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Research Article
Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio
Issue:
Volume 13, Issue 6, December 2025
Pages:
365-392
Received:
12 October 2025
Accepted:
21 October 2025
Published:
22 November 2025
Abstract: This study involves analysis of turbulent natural convection of heat transfer with localized heating and cooling on opposite surfaces of a vertical cylinder. Numerical simulation of turbulent natural convection has been studied in the past using the k-epsilon (k-ε), k-omega (k-ω) and k-ω-SST turbulence models. Further research showed that the k-ω SST model performed better than the k-ε and k-ω models. The study of natural convections in an enclosure has several applications from natural space, warming of household rooms to sections of engineering and atomic installations. This study involves numerical simulation of natural convection flow in a cylindrical enclosure full of air using the k-ω-SST model with an objective of establishing the best position of the heater and the cooler for better distribution of heat in the enclosure. The transfer of heat due to natural convection inside a cylindrical closed cavity was modeled to include the effect of Rayleigh number. The non-linear terms in averaged momentum and energy equation respectively were modeled using k-ω-SST model to close the governing equations. The sidewalls were adiabatic, while the bottom and top surfaces are maintained at 320 K and 298 K, respectively, to induce natural convection. The governing equations, Reynolds-average Navier-Stokes (RANS), energy and turbulence transport, were discretized using the central finite difference method under the Boussinesq approximation. A low Reynolds number k-ω SST turbulence model was employed to accurately resolve turbulent effects. The study explored a range of aspect ratios (AR = 1, 2, 4, 8) while holding the Rayleigh number constant within the turbulent regime Ra =1010 and assuming Prandtl number of 0.71. Simulations were conducted in ANSYS Fluent to obtain vector plot of velocity magnitude, contours of temperature distribution, streamline distributions, effective thermal conductivity, and intensity of turbulence. Results revealed that increasing AR leads to reduced turbulence, weaker convective strength, more stratified temperature fields, and diminished heat transfer efficiency. The findings highlight the critical role of the geometry of the enclosure in shaping the flow structure and thermal behavior in turbulent natural convection.
Abstract: This study involves analysis of turbulent natural convection of heat transfer with localized heating and cooling on opposite surfaces of a vertical cylinder. Numerical simulation of turbulent natural convection has been studied in the past using the k-epsilon (k-ε), k-omega (k-ω) and k-ω-SST turbulence models. Further research showed that the k-ω S...
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Research Article
Optimality Condition and Numerical Methods of Variable-Order Fractional Optimal Control Problem with Full Free Ends
Issue:
Volume 13, Issue 6, December 2025
Pages:
393-411
Received:
2 October 2025
Accepted:
15 October 2025
Published:
26 November 2025
Abstract: In this paper, we studied the necessary conditions for seeking optimal trajectory, optimal control, optimal time and optimal state. Then, we applied these qualitative properties to explore two numerical methods of a variable order fractional optimal control problem until full free ends that the initial time, initial state, terminal time and terminal state are free simultaneously. Based on the relations between variable order fractional calculus operators, i.e., the integral formulas by parts, the necessary conditions of optimality of a variable order fractional optimal control problem until full free ends drove from the Euler-Lagrange equation, applying Hamiltonian and variational principle. To develop the solution methods, we proposed the “optimization first, then discretization” (OFTD) method and the “discretization first, then optimization” (DFTO) method. The OFTD method is to solve the variable order fractional optimal control problem until full free ends by transforming the Euler-Lagrange equation into a nonlinear system using the Grünwald-Letnikov definition and manipulating the transversal conditions as an objective function of error quadratic minimization, i.e., a nonlinear programming type problem with equality constraints. The DFTO method is to solve the problem by transforming the variable order fractional calculus into a classical optimal control problem with integer order using the expansion formulas of the variable order fractional calculus operators. Finally, we demonstrated the validity and accuracy of the proposed methods through various types of numerical test problems.
Abstract: In this paper, we studied the necessary conditions for seeking optimal trajectory, optimal control, optimal time and optimal state. Then, we applied these qualitative properties to explore two numerical methods of a variable order fractional optimal control problem until full free ends that the initial time, initial state, terminal time and termina...
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Research Article
Homological Functor H̃ n: Comp(𝒜) ⟶ Ab Where 𝒜 Is an Abelian Category and 𝓃 Is an Integer in ℤ
Ablaye Diallo*
Issue:
Volume 13, Issue 6, December 2025
Pages:
412-418
Received:
10 October 2025
Accepted:
27 October 2025
Published:
6 December 2025
Abstract: The study of the homological functor has been carried out in particular cases of abelian categories, notably in the category of left A-modules (resp. right A-modules) and Categories of graded A-modules where A is a ring. We call category of complexes of an abelian category 𝒜 the category denoted by Comp(𝒜) whose objects are the complexe sequence of 𝒜 and morphisms are the chain maps of 𝒜. In this paper, we consider the functor H̃n define by the composition of functors Hn ∘ HomComp(𝒜)(X,-), where HomComp(𝒜)(X,-) is define by Comp(𝒜) → Comp(Ab), the functor Hn is define by Comp(Ab) → Ab and X is a projective object of 𝒜. In this article, we study how the homological functor H̃n define by Comp(𝒜) ⟶ Ab where 𝒜 is an abelian category and 𝓃 is an integer in ℤ transforms a short exact sequence into a long exact sequence. The main results of this paper are: the construction of the connecting morphism ϕn associated to the covariant functor H̃n, and show that H̃n transforms all short exact sequence of morphisms in Comp(𝒜) into a long exact sequence of morphisms in Ab, where X is an projectif object in 𝒜 and 𝒜 is an abelian category.
