Symmetry

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13 pages, 1395 KiB

Open AccessArticle

Application of a Partially Invariant Exact Solution of the Thermosolutal Convection Equations for Studying the Instability of an Evaporative Flow in a Channel Heated from Above

by Victoria B. Bekezhanova and Olga N. Goncharova

Symmetry 2023, 15(7), 1447; https://doi.org/10.3390/sym15071447 - 20 Jul 2023

Cited by 1 | Viewed by 847

Abstract

The characteristics of a stationary flow of a volatile liquid driven by a co-current gas flux in a flat horizontal mini-channel upon the non-zero transverse temperature drop are studied. We use an exact solution of the thermosolutal convection equations for describing the heat [...] Read more.

The characteristics of a stationary flow of a volatile liquid driven by a co-current gas flux in a flat horizontal mini-channel upon the non-zero transverse temperature drop are studied. We use an exact solution of the thermosolutal convection equations for describing the heat and mass transfer caused by the combined action of gas pumping, buoyancy, thermocapillarity and linear heating of the channel walls in a two-layer system. The influence of heating from above on the parameters of the ground state and the stability characteristics of the basic flow is explored using an example of the ethanol–air system. We evaluate the thresholds of the linear stability and select the most dangerous modes. Heating from above results in flow stabilization. Instability appears in the form of oscillatory cellular convective patterns. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

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17 pages, 345 KiB

Open AccessArticle

Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for h-Convex Stochastic Process via Interval-Valued Functions

by Waqar Afzal, Evgeniy Yu. Prosviryakov, Sheza M. El-Deeb and Yahya Almalki

Symmetry 2023, 15(4), 831; https://doi.org/10.3390/sym15040831 - 30 Mar 2023

Cited by 8 | Viewed by 1443

Abstract

Mathematical programming and optimization problems related to fluid dynamics are heavily influenced by stochastic processes associated with integral and variational inequalities. Furthermore, symmetry and convexity are intrinsically related. Over the last few years, both have become increasingly interconnected so that we can learn [...] Read more.

Mathematical programming and optimization problems related to fluid dynamics are heavily influenced by stochastic processes associated with integral and variational inequalities. Furthermore, symmetry and convexity are intrinsically related. Over the last few years, both have become increasingly interconnected so that we can learn from one and apply it to the other. The objective of this note is to convert ordinary stochastic processes into interval stochastic processes due to the wide range of applications in various disciplines. We have developed Hermite–Hadamard (

H . H

), Ostrowski-, and Jensen-type inequalities using interval h-convex stochastic processes. Our main results can be applied to a variety of new and well-known outcomes as specific situations. The results of this study are expected to stimulate future research on inequalities using fractional and fuzzy integral operators. Furthermore, we validate our main findings by providing some non-trivial examples. To demonstrate their general properties, we illustrate the connections between the examined results and those that have already been published. The results discussed in this article can be seen as improvements and refinements to results that have already been published. This is a fascinating subject that can be investigated in the future to identify equivalent inequalities for various convexity types. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

15 pages, 1327 KiB

Open AccessArticle

Applications of Orthogonal Polynomials in Simulations of Mass Transfer Diffusion Equation Arising in Food Engineering

by Ishtiaq Ali and Maliha Tehseen Saleem

Symmetry 2023, 15(2), 527; https://doi.org/10.3390/sym15020527 - 16 Feb 2023

Cited by 9 | Viewed by 1631

Abstract

In this paper, Chebyshev polynomials—which are ultraspherical in the first and second kind and hence symmetric, while the third and fourth order are not ultraspherical and are hence non-symmetric—are used for the simulation of two-dimensional mass transfer equation arising during the convective air [...] Read more.

In this paper, Chebyshev polynomials—which are ultraspherical in the first and second kind and hence symmetric, while the third and fourth order are not ultraspherical and are hence non-symmetric—are used for the simulation of two-dimensional mass transfer equation arising during the convective air drying processes of food products subject to Robin and Neumann boundary conditions. These simulations are used to improve the quality of dried food products and for prediction of the moisture distributions. The equation is discretized in both temporal and special variables by using the second order finite difference scheme and spectral method based on Chebyshev polynomial with the help of fast Fourier transform on tensor product grid, respectively. A system of algebraic equations is obtained after applying the proposed numerical scheme, which is then solved by an appropriate iterative method. The error analysis of the proposed scheme is provided. Some numerical examples are presented to confirm the numerical efficiency and theoretical justification of the proposed scheme. Our numerical scheme has an exponential rate of convergence, which means that one can achieve a very accurate solution using a few collocation points, as opposed to the other available techniques which are very slow in terms of convergence and consume a lot of time. In order to further validate the accuracy of our numerical method, a comparison is made with the exact solution using different norms. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

