Abstract

This study presents a novel fractional semi-analytical iterative approach for solving nonlinear fractional Fisher’s equations using the Caputo fractional operator. The primary objective is to provide a method that yields exact solutions to nonlinear fractional equations without requiring assumptions about nonlinear terms. By applying the Temimi-Ansari Method (TAM) with fractional calculus, this approach offers a robust solution to the time-fractional nonlinear Fisher’s equation, a model relevant in fields such as population dynamics, tumor growth, and gene propagation. In this work, tables and graphical illustrations show that the proposed method minimizes computational complexity and delivers significant accuracy across multiple cases of Fisher’s equations. The findings indicate that TAM with fractional order derivatives provides accurate, efficient approximations with reduced computational workload, showcasing the technique’s potential for addressing a wide range of nonlinear fractional differential equations.OPEN ACCESS Received: 19/07/2024 Accepted: 01/11/2024

Abstract

En algunos problemas relevantes de la ingeniería, el campo mecánico está fuertemente acoplado con el de temperatura y el de transporte de masa. La solución de estos problemas es compleja sobre todo cuando las deformaciones son grandes. Por ello, a menudo se acude a aproximaciones numéricas que pueden encontrar todos los campos involucrados en el problema acoplado, sus efectos y sus interacciones. En este artículo se describe una discretización por el método de los elementos finitos del problema acoplado de difusión, temperatura y deformación incluyendo el rango no lineal de deformaciones. La formulación tiene en cuenta todos los acoplamientos posibles entre los tres campos de estudio y se proporcionan todos los detalles necesarios para su completa implementación llenando un hueco de la literatura de estos métodos. Asimismo, el artículo describe la fundamentación termodinámica de los problemas acoplados termo-difusivo-mecánicos, insistiendo en la derivación de las ecuaciones de balance y restricciones que siguen de la segunda ley de la termodinámica. Los resultados del artículo serán de interés para investigadores que necesiten implementar las ecuaciones de problemas acoplados en códigos de elementos finitos y, en particular, para aplicaciones en el modelado de baterías, del comportamiento de metales bajo los efectos del hidrógeno, de geles, etc.

Abstract

En algunos problemas relevantes de la ingeniería, el campo mecánico está fuertemente acoplado con el de temperatura y el de transporte de masa. La solución de estos problemas es compleja sobre todo cuando las deformaciones son grandes. Por ello, a menudo se acude a aproximaciones numéricas que pueden encontrar todos los campos involucrados en el problema acoplado, sus efectos y sus interacciones. En este artículo se describe una discretización por el método de los elementos finitos del problema acoplado de difusión, temperatura y deformación incluyendo el rango no lineal de deformaciones. La formulación tiene en cuenta todos los acoplamientos posibles entre los tres campos de estudio y se proporcionan todos los detalles necesarios para su completa implementación llenando un hueco de la literatura de estos métodos. Asimismo, el artículo describe la fundamentación termodinámica de los problemas acoplados termo-difusivo-mecánicos, insistiendo en la derivación de las ecuaciones de balance y restricciones que siguen de la segunda ley de la termodinámica. Los resultados del artículo serán de interés para investigadores que necesiten implementar las ecuaciones de problemas acoplados en códigos de elementos finitos y, en particular, para aplicaciones en el modelado de baterías, del comportamiento de metales bajo los efectos del hidrógeno, de geles, etc.

Abstract

Measuring and determining the parameters and characteristics of multilayer structures have become an important subject for several recent studies. This importance is due to industry needs and structural health requirements. The eddy current inspection is considered an important practical tool that ensures the safety and efficiency of multilayer structures and responds to the above necessities. The diversity of multilayer structure characteristics is one of the principal problems that must be solved. These physical and electromagnetic parameters are not always available or provided by the suppliers. Another problem that arises in the development of different models related to these structures is the difficulty of obtaining a satisfactory diagnosis. This difficulty returns to the complexity of geometry, the presence of small dimensions and sizes, and the existence of various parameters. In this context, it is necessary to achieve a strategy for the development of software and hardware tools concerning the characterization of multilayer structures. These tools must be applied to surmount the above problems and improve the technical advantages of the eddy current inspection. The principal objective of this work is to investigate the efficacy of the eddy current method applied to aeronautical materials, particularly low thickness multilayer structures. The modeling was performed using the finite element method. A software program was developed to investigate changes in the coil impedance. Results are initially validated and compared against the analytical and computational results given for simple cases. They are very similar, and they present a good agreement for both situations. The error is 5% for the calculus of the induction magnetic B. It also varies from 0.17% to 5.32% for impedance responses that enable the application of the developed code to carry out simulations for complex geometries. For various values of parameters and a wide range of applications, the parameters and properties of the problem can easily be introduced into the code. This permits the analysis and calculation of changes in impedance versus the effect of any variation in parameters. The developed approach is sufficiently general. It can simulate various potential cases of defects in low thickness multilayer structures due to its adequate design. It can generate interpretable results for differentOPEN ACCESS Received: 14/07/2024 Accepted: 02/10/2024

