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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Natural convection of Bingham fluids in rectangular cross- sectional cylindrical annuli with differentially heated vertical walls
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Natural convection of Bingham fluids in rectangular cross- sectional cylindrical annuli with differentially heated vertical walls

机译：宾汉流体在具有垂直加热壁的矩形截面圆柱环中的自然对流

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Purpose This paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state simulations have been conducted for a range of different values of normalised internal radius (r(i)/L 1/8 to 16, where L is the difference between outer and inner radii); aspect ratio (AR = H/L from 1/8 to 8 where H is the enclosure height); and nominal Rayleigh number (Ra from 10(3) to 10(6)) for a single representative value of Prandtl number (Pr is 500). Design/methodology/approach The Bingham model has been used to mimic the yield stress fluid motion, and numerical simulations have been conducted for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the vertical side walls. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity. Findings It is found that the mean Nusselt number based on the inner periphery Nu over bar (i) increases (decreases) with an increase in Ra (Bn) due to augmented buoyancy (viscous) forces irrespective of the boundary condition. The ratio of convective to diffusive thermal transport increases with increasing r(i)/L for both Newtonian (i.e. Bn = 0) and Bingham fluids regardless of the boundary condition. Moreover, the mean Nusselt number Nu over bar (i) normalised by the corresponding Nusselt number due to pure conductive transport (i.e. Nu over bar (i)/(Nu over bar (i))(cond)) shows a non-monotonic trend with increasing AR in the CWT configuration for a given set of values of Ra, Pr, L-i for both Newtonian (i.e. Bn = 0) and Bingham fluids, whereas Nu over bar (i)/(Nu over bar (i))(cond) increases monotonically with increasing AR in the CWHF configuration. The influences of convective thermal transport strengthen while thermal diffusive transport weakens with increasing AR, and these competing effects are responsible for the non-monotonic Nu over bar (i)/(Nu over bar (i))(cond) variation with AR in the CWT configuration. Originality/value Detailed scaling analysis is utilised to explain the observed influences of Ra, BN, r(i)/L and AR, which along with the simulation data has been used to propose correlations for Nu over bar (i).
机译：目的本文旨在对矩形截面圆柱环形外壳中屈服应力流体的自然对流进行数值分析。已针对标准化内半径的一系列不同值（r（i）/ L 1/8到16，其中L是内外半径之差）进行了层流稳态仿真；长宽比（AR = H / L从1/8到8，其中H是外壳高度）；和名义瑞利数（Ra从10（3）到10（6））代表普朗特数的单个代表值（Pr为500）。设计/方法/方法Bingham模型已用于模拟屈服应力流体运动，并且针对垂直侧壁的恒定壁温（CWT）和恒定壁热通量（CWHF）边界条件进行了数值模拟。质量，动量和能量的守恒方程已使用有限体积法以耦合方式求解，其中扩散项使用二阶中心微分方案，对流项使用二阶迎风方案。压力链接方程算法采用众所周知的半隐式方法进行压力和速度的耦合。结果发现，由于浮力（粘性）力的增加，基于边界（i）的内周Nu的平均努塞尔特数随着Ra（Bn）的增加而增加（减小），而与边界条件无关。无论边界条件如何，对于牛顿流体（即Bn = 0）和宾厄姆流体，对流与扩散热传递之比均随r（i）/ L的增加而增加。此外，由于纯导电传输，通过相应的努塞尔特数归一化后的平均努塞尔特数Nu（bar）（即，Nu over bar（i）/（Nu over bar（i））（cond））呈现非单调趋势对于牛顿流体（即Bn = 0）和宾厄姆流体，在给定的Ra，Pr，Li给定值集合的情况下，随着CWT配置中AR的增加，Nu超过bar（i）/（Nu超过bar（i））（cond ）随CWHF配置中AR的增加而单调增加。随着AR的增加，对流热传输的影响增强，而热扩散传输的强度减弱，并且这些竞争效应是造成非单调Nu随bar（i）/（Nu超过bar（i））（cond）随AR在AR中变化的原因。 CWT配置。独创性/值详细的比例分析用于解释Ra，BN，r（i）/ L和AR的观察到的影响，并与模拟数据一起用于提出关于bar（i）上Nu的相关性。

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