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16 pages, 5365 KiB

Open AccessArticle

Effects of Tip Clearance and Impeller Eccentricity on the Aerodynamic Performance of Mixed Flow Fan

by Shulian Liu, Yizhe Guo, Yuchi Zhang, Cunkai Gu and Likang Yang

Symmetry 2023, 15(1), 201; https://doi.org/10.3390/sym15010201 - 10 Jan 2023

Viewed by 2011

Abstract

The tip clearance and eccentricity of the impeller will affect the aerodynamic performance of the fan, and the impeller installation and vibration characteristics are relatively highly required if the tip clearance is too small. A reasonable tip clearance and excellent coaxially are necessary [...] Read more.

The tip clearance and eccentricity of the impeller will affect the aerodynamic performance of the fan, and the impeller installation and vibration characteristics are relatively highly required if the tip clearance is too small. A reasonable tip clearance and excellent coaxially are necessary to ensure that the impeller does not rub with the shell and has superior aerodynamic performance when the fan is working. In the current study, a mixed flow fan was taken as the object and experimental explorations were performed on the C-type test rig designed according to GB/T1236 2000 Industrial fans-performance testing using standardized airways. By moving the airways to change the tip clearance, it was found that an overlarge tip clearance made the fan efficiency decrease significantly, and the efficiency change gradient was large. However, the gradient of efficiency change became smaller when reaching a certain clearance. Similarly, as the eccentricity became larger, the efficiency also decreased. To explore the influence of the optimal clearance and eccentricity of the fan on the fan’s performance, numerical simulations of the flow field inside the fan were carried out using FLUENT software corresponding to the experimental conditions. The influence of the tip clearance and eccentricity on the aerodynamic performance of the fan was revealed from the energy leakage perspective. Through theoretical and experimental analysis, we try to provide guidance on the design, installation and commissioning of fan tip clearance. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

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16 pages, 2677 KiB

Open AccessArticle

Finite Difference Simulation of Nonlinear Convection in Magnetohydrodynamic Flow in the Presence of Viscous and Joule Dissipation over an Oscillating Plate

by Muhammad Samad Khan, Mubashir Ali Siddiqui and Muhammad Idrees Afridi

Symmetry 2022, 14(10), 1988; https://doi.org/10.3390/sym14101988 - 23 Sep 2022

Cited by 8 | Viewed by 1926

Abstract

Engineers and researchers are interested in the study of nonlinear convection, viscous dissipation, and Joule heating in various flow configurations due to their various applications in engineering processes. That is why the present study deals with the influence of nonlinear convection, viscous, and [...] Read more.

Engineers and researchers are interested in the study of nonlinear convection, viscous dissipation, and Joule heating in various flow configurations due to their various applications in engineering processes. That is why the present study deals with the influence of nonlinear convection, viscous, and Joule dissipation of the temperature and velocity profile of incompressible fluid over a flat plate. In this study, the magnetic field acts perpendicular to the fluid flow and is supposed to be of uniform magnitude. Further, the Newtonian fluid, which is electrically conducting, passes over an infinite vertical flat plate under an oscillatory motion. The term representing the influence of the nonlinear convection phenomenon is integrated into the Navier–Stokes equation. The governing equations of the mentioned study were modeled in the form of non-linear PDEs and modified as non-dimensional equations via appropriate scaling analyses, which resulted in coupled and non-linear PDEs. For the numerical solution of the transformed non-linear PDEs, the finite difference method was applied. Finally, we present the effects of various flow parameters via graphical illustrations. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

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16 pages, 8000 KiB

Open AccessArticle

Magneto-Nanofluid Flow via Mixed Convection Inside E-Shaped Square Chamber

by Hossam A. Nabwey, Ahmed M. Rashad, Mohamed A. Mansour and Taha Salah

Symmetry 2022, 14(6), 1159; https://doi.org/10.3390/sym14061159 - 4 Jun 2022

Cited by 3 | Viewed by 1459

Abstract

Nanofluids play a crucial role in the augmentation of heat transfer in several energy systems. They exhibit better thermal conductivity and physical strength compared to normal fluids. Here, we conduct an evaluative investigation of the magnetized flow of water–copper nanofluid and its heat [...] Read more.

