Abstract
This paper re-investigates the mathematical transport model of chlorine used as a water treatment model, when a variable order partial derivative is incorporated for describing the chlorine transport system. This model was introduced in the literature and governed by a fractional partial differential equation (FPDE) with prescribed boundary conditions. The obtained solution in the literature was based on implementing the Laplace transform (LT) combined with the method of residues and expressed in terms of regular exponential functions. However, the present analysis avoids such a method of residues, and thus a new analytical solution is introduced in this paper via Mittag-Leffler functions. Therefore, an effective approach is developed in this paper to solve the chlorine transport model with non-integer order derivative. In addition, our results are compared with several studies in the literature in case of integer-order derivative and the differences in results are explained.
Highlights
IntroductionThe quality of water can be enhanced through suitable values of injection and maintaining residual chlorine in a network not by reducing chlorine
Water sciences is a growing field of research
The separation of variables method (SOV) method combined with the Laplace transform (LT) were applied to solve the current model
Summary
The quality of water can be enhanced through suitable values of injection and maintaining residual chlorine in a network not by reducing chlorine. Chlorine decay is not much more than that in the use of water networks operation and water quality control. This procedure is widely used in most countries to ensure the disinfection capacity of distributed water [1,2]. Biswas et al [4] formulated the standard model of chlorine transport in pipes. The standard model [4] (with integer-order derivative) has been re-analyzed utilizing different approximate methods [5,6].
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