A numerical study on the effect of a heated hollow cylinder on mixed convection in a ventilated cavity

The present work is aimed to study mixed convection heat transfer characteristics within a ventilated square cavity having a heated hollow cylinder. The heated hollow cylinder is placed at the center of the cavity. In addition, the wall of the cavity is assumed to be adiabatic. Flows are imposed through the inlet at the bottom of the left wall and exited at the top of the right wall of the cavity. The present study simulates a practical system such as air-cooled electronic equipment with a heat component or an oven with heater. Emphasis is sited on the influences of the cylinder diameter and the thermal conductivity of the cylinder in the cavity. The consequent mathematical model is governed by the coupled equations of mass, momentum and energy and solved by employing Galerkin weighted residual method of finite element formulation. A wide range of pertinent parameters such as Reynolds number, Richardson number, cylinder diameter and the solid-fluid thermal conductivity ratio are considered in the present study. Various results such as the streamlines, isotherms, heat transfer rates in terms of the average Nusselt number and average fluid temperature in the cavity are presented for different aforesaid parameters. It is observed that the cylinder diameter has significant effect on both the flow and thermal fields but the solid-fluid thermal conductivity ratio has significant effect only on the thermal field.     

Numerical study on the conjugate effect of joule heating and magnato-hydrodynamics mixed convection in an obstructed lid-driven square cavity

Conjugate effect of joule heating and magnetic force, acting normal to the left vertical wall of an obstructed lid-driven cavity saturated with an electrically conducting fluid have been investigated numerically. The cavity is heated from the right vertical wall isothermally. Temperature of the left vertical wall, which has constant flow speed, is lower than that of the right vertical wall. Horizontal walls of the cavity are adiabatic. The physical problem is represented mathematically by sets of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. To see the effects of the presence of an obstacle on magnetohydrodenamic mixed convection in the cavity, we considered the cases of with and without obstacle for different values of Ri varying in the range 0.0 to 5.0. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the magnetic parameter, Ha and Joule heating parameter J. The results showed that the obstacle has significant effects on the flow field at the pure mixed convection region and on the thermal field at the pure forced convection region. It is also found that the parameters Ha and J have notable effect on flow fields; temperature distributions and heat transfer in the cavity. Numerical values of average Nusselt number for different values of the aforementioned parameters have been presented in tabular form.     

Numerical simulation of mixed convection flows in a square lid-driven cavity partially heated from below using nanofluid

The present numerical study deals with mixed convection in a square lid-driven cavity partially heated from below and filled with water-base nanofluid containing various volume fractions of Cu, Ag, Al₂O₃ and TiO₂. Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely, Reynolds number, solid volume fraction, different values of the heat source length and different locations of the heat source on the streamlines and isotherms contours as well as Nusselt number and average Nusselt number along the heat source were considered. The present results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed.     

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

The objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 10³–10⁵, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nu_av), drag force (D), and maximum bulk temperature (θ_max). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21002     

Second law analysis in a three dimensional lid-driven cavity

Three dimensional analyses of laminar mixed convection and entropy generation in a cubic lid-driven cavity have been performed numerically. Left side of cavity moves in + y (Case I) or −y (Case II) direction. The cavity is heated from left side and cooled from right while other surfaces are adiabatic. Richardson number is the main parameter which changes from 0.01 to 100. Prandtl number is fixed at Pr = 0.71. Results are presented by isotherms, local and mean Nusselt number, entropy generation due to heat transfer and fluid friction, velocity vectors and Bejan number. Total entropy generation contours are also presented. It is found that direction of lid is an effective parameter on both entropy generation and heat and fluid flow for low values of Richardson number but it becomes insignificant at high Richardson number.     

