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
DOI:
10.11648/j.ajam.20251306.11
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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
DOI:
10.11648/j.ajam.20251306.12
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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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,
Johana Kibet Sigey
