The performance and thermal properties of convective-radiative rectangular and moving exponential porous fins with variable thermal conductivity together with internal heat generation are investigated. The second law of thermodynamics is used to investigate entropy generation in the proposed fins. The model is numerically solved using shooting technique. It is observed that the entropy generation depends on porosity parameter, temperature ratio, temperature distribution, thermal conductivity and fins structure. It is noted that entropy generation for a decay exponential fin is higher than that of a rectangular fin which is greater than that of a growing exponential fin. Moreover, entropy generation decreases as thermal conductivity increases. The results also reveal that entropy generation is maximum at the fin's base and the average entropy production depends on porosity parameters and temperature ratio. It is further reveal that the temperature ratio has a smaller amount of influence on entropy as compared to porosity parameter. It is concluded that when the temperature ratio is increases from 1.1 to 1.9, the entropy generation number is also increase by [Formula: see text] approximately. However, increasing porosity from 1 to 80 gives 14-fold increase in average entropy generation.
The current manuscript deals with the fractional dynamical system of transmission along with co-infection of TB in the HIV community including ten classes. We study the necessary conditions for the existence and uniqueness of the solution of the considered system under the fractional operator known as Atangana–Baleanu in Caputo sense. By using fixed-point theory, the qualitative analysis of the result and Ulam–Hyers stability involving fractional operator for the proposed system is derived. For numerical simulations, we applied the fractional Adams–Bashforth method to the system. The obtained results are demonstrated explicitly to illustrate the validity of the considered technique for solving the proposed model under the above-mentioned operator. We observed that, if HIV-infected or unprotected individuals are in contact with TB infected individuals, the disease will grow in society. The dynamical behavior is shown for different arbitrary orders between 0 and 1, which converges to the integer-order one.
<p>The purpose of fins or extended surfaces is to increase the dissipation of heat from hot sources into their surroundings. Fins like annular fins, longitudinal fins, porous fins, and radial fins are used on the surface of equipments to enhance the rate of heat transfer. There are many applications of fins, including superheaters, refrigeration, automobile parts, combustion engines, electrical equipment, solar panels, and computer CPUs. Based on a wide range of applications, the effects of stretching/shrinking on a fully wet trapezoidal fin with internal heat generation is investigated. The shooting approach is used to calculate the trapezoidal fin's thermal profile, tip temperature, and efficiency. It is observed that with an increase in the shrinking and wet parameter, the temperature distribution decreases and efficiency increases. On the other hand, when stretching increases, the temperature distribution increases and efficiency diminishes. Using the computed results, it is concluded that shrinking trapezoidal fins improves the effectiveness and performance of the system.</p>
We consider a spatially inhomogeneous sine-Gordon equation with a double-well potential, describing long Josephson junctions with phase-shifts. We discuss the interactions of symmetric and antisymmetric bound states in the system. Using a multiple scale expansion, we show that the modes decay algebraically in time due to the energy transfer from the discrete to the continuous spectrum. In particular, exciting the two modes at the same time yields an increased decay rate. An external time-periodic drive is shown to sustain symmetric state, while it damps the antisymmetric one.
<abstract><p>In this article, the dynamical behavior of a complex food chain model under a fractal fractional Caputo (FFC) derivative is investigated. The dynamical population of the proposed model is categorized as prey populations, intermediate predators, and top predators. The top predators are subdivided into mature predators and immature predators. Using fixed point theory, we calculate the existence, uniqueness, and stability of the solution. We examined the possibility of obtaining new dynamical results with fractal-fractional derivatives in the Caputo sense and present the results for several non-integer orders. The fractional Adams-Bashforth iterative technique is used for an approximate solution of the proposed model. It is observed that the effects of the applied scheme are more valuable and can be implemented to study the dynamical behavior of many nonlinear mathematical models with a variety of fractional orders and fractal dimensions.</p></abstract>
We study the efficiency of shrinking/stretching radiative fins to improve heat transfer rate. To evaluate the competence of suggested fins, the influence of shrinking/stretching, thermogeometric parameters, surface temperature, convection conduction, radiation conduction, and Peclet number is investigated. The problem is solved numerically using a shooting method. To validate the numerical solution, the results are compared with the solution of a differential transform method. Temperature distribution increases with a rise in convection and radiation conduction parameters when Peclet number, stretching/shrinking, ambience, and surface temperatures are raised. The temperature of the fin’s tip increases as ambient temperature, Peclet number, and surface temperature increase, and decreases for enhanced radiation and convection conduction parameters. Radiation and convection cause the efficiency of the fin to increase for shrinking and decrease for stretching, which shows an important role in heat transfer analysis in mechanical engineering. The formulated model is also studied analytically, and the result is compared to numerical solution, which shows qualitatively good agreement.
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