Control of mixed convection in lid-driven enclosures using conductive triangular fins

Control of mixed convection (combined forced and natural convection) in a lid-driven square cavity is performed using a short triangular conductive fin. A numerical technique is used to simulate the flow and temperature fields. The vertical walls of the cavity are differentially heated. Both the top lid and the bottom wall are adiabatic. The fin is located on one of the motionless walls of the cavity. Three different cases have been studied based on the location of the fin. In this context, Cases I, II and III refer to the fin on the left, bottom and right walls, respectively. Results are presented for +x and −x directions of the top lid in horizontal axis and different Richardson numbers as Ri = 0.1, 1.0 and 10.0. It is observed that the triangular fin is a good control parameter for heat transfer, temperature distribution and flow field.     

Heat and mass transfer under MHD mixed convection in a four-sided lid-driven square cavity

This paper investigates the heat and mass transfer under magnetohydrodynamic mixed convection flow of a binary gas mixture in a four-sided lid-driven square cavity. The enclosure's left wall is sinusoidally heated and acts as a source term, while the right wall functions as a sink. The cavity's horizontal walls are adiabatic and impermeable to mass transfer. The governing equations under Boussinesq approximation and stream function-vorticity formulation are solved using the alternating-direction-implicit scheme, a finite-difference method. The numerical scheme's consistency and stability are demonstrated using the matrix method. The MATLAB code is written, validated against some existing studies, and used to perform numerical simulations. The numerical solutions are graphically examined by visualizing the streamline, isotherm, and concentration contours for nondimensional parameters, such as Hartmann number $\left(0\le Ha\le 100\right)$, heat absorption or generation coefficient $\left(-2\le \varphi \le 2\right)$, Richardson number $\left(0.01\le Ri\le 100\right)$, and buoyancy ratio $\left(-6\le N\le 6\right)$. The magnetic field modifies the temperature and concentration distribution in the cavity, depending on the convection mode. The magnetic field forces the fluid to stagnate in different regions of the cavity, depending on the mode of convection. It was found that the difference between the maximum and minimum temperature and concentration at the cavity's midpoint increases up to 13 and 10 times, respectively, in the natural convection compared with the forced convection. The average Nusselt number on the vertical walls of the cavity is maximum in natural convection in the absence of a magnetic field but reaches a minimum value at $Ha=100$ in forced and mixed convection. The average Sherwood number on the cavity's vertical walls decreases with the magnetic field in mixed and natural convection.     

Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid

A numerical investigation of laminar mixed convection flows through a copper–water nanofluid in a square lid-driven cavity has been executed. In the present study, the top and bottom horizontal walls are insulated while the vertical walls are maintained at constant but different temperatures. The study has been carried out for the Rayleigh number 10⁴ to 10⁶, Reynolds number 1 to 100 and the solid volume fraction 0 to 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics have been investigated and discussed. It is found that at the fixed Reynolds number, the solid concentration affects on the flow pattern and thermal behavior particularly for a higher Rayleigh number. In addition it is observed that the effect of solid concentration decreases by the increase of Reynolds number.     

A numerical study of mixed convection in a two-sided lid-driven tall cavity containing a heated triangular block for non-Newtonian power-law fluids

The study of hydrodynamics and thermal characteristics inside a lid-driven cavity has been one of the most captivating problems in computational fluid dynamics. In this numerical work, the mixed convection phenomenon inside a two-dimensional, tall lid-driven cavity with top and bottom lids moving in opposite directions, +x and –x, respectively, has been explored for non-Newtonian power-law fluids. The cavity contains a uniformly heated equilateral triangular obstacle at its geometric center.  Numerical experimentation is performed for a range of flow governing parameters, such as aspect ratio (0.25, 0.5, and 0.75), Prandtl number (1, 50, and 100) Richardson number (0.1, 1, and 10), power-law index (0.6–1.4) and Grashof number of 10⁴. The physical perceptions of the cavity are explained by using streamline and isotherm contours. The fluid movement is limited adjacent to the moving wall concerning the Richardson number at the lower Prandtl number. With a rise in the aspect ratio of the cavity, the flow-pattern becomes more dispersed inside the cavity. Heat transfer enhancement is observed at a lower aspect ratio equal to 0.25.     

