Mixed Convection Heat and Mass Transfer in a Micropolar Fluid with Soret and Dufour Effects

A mathematical model for the steady, mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a micropolar fluid in the presence of Soret and Dufour effects is presented. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms using local similarity transformations. The resulting system of equations is then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration profiles are displayed graphically for different values of coupling number, Soret and Dufour numbers. In addition, the skin-friction coefficient, the Nusselt number and Sherwood number are shown in a tabular form.     

三维方腔内竖直平板混合对流换热的数值研究

本文建立了三维方腔内竖直板混合对流换热的数学模型,探讨Re数,进风口位置、竖直板位置对混合对流换热的影响.结果表明:随Re数增加,竖直板下部的平均Nu2下降,而总体平均Nu1增加.随送风口高度增加,竖直板对流换热量增加.在竖直板位置L1/H=0.5～1.5的范围内,竖直板处于中间位置L1/H=1.0时,竖直板混合对流换...     

Laminar Natural Convection in a Square Cavity with a Partition on the Heated Vertical Wall

Abstract

The laminar natural convection in an air-filled square cavity with a partition on the heated vertical wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number Gr _H of approximately 1.4 × 10⁸) and non dimensional top wall temperatures θ _T of 0.57 (insulated) to 2.3. Experiments were performed with an aluminum partition with non dimensional height H _P /H of 0.0625 and 0.125 attached to the heated vertical wall at y/H = 0.65 and 0.95. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields but were mainly limited to the vicinity of the partition. For the cases with the heated top wall, the change in the height of the partition at y/H = 0.95 resulted in changes to the ambient temperature outside the boundary layer due to the reduction of the size of the recirculating flow in the corner region. The changes in the partition height and the top wall temperature affected the blockage effect of the partition, resulting in the local Nusselt number near the corner region to be affected. The local Nusselt number over most of the heated vertical wall of the partitioned cavity (y/H < 0.7) was correlated to the local Rayleigh number in the form Nu = C · Ra ⁿ .     

Experimental Investigation of Mixed Convection in a Channel With an Open Cavity

Mixed convection in an open cavity with a heated wall bounded by a horizontally unheated plate is investigated experimentally. The cavity has the heated wall on the inflow side. Mixed convection fluid flow and heat transfer within the cavity is governed by the buoyancy parameter, Richardson number (Ri), and Reynolds number (Re). The results are reported in terms of wall temperature profiles of the heated wall and flow visualization for Re = 100 and 1000, Ri in the range 30–110 (for Re = 1000) and 2800–8700 (for Re = 100), the ratio of the length to the height of cavity (L/D) is in the range 0.5–1.5, and the ratio of the channel height to cavity height (H/D) is in the range of 0.5 and 1.0. The present results show that the maximum dimensional temperature rise values decrease as the Reynolds and the Richardson numbers decrease. The flow visualization points out that for Re = 1000 there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100 the effect of a stronger buoyancy determines a penetration of thermal plume from the heated plate wall into the upper channel. Nusselt numbers increase when L/D increase in the considered range of Richardson numbers.     

Experimental Investigation of Opposing Mixed Convection in a Channel with an open Cavity Below

Abstract

In this article, mixed convection in an open cavity with a heated wall bounded by a horizontal unheated plate is investigated experimentally. The heated wall is on the opposite side of the forced inflow. The results are reported in terms of wall temperature profiles of the heated wall and flow visualization. The range of pertinent parameters used in this experiment are Reynolds numbers (Re) from 100 to 2,000 and Richardson numbers (Ri) from 4.3 to 6,400. Also, the ratio between the length and the height of cavity (L/D) ranges from 0.5–2.0, and the ratio between the channel and cavity height (H/D) is equal to 1.0. The lack of experimental results on mixed convection in a channel with an open cavity below was an impetus for investigating this configuration when one cavity vertical wall is heated at uniform heat flux. The present results show that at the lowest investigated Reynolds number, the surface temperatures are lower than the corresponding surface temperatures for Re = 2,000 at the same ohmic heat flux. The flow visualization shows that for Re = 1,000, there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100, the effect of a stronger buoyancy determines a penetration of thermal plumes from the heated plate wall into the upper channel. Moreover, the flow visualization shows that for lower Reynolds numbers, the forced motion penetrates inside the cavity, and a vortex structure is adjacent to the unheated vertical plate. At higher Reynolds numbers, the vortex structure has a larger extension while L/D is held constant.     

Impacts of Uniform Magnetic Field and Internal Heated Vertical Plate on Ferrofluid Free Convection and Entropy Generation in a Square Chamber

The heat transfer enhancement and fluid flow control in engineering systems can be achieved by addition of ferric oxide nanoparticles of small concentration under magnetic impact. To increase the technical system life cycle, the entropy generation minimization technique can be employed. The present research deals with numerical simulation of magnetohydrodynamic thermal convection and entropy production in a ferrofluid chamber under the impact of an internal vertical hot sheet. The formulated governing equations have been worked out by the in-house program based on the finite volume technique. Influence of the Hartmann number, Lorentz force tilted angle, nanoadditives concentration, dimensionless temperature difference, and non-uniform heating parameter on circulation structures, temperature patterns, and entropy production has been scrutinized. It has been revealed that a transition from the isothermal plate to the non-uniformly warmed sheet illustrates a rise of the average entropy generation rate, while the average Nusselt number can be decreased weakly. A diminution of the mean entropy production strength can be achieved by an optimal selection of the Lorentz force tilted angle.     