Abstract

The problem of uneven ventilation in pig houses must be solved to effectively improve the winter environmental quality of pig nurseries in cold regions. In this study, the airflow field and airflow uneven coefficients of pig nurseries with duct ventilation were simulated and calculated using computational fluid dynamics, and compared with pig nurseries with different duct diameters, inlet and outlet air velocities and air supply angles. The average relative error between the simulated and measured values was 12 %. Comparison of simulation results and airflow uneven coefficients showed that the airflow uneven coefficients of the fences were reduced, and the airflow field was uniformly distributed with a duct diameter of 0.3 m , inlet and outlet air velocities of 1.5 and 2.0 \mathrm{~m} / \mathrm{s}, respectively, and an air supply angle of 45^{\circ }. These improvements resulted in a more homogeneous ventilation, which led to more uniform ventilation and contributed to discharging dirty air outdoors. Then the test pig nursery was modified based on the simulation and analysis results. Difference analyses were carried out between the control and the test pig nurseries. Comparative analyses showed the differences between the test data and the monitoring data were smaller, and the duct ventilation was more uniform, which was suitable for the healthy growth of piglets.

Abstract

The problem of uneven ventilation in pig houses must be solved to effectively improve the winter environmental quality of pig nurseries in cold regions. In this study, the airflow field and airflow uneven coefficients of pig nurseries with duct ventilation were simulated and calculated using computational fluid dynamics, and compared with pig nurseries with different duct diameters, inlet and outlet air velocities and air supply angles. The average relative error between the simulated and measured values was {| class="formulaSCP" style="width: 100%; text-align: center;" |- | 12\% |} . Comparison of simulation results and airflow uneven coefficients showed that the airflow uneven coefficients of the fences were reduced, and the airflow field was uniformly distributed with a duct diameter of 0.3 m , inlet and outlet air velocities of 1.5 and {| class="formulaSCP" style="width: 100%; text-align: center;" |- | 2.0\, m/s |} , respectively, and an air supply angle of {| class="formulaSCP" style="width: 100%; text-align: center;" |- | {45}^{\circ } |} . These improvements resulted in a more homogeneous ventilation, which led to more uniform ventilation and contributed to discharging dirty air outdoors. Then the test pig nursery was modified based on the simulation and analysis results. Difference analyses were carried out between the control and the test pig nurseries. Comparative analyses showed the differences between the test data and the monitoring data were smaller, and the duct ventilation was more uniform, which was suitable for the healthy growth of piglets.

Abstract

The problem of uneven ventilation in pig houses must be solved to effectively improve the winter environmental quality of pig nurseries in cold regions. In this study, the airflow field and airflow uneven coefficients of pig nurseries with duct ventilation were simulated and calculated using computational fluid dynamics, and compared with pig nurseries with different duct diameters, inlet and outlet air velocities and air supply angles. The average relative error between the simulated and measured values was 12 %. Comparison of simulation results and airflow uneven coefficients showed that the airflow uneven coefficients of the fences were reduced, and the airflow field was uniformly distributed with a duct diameter of 0.3 m , inlet and outlet air velocities of 1.5 and 2.0 \mathrm{~m} / \mathrm{s}, respectively, and an air supply angle of 45^{\circ }. These improvements resulted in a more homogeneous ventilation, which led to more uniform ventilation and contributed to discharging dirty air outdoors. Then the test pig nursery was modified based on the simulation and analysis results. Difference analyses were carried out between the control and the test pig nurseries. Comparative analyses showed the differences between the test data and the monitoring data were smaller, and the duct ventilation was more uniform, which was suitable for the healthy growth of piglets.