含加热圆管方腔内自然对流的数值研究

采用数值计算方法对含不同直径圆管以及相同直径圆管位置不同方腔内的层流自然对流进行了研究。以冷热壁面温度差为基准的瑞利数Rn为10^6,以圆管壁面热流密度为基准的Ra为10^8。计算结果表明,当圆管处于方腔中间位置时,随着圆管直径的增大,圆管表面局部努塞尔数呈减小趋势。当圆管直径不变时,由于在不同位置处浮力作用的强弱不同,随着圆管在方腔内位置的改变,方腔内流场结构和温度场分布也会发生变化。整个计算结果可为工程设计提供参考。     

Numerical investigation of mixed convection of non-Newtonian fluid in a vented square cavity with fixed baffle

This paper numerically investigates mixed convective heat transfer in a vented square cavity incorporated with a baffle that is subjected to external non-Newtonian fluids (NNFs). Adiabatic conditions are imposed on the top and bottom walls, while cold temperature conditions are applied to the right and left solid boundaries. Heated NNF enters the cavity through the inlet and goes out through the outlet at three different locations, and it passes on a vertical baffle fixed at the base placed at different lengths. To examine the impact of the inlet and outlet positions, three different shapes of the outlet port located on the right wall and the inlet port on the left bottom wall were investigated. The impacts of Reynolds number (Re) of 100 ≤ Re ≤ 1000, Richardson number (Ri) of 0.1 ≤ Ri ≤ 3, power law index (n) of 0.6 ≤ n ≤ 1.4, length of baffle (L_b) of 0.2 ≤ L_b ≤ 0.6 and the outlet hole positions (S) of $0\le S\le 0.9$ on the thermal and flow distributions in the cavity are taken into consideration in this paper. The results demonstrated that the flow's intensity and heat transfer increase with improvement in the Re and n at any baffle length. When the Ri increased from 0.1 to 3, $N{u}_{\mathrm{avg}}$ increased by 23.3% at $n=0.6$, and 13.8% at $n=1.2$. Also, the Ri increment results in the augmentation of the average heat transfer.     

Conjugate-mixed convection heat transfer in a lid-driven enclosure with thick bottom wall

Conjugate heat transfer by mixed convection and conduction in lid-driven enclosures with thick bottom wall has been studied by a numerical method. The enclosure is heated from the bottom wall isothermally. Temperature of the top moving wall, which has constant flow speed, is lower than that of the outside of bottom wall. Vertical walls of the enclosure are adiabatic. Governing parameters are solved for a wide range of Richardson numbers (0.1 ≤ Ri ≤ 10), ratio of height of bottom wall to enclosure height (0.1 ≤ h/H ≤ 0.5) and thermal conductivity ratio (0.01 ≤ λ_f/λ_s ≤ 10). Obtained results showed that heat transfer decreases with increasing of λ_f/λ_s ratio, Richardson number and thickness ratio of the wall. Flow strength is affected for only higher values of λ_f/λ_s ratio.     

Effects of diameter ratio of adiabatic circular cylinder and tilt angle on natural convection from a square open tilted cavity

A numerical analysis is carried out to study the performance of natural convection inside a square open tilted cavity filled with air. An adiabatic circular solid cylinder is placed at the center of the cavity and the sidewall in front of the breathing space is heated by a constant heat flux. The top and bottom walls are kept at the ambient constant temperature. Two‐dimensional forms of Navier–Stokes equations along with the energy equations are solved using the Galerkin finite element method. Results are obtained for a range of Grashof numbers from 10³ to 10⁶ at Pr = 0.71 while the tilt angle varies from 0 to 45° and the diameter ratio of the cylinder is considered to be 0.2, 0.3, and 0.4 with constant physical properties. The parametric studies for a wide range of cylinder diameter ratios and cavity tilt angles show significant features of the present problem in terms of stream functions and temperature profiles. The computational results indicate that the heat transfer coefficient is strongly influenced by the above governing parameters. It is also found that the average Nusselt number decreases when the diameter ratio increases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21001     

Numerical study of mixed convection nanofluid in an annulus enclosure between outer rotating cylinder and inner corrugation cylinder