Abstract: The study of the homological functor has been carried out in particular cases of abelian categories, notably in the category of left A-modules (resp. right A-modules) and Categories of graded A-modules where A is a ring. We call category of complexes of an abelian category 𝒜 the category denoted by Comp(𝒜) whose objects are the complexe sequence ...
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Research Article
Comparative Study of Wavelet Solutions for Forced Oscillatory Problems Arising with and Without Damping
Preeti*,
Inderdeep Singh
Issue:
Volume 13, Issue 6, December 2025
Pages:
419-427
Received:
29 October 2025
Accepted:
19 November 2025
Published:
17 December 2025
DOI:
10.11648/j.ajam.20251306.14
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Views:
Abstract: Oscillatory problems are a class of mathematical and physical phenomena in which the solutions display periodic or quasi-periodic variations with respect to time or space. Oscillatory systems subject to external forcing are central in many physical and engineering contexts, and the presence or absence of damping critically influences their behavior. In this comparative study, we develop and evaluate wavelet-based numerical schemes for forced oscillatory differential equations, considering both damped and undamped regimes. Specifically, we employ second-kind Chebyshev wavelets and Haar wavelets, together with their operational integration matrices, to discretize and approximate the solutions of second-order forced oscillators. The wavelet formulations transform the differential problems into systems of algebraic equations, which we then solve under a variety of forcing frequencies and damping parameters. Our numerical experiments demonstrate that Chebyshev wavelets, due to their higher smoothness and spectral accuracy, are particularly effective in capturing the transient decay and subtle features of damped oscillations. In contrast, Haar wavelets provide a computationally efficient and stable approximation in undamped systems, especially in scenarios prone to resonance. We compare these methods across key metrics such as convergence rate, error behavior, and computational cost. The numerical results confirm that Chebyshev wavelets are particularly effective in capturing the fine decay dynamics of damped oscillations, while Haar wavelets deliver fast, stable approximations for undamped systems, especially under resonant forcing. These findings are supported by several computational experiments, which validate both the accuracy and efficiency of the proposed wavelet schemes. These insights offer practical guidance for selecting suitable wavelet approaches tailored to the physical damping conditions of forced oscillatory problems.
Abstract: Oscillatory problems are a class of mathematical and physical phenomena in which the solutions display periodic or quasi-periodic variations with respect to time or space. Oscillatory systems subject to external forcing are central in many physical and engineering contexts, and the presence or absence of damping critically influences their behavior...
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Research Article
Derivation of Worth Growth Rate of an Investor’s Portfolio Under Multi-fractal Analysis
Joy Ijeoma Adindu-Dick*
Issue:
Volume 13, Issue 6, December 2025
Pages:
428-437
Received:
30 October 2025
Accepted:
13 November 2025
Published:
17 December 2025
DOI:
10.11648/j.ajam.20251306.15
Downloads:
Views:
Abstract: The fractal dimension is the basic notion for describing structures that have a scaling symmetry. In finance, multi-fractality is one of the well known facts which characterized non-trivial properties of financial time series. The stock price (or index) fluctuations can be described in terms of long-range temporal correlations by a spectrum of the Holder exponents and a set of fractal dimensions. To forecast the market risk, assessing the stock price indices is the foundation. Multi-fractal has lots of advantages when explaining the volatility of the stock prices. The asset price returns are multi-period market depending on market scenarios which are the measure points. In this work, we use some tools of multi-fractal analysis to derive the worth growth rate of an investor’s portfolio for particular and general cases. For the particular case, we considered the situation when the mean interest rate of some stocks does not depend on other stocks in the market. That is, an investor has invested his money in a stock with a linear mean return. Under the general case, we considered a market comprising some units of assets in long position and a unit of the option in short position. Using Ito’s formula on the present value of the market, we derived the growth rate of investor’s portfolio. Our model equations, which are based on multiplicative processes, capture all the features of the returns. They are tested using data from Zenith Bank of Nigeria stock prices. From our graphs, the worth of investment grows as stock price increases and also decreases with stock price.
Abstract: The fractal dimension is the basic notion for describing structures that have a scaling symmetry. In finance, multi-fractality is one of the well known facts which characterized non-trivial properties of financial time series. The stock price (or index) fluctuations can be described in terms of long-range temporal correlations by a spectrum of the ...
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