter measurements in thermal medical practices and for the studies of thermomechanical interaction of biological bodies at high temperature.We examine a mathematical model based on the classical well-known Pennes equation for heat transfer in biological bodies. A finite difference discretization scheme is used to discretize the governing partial differential equation. A preconditioned iterative solver is employed to solve the resulting sparse linear system at each time step. Numerical results are obtained to demonstrate the efficacy of the proposed numerical methods.