Numerical investigations are presented for mixed convection problems in a concentric inner sinusoidal cylinder and an outer rotating circular cylinder, which were kept at constant hot and cold temperatures, respectively. The free space between the cylinders and the enclosure walls was filled with a water‐Cu nanofluid. The governing equations are formulated for velocity, pressure, and temperature formulation and are modeled in COMSOL5.2a, a partial differential equation solver based on the Galerkin finite element method. The governing parameters considered are the solid volume fraction, [0, 0.02, 0.04, and 0.06], Re (1, 25, 100, 200, and 300), and Ra (less than 10⁴), and the inner cylinder corrugation frequencies varied from (N = 3, 6, and 9). According to the calculations, the Reynolds number, the Rayleigh number, the nanoparticle volume fraction, and the number of corrugations play an important role of forming the stream and isothermal lines, the local and the average Nusselt number inside the annulus enclosure. The average Nusselt number decreases with increasing Reynolds number and the number of corrugations, while it increases as the Rayleigh number and the volume fraction increase.     

Lattice Boltzmann simulation of nanofluid in lid-driven cavity

Lattice Boltzmann Method is applied to investigate the mixed convection flows utilizing nanofluids in a lid-driven cavity. The fluid in the cavity is a water-based nanofluid containing Cu, Cuo or Al₂O₃ nanoparticles. The effects of Reynolds number and solid volume fraction for different nanofluids on hydrodynamic and thermal characteristics are investigated. The effective thermal conductivity and viscosity of nanofluid are calculated by Chon and Brinkman models, respectively. The results indicate that the effects of solid volume fraction grow stronger sequentially for Al₂O₃, Cuo and Cu. In addition the increases of Reynolds number leads to decrease the solid concentration effect.     

Enhanced thermal performance and entropy generation analysis in a novel cavity design with circular cylinder

Analyzing fluid dynamics and heat transfer holds significant importance in the design and enhancement of engineering systems. The current investigation utilizes the finite element method to explore natural convection and heat transfer intricacies within a novel cavity containing an inner circular cylinder under steady and laminar flow conditions. The principal aim of this study is to assess the impact of Rayleigh number (Ra), Bejan number (Be), and the presence of adiabatic, hot, and cold cylinders on heat transfer, entropy generation, and fluid flow. The range of Ra considered in this investigation spans from 10³ to 10⁶, while the Prandtl number for the air is fixed at 0.71. The findings illustrate that the presence of a cylinder leads to higher Be as Ra increase, compared to scenarios where no cylinder is present. This observation suggests that buoyancy forces dominate in the absence of a cylinder, resulting in significantly enhanced convective heat transfer efficiency. However, the presence of a heated cylinder within the tooth-shaped cavity exerts a substantial influence on the overall thermal performance of the system. Notably, the average Nusselt Number (Nu) experiences a remarkable increase of 41.97% under the influence of a heated cylinder, when compared to situations where a cold cylinder is present. This elevated average Nu signifies improved heat transfer characteristics, ultimately resulting in an overall improvement in the thermal system's efficiency.     

Numerical investigation of fluid flow and heat transfer around a solid circular cylinder utilizing nanofluid

In this study, flow-field and heat transfer through a copper–water nanofluid around circular cylinder has been numerically investigated. Governing equations containing continuity, N–S equation and energy equation have been developed in polar coordinate system. The equations have been numerically solved using a finite volume method over a staggered grid system. SIMPLE algorithm has been applied for solving the pressure linked equations. Reynolds and Peclet numbers (based on the cylinder diameter and the velocity of free stream) are within the range of 1 to 40. Furthermore, volume fraction of nanoparticles (φ) varies within the range of 0 to 0.05. Effective thermal conductivity and effective viscosity of nanofluid have been estimated by Hamilton–Crosser and Brinkman models, respectively. The effect of volume fraction of nanoparticles on the fluid flow and heat transfer characteristics are investigated. It is found that the vorticity, pressure coefficient, recirculation length are increased by the addition of nanoparticles into clear fluid. Moreover, the local and mean Nusselt numbers are enhanced due to adding nanoparticles into base fluid.