No abstract

In this paper, the temperature and concentration of species around a vessel using the reaction and diffusion relations were investigated. The reactions between 3 chemical species, and the relationship between temperature changes and the rate of chemical reactions were studied. The novelty of this paper is the use of different coefficients of material with diffusion constants and also considering the concentration and temperature of materials involved in the reaction with non-heat sources and with heat source modes. So that showed the concentration and heat transfer rate of substances involved in the chemical reactions in the form of two-dimensional and three-dimensional diagrams about their distance from the borders of the vessel. The finite element method is utilized for calculated differential equations. According to the results obtained, when the temperature of the reactants increased more heat is released; the concentration also changed a lot, and its amount increased. However, in products such as substance (c), it has an inverse relationship with reactants (a) and (b) in such a way that as the concentration and temperature of the reactants increased, these values decreased in the product. On average, concentration changes in the distance from the center to the surroundings the maximum heat source mode was about 76% less than the average heat source mode and about 14% less than the non-heat source mode.

No abstract

No abstract

In this essay, the nonlinear fractional integral equation is studied. Akbari-Ganji’s Method (AGM), Homotopy Perturbation Method (HPM) and Vibrational Iteration Method (VIM) are applied to obtain its solution. We present a new strategy for finding the approximate solutions to Fractional differential equations. We experience Fractional differential equations, which are broadly utilized in fluids. In this article, we have used analytical methods to check the correctness of the answers. Ordinary equations and fractional differential equations are related to entropy and wavelets, and so on. A few examples are employed to appear accurate and simple to implement and demonstrate the method. The solutions are clarified in convergent series. Some well-known models for anticipating the oscillation behavior of the action in a vibrating system are presented, then with the help of fractional calculus which could exceptionally powerful tool in mathematics and modeling of complex systems, a model for the same system is proposed. Compare the models and finally show that the proposed fractional model not only includes non-fractional models but also predicts the behavior of the system more comprehensively.