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Research Article
Mathematical Modelling of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surface of a Vertical Cylinder
Issue:
Volume 14, Issue 4, August 2025
Pages:
183-192
Received:
31 May 2025
Accepted:
12 June 2025
Published:
4 July 2025
Abstract: Turbulent natural convection in cylindrical enclosures is a significant phenomenon in most engineering and industrial applications, such as thermal insulation, electronics cooling, and building climate control. An explicit understanding of the transition of flow from laminar to turbulent and its influence on heat transfer is essential in terms of optimizing system performance. The study solves two major objectives: Model the governing equations of turbulent natural convection in a cylindrical enclosure using K-Omega turbulence model, and compute the effective thermal conductivity, turbulence intensity, and streamline distribution as functions of Rayleigh number. The enclosure that has been considered is an insulated vertical sidewall enclosure with a top wall at 298 K and a bottom wall at 320 K. The mathematical formulation consists of the Reynolds-Averaged Navier–Stokes (RANS) equations, the energy equation, and transport equations for turbulence, subject to the Boussinesq approximation to model buoyancy. A low-Reynolds-number two-equation model is used to model turbulence close to the walls, and the Prandtl number is set to 0.71 to model air as the working fluid. Numerical solutions are achieved by the use of the finite difference technique and verified by simulations done in ANSYS Fluent. The simulation identifies how structures flow and mechanisms of heat transfer change with increasing Rayleigh numbers. At small Rayleigh numbers, the flow is steady, conduction-dominated, with smooth streamlines and little or no turbulence. It is noted that as the Rayleigh number increases, buoyancy-driven convection becomes more significant, leading to the formation of vortices, intensified turbulence, and enhanced mixing, which collectively improve the effective thermal conductivity. The streamline distribution becomes increasingly complex and disordered, reflecting the transition to chaotic flow. These results demonstrate that the Rayleigh number is a key parameter influencing thermal and flow characteristics in cylindrical enclosures. The study provides practical insights in designing and optimizing systems involving buoyancy-induced turbulent heat transfer.
Abstract: Turbulent natural convection in cylindrical enclosures is a significant phenomenon in most engineering and industrial applications, such as thermal insulation, electronics cooling, and building climate control. An explicit understanding of the transition of flow from laminar to turbulent and its influence on heat transfer is essential in terms of o...
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Research Article
Stabilization of Nonhomogeneous Euler-Bernoulli Beam with a Point Controlled by Combined Feedback Force and Indefinite Damping
Kouassi Ayo Ayébié Hermith*,
Bouallagui Zied,
Diop Fatou N’diaye,
Touré Kidjégbo Augustin
Issue:
Volume 14, Issue 4, August 2025
Pages:
193-209
Received:
6 May 2025
Accepted:
9 June 2025
Published:
5 August 2025
Abstract: The transportation of masses or objects by cranes, necessary in the construction sector to increase productivity, often causes transverse vibrations of the system, which degrades production or process performance, and can even cause breakdowns. Actively controlling or mitigating these vibrations is becoming essential in many fields, such as the construction of satellite panels, etc. Therefore, many efforts have been made in recent years to find effective ways to eliminate these unwanted vibrations. Thus, the vibration behavior of a crane on a construction site, transporting a mass represented by beams, is translated into an equation using the theory of Euler-Bernoulli beam equations. These vibration effects are thus model led in a very reduced manner by a nonhomogeneous Euler-Bernoulli beam fixed at one end and subjected to a point mass at the free end. In this research article, we have generalized Wang’s results. We began by defining some fundamental properties of the closed-loop system and then analyzed its spectrum. Using the theory of perturbed problems, we obtained the basic Riesz property. The spectrum-determined growth condition and exponential stability were also derived. Moreover, when the damping was undefined, we provided a condition on the negative value of the damping without destroying the exponential stability of the system.
Abstract: The transportation of masses or objects by cranes, necessary in the construction sector to increase productivity, often causes transverse vibrations of the system, which degrades production or process performance, and can even cause breakdowns. Actively controlling or mitigating these vibrations is becoming essential in many fields, such as the con...
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Research Article
The Expectation of Generating Certain Finite Nilpotent Groups and Non-abelian Groups
Issue:
Volume 14, Issue 4, August 2025
Pages:
210-215
Received:
21 June 2025
Accepted:
7 July 2025
Published:
5 August 2025
Abstract: Let G be a finite group. Define λn(G) to be the probability that n elements drawn at random with replacement from G generate G. Define E(G) to be the expected number of elements of G which have to be drawn at random with replacement from G before a set of generators is found. The purpose of this paper is to compute λn(G) and E(G) for certain finite nilpotent groups including non-abelian groups. In this paper we have, in particular, computed λn(G) as a first step then E(G) for the groups G where G is a nilpotent group isomorphic to the direct product of its pi-Sylow subgroups, for cyclic groups ℤq, q is a power of a prime p and for non-abelian groups of order p4 of the shape ℤp2 ⋊ ℤp2 the semi-direct product of two copies of ℤp2. These results are knew and could lead to give some alternative description of the structure of the group and its elements. In general probabilistic group theory has applications on probabilistic methods to prove deterministic theorems in group theory.
Abstract: Let G be a finite group. Define λn(G) to be the probability that n elements drawn at random with replacement from G generate G. Define E(G) to be the expected number of elements of G which have to be drawn at random with replacement from G before a set of generators is found. The purpose of this paper is to compute λn(G) and E(G) for certain finite...
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Research Article
Comparison Principle for Fractional Differential Inequalities with Variable Order Caputo Derivative
Jayashree Vinayakrao Patil
,
Monali Manikrao Janjal*
Issue:
Volume 14, Issue 4, August 2025
Pages:
216-222
Received:
23 June 2025
Accepted:
7 July 2025
Published:
5 August 2025
Abstract: Fractional differential inequalities have emerged as powerful tools for modeling and analyzing dynamic systems with fractional-order derivatives, offering a sophisticated framework to capture the complexities of real-world processes. Among the various analytical techniques, the comparison principle stands out as a fundamental approach in understanding the behavior of solutions to fractional differential inequalities. This study focuses on the development and analysis of comparison principles for some of the fractional differential inequalities involving the variable-order Caputo fractional derivative which is a generalization of the classical Caputo derivative that allows the order of differentiation to vary with respect to time or space. Such flexibility is important for modeling systems whose memory characteristics change over time or space. We formulate both weak and strong versions of the comparison principle with variable order Caputo fractional derivative. Our approach combines analytical techniques from fractional calculus and the theory of differential inequalities to establish some results. To have the applicability and relevance of our theoretical work, we provide an example demonstrating the effectiveness of the proposed comparison theorems. The findings of this paper not only contribute to the theoretical advancement of fractional differential inequalities with variable order but also applicable to systems where dynamic memory effects are prominent.
Abstract: Fractional differential inequalities have emerged as powerful tools for modeling and analyzing dynamic systems with fractional-order derivatives, offering a sophisticated framework to capture the complexities of real-world processes. Among the various analytical techniques, the comparison principle stands out as a fundamental approach in understand...
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