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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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Research Article
Pulmonary Tuberculosis and Pneumonia Co-Dynamics: A Mathematical Modelling Approach
Issue:
Volume 14, Issue 4, August 2025
Pages:
223-241
Received:
7 July 2025
Accepted:
22 July 2025
Published:
20 August 2025
Abstract: This study presents a novel mathematical model that captures the co-dynamics of pulmonary tuberculosis in the presence of opportunistic pneumonia. The model integrates opportunistic pneumonia into the classical pulmonary tuberculosis transmission framework, based on clinical evidence of a lethal synergism between the two diseases. A Holling-type saturation function is utilized to reflect the impact of natural immunity on the progression from latent tuberculosis infection to active disease. Asymptomatic infectious individuals can transmit the infection unnoticed, thereby significantly contributing to the high rate of transmission. Thus, the screening of asymptomatic individuals is incorporated into the model as a strategy to mitigate the prevalence of co-infections. A comprehensive sensitivity analysis and numerical simulations were conducted to evaluate the effects of various interventions, including enhancing natural immunity, screening asymptomatic and latently infected individuals, improving vaccine efficacy, and treating patients with severe pulmonary tuberculosis. The sensitivity analysis reveals that improving vaccine efficacy is the most effective strategy for minimizing co-infections. Simulations also demonstrate that increased screening and treatment rates significantly reduce the burden of pulmonary tuberculosis-pneumonia co-infections. These results underscore the need to develop vaccines with higher efficacy to reduce co-infections of pulmonary tuberculosis and opportunistic pneumonia. Additionally, the study recommends expanded screening of asymptomatic tuberculosis cases and the strengthening of immunity among latently infected populations.
Abstract: This study presents a novel mathematical model that captures the co-dynamics of pulmonary tuberculosis in the presence of opportunistic pneumonia. The model integrates opportunistic pneumonia into the classical pulmonary tuberculosis transmission framework, based on clinical evidence of a lethal synergism between the two diseases. A Holling-type sa...
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Research Article
A Deep Understanding of Non-linear Boussinesq-Burger System of Equation Using Wavelets
Ratesh Kumar,
Sonia Arora*
Issue:
Volume 14, Issue 4, August 2025
Pages:
242-252
Received:
20 June 2025
Accepted:
22 July 2025
Published:
26 August 2025
Abstract: This research proposal develops a systematic and efficient mathematical approach of solving the non-linear Boussinesq-Burger's equations system. The primary objective is to develop a scale-3 Haar wavelet-based numerical scheme. In order to authenticate the efficiency, the study investigates a range of numerical problems with different source terms. In order to tackle the intrinsic challenges of nonlinearity of the problems, quasi-linearization method is employed. Explicit analytical expressions for the integrals involved are also derived for both cases under consideration. Validity and accuracy of the proposed scheme are checked by solving problems whose exact solutions are known and by comparing the solutions with special values of parameters. The results show that the Haar scale-3 wavelet method is more efficient with higher accuracy compared to the Haar scale-2 method, as confirmed by comparisons with available studies in the literature.
Abstract: This research proposal develops a systematic and efficient mathematical approach of solving the non-linear Boussinesq-Burger's equations system. The primary objective is to develop a scale-3 Haar wavelet-based numerical scheme. In order to authenticate the efficiency, the study investigates a range of numerical problems with different source terms....
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