Generalized Hybrid Nanofluid Model with the Application of Fully Developed Mixed Convection Flow in a Vertical Microchannel *

The fully developed mixed convection hybrid nanofluid flow in a vertical microchannel is examined in detail. The simplified hybrid model that omits the nonlinear terms due to the interaction of different nanoparticle volumetric fractions is derived and compared with the existing one. The generalized model describing hybrid nanofluid suspended with multiple kinds of solid particles is suggested. The argument that the corresponding nanofluid solutions obtained by the homogenous model can be recovered from the results of the regular problems through simple arithmetic operations is checked. Solutions in similarity form for this flow problem are formulated by means of a set of similarity variables. The effects of various parameters on important physical quantities are analyzed and discussed.     

Fully HOC Scheme for Mixed Convection Flow in a Lid-Driven Cavity Filled with a Nanofluid

A fully higher-order compact (HOC) finite difference scheme on the 9-point two-dimensional (2D) stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-$Al_2O_3$ nanofluid. Two cases are considered depending on the direction of temperature gradient imposed (Case I, top and bottom; Case II, left and right). The developed equations are given in terms of the stream function-vorticity formulation and are non-dimensionalized and then solved numerically by a fourth-order accurate compact finite difference method. Unlike other compact solution procedure in literature for this physical configuration, the present method is fully compact and fully higher-order accurate. The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and averaged Nusselt number. Comparisons with previously published work are performed and found to be in excellent agreement. A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.     

考虑Soret和Dufour效应的方腔内双扩散自然对流格子Boltzmann模拟

采用格子Boltzmann方法,考虑Soret和Dufour效应,对内置高浓度发热圆的方腔内部双扩散自然对流现象进行数值模拟.高浓度发热圆位于方腔中心,四周壁面均为低温低浓度.在该模型中,用三个独立的LBGK方程分别模拟速度场、温度场和浓度场,并通过Boussinesq近似将它们耦合起来.分析Soret数和Dufour数对方腔内部双扩散自然对流的影响,得到流线图、等温线图、等浓度线图、发热圆表面平均Nusselt数和平均Sherwood数.结果表明：Soret和Dufour效应对方腔内双扩散自然对流影响明显,不能忽略.     

An Experimental and Theoretical Investigation into the Thermal Performance Characteristics of a Staggered Vertical Pin Fin Array Heat Sink with Assisting Mixed Convection in External and In-Duct Flow Configurations

A theoretical and experimental study was carried out on the thermal performance of a pin fin array heat sink. A theoretical model was utilized based on the success of prior research that has the capability of predicting the influence of various geometrical, thermal, and flow parameters on the effective thermal resistance of the heat sink. An experimental investigation was carried out for measuring the thermal performance of the heat sink, and the overall convective heat transfer coefficient for the fin bundle, including the thermal and flow bundle effect. Utilizing the new empirical correlations, theoretical predictions were made and experimentally validated for a wide range of parameters for combined forced and natural convection in the assisting flow configuration. Both the theoretical model and experimental data indicated the existence of optimal fin spacing.     

Temperature-Dependent Viscosity Effects on Non-Darcy Hydrodynamic Free Convection Heat Transfer from a Vertical Wedge in Porous Media

An analysis is presented to investigate the effect of temperature-dependent viscosity on free convection flow along a vertical wedge adjacent to a porous medium in the presence of heat generation or absorption. The governing fundamental equations are transformed into the system of ordinary differential equations using scaling group of transformations and are solved numerically by using the fifth-order Rung-Kutta method with shooting technique for various values of the physical parameters. The effects of variable viscosity parameter on the velocity, temperature and concentration are discussed. Numerical results for the problem considered are given and illustrated graphically.     

Effects of inclined magnetic field on mixed convection in a nanofluid filled double lid-driven cavity with volumetric heat generation or absorption using finite element method

A computational analysis has been performed on mixed convection in a double sided lid-driven cavity in the presence of volumetric heat generation or absorption. Effects of inclined magnetic field are also studied. The governing parameters are solved via Galerkin weighted residual finite element method in space and the Crank–Nicolson in time. Governing parameters are nanoparticle volume fraction (0.0?≤???≤?0.04), Richardson number (0.01?≤?Ri?≤?10), internal heat generation or absorption parameter $(?10\le q\le 10),$ inclination angle of magnetic field (0°?≤?γ?≤?90°) and Hartmann number (0?≤?Ha?≤?100). It is observed that the highest heat transfer is obtained in case of the maximum value of heat absorption. As a further finding, heat transfer decreases with increasing of Hartmann number and increases with increasing of nanoparticle volume fraction.