Abstract
Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model.
Highlights
Due to the relevance of non-Newtonian fluids in some of the optimization processing of food items, the heat transfer phenomenon is an important research area
Symmetry 2019, 11, 1295 much more, but Casson fluids among them have been investigated by a small number of researchers
The Casson fluid model plays a vital role in many materials such as chocolate and blood, according to Mukhopadhyay and Mandal [5]
Summary
Due to the relevance of non-Newtonian fluids in some of the optimization processing of food items, the heat transfer phenomenon is an important research area. Symmetry 2019, 11, 1295 much more, but Casson fluids among them have been investigated by a small number of researchers. This model was introduced by Casson in 1959 [1]. This fluid has great importance in many fields of industries and medicines; see for examples, Qasim and Ahmad [2], Shehzad et al [3], and Qasim and Noreen [4]. The metachronal coordination between the beating cilia in a cylindrical tube is one of the factors under which inspiration, and some mathematical formulations, is made to analyze Casson fluid flow, according to Siddiqui et al [6]. Simplification is taken place by inducting long wavelength and low Reynolds number assumptions
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