A computational study of unsteady radiative magnetohydrodynamic Blasius and Sakiadis flow with leading‐edge accretion (ablation)

The present study investigates the influence of the magnetic field, thermal radiation, Prandtl number, and leading‐edge accretion/ablation on Blasius and Sakiadis flow. The convective boundary condition is employed to investigate the heat transfer. The nondimensional governing boundary layer equations have been solved by the homotopy analysis method for different values of the pertinent parameters. The effects of these parameters on the dimensionless velocity, temperature, skin friction, and Nusselt number are also investigated for various values of relevant parameters affecting the flow and heat transfer phenomena. The most relevant outcomes of the present study are that enhancement in magnetic field strength undermines the flow velocity establishing thinner velocity boundary layer for both Blasius and Sakiadis flows while an increase in accretion/ablation effect at leading‐edge manifests in a deceleration in velocity for Blasius case and the opposite trend is observed for Sakiadis flow. Another important outcome is that an increase in radiation and accretion/ablation at leading‐edge upsurges the fluid temperature leading to enhancement in the thermal boundary layer. For both Blasius and Sakiadis flow, the skin friction coefficient and the heat transfer rate decline with the enhancement of the leading‐edge accretion parameter. The results are compared with the existing data and are found in good agreement.     

About bubble breakup models to predict bubble size distributions in homogeneous flows

We present results of a study of the equilibrium between coalescence and breakup of bubbles in homogeneous media with isotropic turbulence. The Boltzmann equation for the particle distribution function (pdf) was evaluated in steady state, using a multigroup approach. Binary bubble breakup was assumed. We used uniform function, delta function, and the model proposed by Luo and Svendsen (1996) for the bubble size distributions resulting from a breakup. The bubble breakup rate was calculated with Luo and Svendsen (1996) and Prince and Blanch (1990) models. Significant differences in bubble breakup rate, and therefore in bubble size distribution, are predicted by both models. The models were compared to the bubble size distributions measured by Boyd and Varley (1998) in air-water flow. The transient response of the bubble size distribution and interfacial area density was also analyzed. This work is of significance in the prediction of reaction rates when they are dependent on bubble size distribution.     

Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet

The effect of radiation on the boundary layer flow and heat transfer of a viscous fluid over an exponentially stretching sheet is studied. The homotopy analysis method (HAM) is employed to determine the convergent series expressions of velocity and temperature. The physical interpretation to these expressions is assigned through graphs. It is found that the effects of Prandtl and radiation numbers on the temperature are opposite.     

Numerical comparison of methods for solving fractional differential–algebraic equations (FDAEs)

In this paper, the variational iteration method (VIM) and the Adomian decomposition method (ADM) are implemented to give approximate solutions for fractional differential–algebraic equations (FDAEs). Both methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. This paper presents a numerical comparison between these two methods and the homotopy analysis method (HAM) for solving FDAEs. Numerical results reveal that the VIM and the ADM are quite accurate and applicable.     

Effects of non‐Darcian and temperature dependent heat source on two‐phase flow in a vertical porous space with thermal radiation

In this article, influences of viscous dissipation and thermal radiation on MHD flow of two immiscible fluids in a vertical channel filled with porous materials have been studied theoretically. The equations governing the problem are transformed to a system of ODE and are solved by homotopy analysis method (HAM). The effects of physical parameters on flow and heat transfer characteristics have been discussed with the help of graphs. It is found that viscous dissipation parameter, heat source parameter, thermal parameter lead to enhance velocity as well as temperature field. Also, increasing Brinkmann number and heat source parameter lead to suppress Coefficient of skin friction at the left wall but the opposite is true at the other wall. However, these parameters give reverse trend on Nusselt number distribution. Further, increasing thermal conductivity ratio and fluids height ratio leads to increase heat transfer coefficient significantly at the left wall. In addition, we have compared present HAM solution with analytical solution of the problem (ie, absence of radiation parameter and Brinkmann number).     

Influence of nonlinear radiation on MHD micropolar fluid flow with viscous dissipation

This study takes account of the impact of the convective boundary conditions. The energy equation consists of Joule heating and thermal nonlinear radiation impacts. Contact between the solid and the fluid is also susceptible to a velocity slip. The resultant differential equations system is solved using homotopy analysis method. To find all numerical computations, Mathematica is utilized. The behavior, with graphical results, of pertinent parameters in micropolar fluid flow characteristics is studied. We look at the impact of the material parameter, magnetic parameter, slip parameter, and electrical parameter to grasp the physics of the problem better. Different values of skin friction, wall couple stress, and Nusselt and Sherwood numbers are discussed.     

Overview of pressure coefficient data in building energy simulation and airflow network programs

Wind pressure coefficients (C_p) are influenced by a wide range of parameters, including building geometry, facade detailing, position on the facade, the degree of exposure/sheltering, wind speed and wind direction. As it is practically impossible to take into account the full complexity of pressure coefficient variation, building energy simulation (BES) and Airflow network (AFN) programs generally incorporate it in a simplified way. This paper provides an overview of pressure coefficient data and the extent to which they are currently implemented in BES–AFN programs. A distinction is made between primary sources of C_p data, such as full-scale measurements, reduced-scale measurements in wind tunnels and computational fluid dynamics (CFD) simulations, and secondary sources, such as databases and analytical models. The comparison between data from secondary sources implemented in BES–AFN programs shows that the C_p values are quite different depending on the source adopted. The two influencing parameters for which these differences are most pronounced are the position on the facade and the degree of exposure/sheltering. The comparison of C_p data from different sources for sheltered buildings shows the largest differences, and data from different sources even present different trends. The paper concludes that quantification of the uncertainty related to such data sources is required to guide future improvements in C_p implementation in BES–AFN programs.     

Three-dimensional rotating flow between two porous walls with slip and heat transfer

This article looks at the entrained flow and heat transfer of a viscous fluid in a porous channel. Analysis has been carried out in the presence of rotation and slip effects. Similarity relations transform the partial differential equation into coupled nonlinear ordinary differential equations. Nonlinear flow problem is computed successfully. Emphasis has been mainly given to the combined effects of slip, magnetic field and suction/injection at the walls. Graphs are plotted to analyze the behavior of such physical parameters.     

四边固支对称蜂窝夹层板主共振非线性动力学计算

应用同伦分析方法(HAM)研究了四边固支对称蜂窝夹层板主共振情况下的非线性动力学特性。将铝基蜂窝芯层等效为一正交异性层, 等效弹性参数由修正后的Gibson方程得出。基于经典叠层板理论(CPT)和几何大变形理论建立了四边固支蜂窝夹层板受横向激振力作用下的受迫振动微分方程, 通过振型正交化将蜂窝夹层板受迫振动微分方程简化成双模态下的动力学控制方程, 得到了主共振情况下的平均方程, 研究了不同结构参数对动力学特性的影响。计算结果表明, 蜂窝夹层板的幅频特性曲线类似单自由度Duffing方程响应曲线, 随着结构参数的增大, 硬特性明显加大并且振幅的峰值明显减小, 所得结论可为蜂窝夹层板的设计和实际应用提供理论依据。