An Optimistic Solver for the Mathematical Model of the Flow of Johnson Segalman Fluid on the Surface of an Infinitely Long Vertical Cylinder

In this paper, a novel soft computing technique is designed to analyze the mathematical model of the steady thin film flow of Johnson–Segalman fluid on the surface of an infinitely long vertical cylinder used in the drainage system by using artificial neural networks (ANNs). The approximate series solutions are constructed by Legendre polynomials and a Legendre polynomial-based artificial neural networks architecture (LNN) to approximate solutions for drainage problems. The training of designed neurons in an LNN structure is carried out by a hybridizing generalized normal distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP). To investigate the capabilities of the proposed LNN-GNDO-SQP algorithm, the effect of variations in various non-Newtonian parameters like Stokes number (St), Weissenberg number (We), slip parameters (a), and the ratio of viscosities (ϕ) on velocity profiles of the of steady thin film flow of non-Newtonian Johnson–Segalman fluid are investigated. The results establish that the velocity profile is directly affected by increasing Stokes and Weissenberg numbers while the ratio of viscosities and slip parameter inversely affects the fluid’s velocity profile. To validate the proposed technique’s efficiency, solutions and absolute errors are compared with reference solutions calculated by RK-4 (ode45) and the Genetic algorithm-Active set algorithm (GA-ASA). To study the stability, efficiency and accuracy of the LNN-GNDO-SQP algorithm, extensive graphical and statistical analyses are conducted based on absolute errors, mean, median, standard deviation, mean absolute deviation, Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE). Statistics of the performance indicators are approaching zero, which dictates the proposed algorithm’s worth and reliability.

Development of Nusselt number correlation in natural convection over the walls of a blast furnace: A CFD approach

Blast furnaces are large and costly devices, and contribute enormous wealth to world economy. A tiny improvement of furnace performance can translate to huge saving not only in cost of operation but also in air pollution. It presents a numerical solution of the continuity, momentum, and energy equations for a fluid domain surrounding the outer cylindrical surface of a vertical cylinder with the specific longitudinal section using ANSYS FLUENT 18. The main parameters of this study are the dimensionless ratio of cylinder length to the maximum diameter varying between 3.24 and 5.4, the Rayleigh number ranging between 104 and 107, and the cylinder surface temperature ([Formula: see text]) varying between 375 K and 600 K, the ambient temperature being taken as 300 K. These parameters have been varied during the simulation to determine their influence on the free convection characteristics. The study clearly shows that the computed Nusselt number increases with increase of Rayleigh number and surface temperature, the increment being minimal for high values of length to the maximum diameter. It is also observed from the simulation that the rate of heat transfer goes down with increase of length to the maximum diameter. The results present local heat transfer and skin friction coefficients over the outer cylindrical surface of the blast furnace of chosen dimensions. The thermal plume and the velocity vector field around the furnace are displayed. An empirical Nusselt number to Rayleigh number relationship has been proposed for the blast furnace of any size within range of Rayleigh numbers covered in this study. This formula derived is correct within ±5%, and is expected to be very useful to field engineers.

Numerical Modelling of Liquid Film Spreading Dynamics over Smooth Vertical Surface under Isothermal Conditions

The paper presents numerical modelling of the liquid film spreading dynamics of the R21 (mol. fraction: 0.9) and R114 refrigerants mixture. We considered an outer flow along a round vertical cylinder at Reynolds number of 104 and various contact angles. The simulation was performed in OpenFOAM software on the basis of the volume of fluid (VOF) method. We have shown that the wetting front deforms at wetting angles of 30 and 50 degrees, and regular jets form. At the same time, it was demonstrated that at the wetting angle of 10 degrees the spreading front has practically a flat shape, but one may see some regular thickenings of the liquid film along the contact line of the front.

Vertical Cylinder-to-Lamella Transition in Thin Block Copolymer Films Induced by In-Plane Electric Field

Morphological transition between hexagonal and lamellar patterns in thin polystyrene–block–poly(4-vinyl pyridine) films simultaneously exposed to a strong in-plane electric field and saturated solvent vapor is studied with atomic force and scanning electron microscopy. In these conditions, standing cylinders made of 4-vinyl pyridine blocks arrange into threads up to tens of microns long along the field direction and then partially merge into standing lamellas. In the course of rearrangement, the copolymer remains strongly segregated, with the minor component domains keeping connectivity between the film surfaces. The ordering tendency becomes more pronounced if the cylinders are doped with Au nanorods, which can increase their dielectric permittivity. Non-selective chloroform vapor works particularly well, though it causes partial etching of the indium tin oxide cathode. On the contrary, 1,4-dioxane vapor selective to polystyrene matrix does not allow for any morphological changes.