Nanofluids play a crucial role in the augmentation of heat transfer in several energy systems. They exhibit better thermal conductivity and physical strength compared to normal fluids. Here, we conduct an evaluative investigation of the magnetized flow of water–copper nanofluid and its heat transport inside a symmetrical E-shaped square chamber via mixed convective impact with a heated corner. The chamber was constructed symmetrically with an inclined magnetic field strength, and the upper surface of the chamber was isolated and set to move at a fixed velocity. The heated corner was set at a fixed hot temperature in both the left and lower directions. The right side was maintained at a fixed cold temperature, while the remaining portions of the left and lower parts were isolated. The investigation was implemented computationally, solving each of the energy and Navier–Stokes models via the application of a symmetrical finite volume method. The following topics have been addressed in this study: the consequences of the magnetic field, the volumetric fraction of nanoparticles, the heat generation–absorption parameters, and the effects of heat-source length and Richardson number on the fluid comportment and heat transport. The outputs of this symmetric study enabled us to arrive at the following derivation: the magnetic field reduces the fluid circulation inside the E-shaped square chamber. The augmentation of the Richardson number leads to an increase in the heat transfer. Moreover, the decrease in heat generation coefficient lowers the nanofluid temperature and weakens the flow fields. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

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15 pages, 2951 KiB

Open AccessArticle

Analytical Solution for the MHD Flow of Non-Newtonian Fluids between Two Coaxial Cylinders

by Li Chen, Munawwar Ali Abbas, Wissam Sadiq Khudair and Bo Sun

Symmetry 2022, 14(5), 953; https://doi.org/10.3390/sym14050953 - 7 May 2022

Cited by 7 | Viewed by 1722

Abstract

This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible [...] Read more.

This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible outer tube had a Sine wave moving down its wall. The analytical solutions for velocity and temperature were obtained as functions (Bessell functions of the first and second types). The solution for velocity profile, temperature, and concentration distribution were obtained as functions of the physical parameters of the problem (Darcy number, magnetic parameter, Grasoff thermal number, Reynolds number, Prantl number, and Schmidt number) along with other physical parameters. The effect of the physical parameters was discussed graphically. A comparison with previously published graphical results was also carried out. The ambition of the present paper is to contribute to practical applications in geographical and physiological fluid dynamics, such as on sandstone, in the human lungs, on beach sand, on limestone, and in the bile duct. This study is based on theoretical research and can be helpful in the fields of fluid mechanics and mathematics. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

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24 pages, 9915 KiB

Open AccessArticle

Significance of Chemical Reaction and Lorentz Force on Third-Grade Fluid Flow and Heat Transfer with Darcy–Forchheimer Law over an Inclined Exponentially Stretching Sheet Embedded in a Porous Medium

by Amir Abbas, Ramsha Shafqat, Mdi Begum Jeelani and Nadiyah Hussain Alharthi

Symmetry 2022, 14(4), 779; https://doi.org/10.3390/sym14040779 - 8 Apr 2022

Cited by 33 | Viewed by 2408

Abstract

The combined impact of a linear chemical reaction and Lorentz force on heat and mass transfer in a third-grade fluid with the Darcy–Forchheimer relation over an inclined, exponentially stretching surface embedded in a porous medium is investigated. The proposed process is mathematically expressed [...] Read more.

The combined impact of a linear chemical reaction and Lorentz force on heat and mass transfer in a third-grade fluid with the Darcy–Forchheimer relation over an inclined, exponentially stretching surface embedded in a porous medium is investigated. The proposed process is mathematically expressed in terms of nonlinear and coupled partial differential equations, with the symmetry of the conditions normal to the surface. To solve the mathematical model of the proposed phenomenon, the partial differential equations are first reduced to ordinary differential equations; then, MATLAB built-in Numerical Solver bvp4c is used to obtain the numerical results of these equations. The influence of all the pertinent parameters that appeared in the flow model on the unknown material properties of interest is depicted in the forms of tables and graphs. The physical attitude of the unknown variables is discussed with physical reasoning. From the numerical solutions, it is inferred that, as Lorentz force parameter

M

is increased, the velocity of the fluid decreases, but fluid temperature and mass concentration increase. This is due to the fact that Lorentz force retards the motion of fluid, and the increasing resistive force causes the rise in the temperature of the fluid. It is also noted that, owing to an increase in the magnitude of chemical reaction parameter

R

, the velocity profile and the mass concentration decline as well, but the fluid temperature increases in a reasonable manner. It is noted that, by augmenting the values of the local inertial coefficient

F r

and the permeability parameter

K^{*}

, the velocity field decreases, the temperature field increases, and mass concentration also increases with reasonable difference. Increasing values of Prandtl number

P r

results in a decrease in the profiles of velocity and temperature. All the numerical results are computed at the angle of inclination

α = π / 6

. The current results are compared with the available results in the existing literature for this special case, and there is good agreement between them that shows the validation of the present study. All the numerical results show asymptotic behavior by satisfying the given boundary conditions. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

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