Applications of non-integer differential operators in transport phenomena
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Date
2022-10-14
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UMT Lahore
Abstract
The aim of this dissertation is to analyze the heat and mass transference of non-Newtonian fluids over a vertical plate with different set of thermal boundary condition such as ramped conditions, Newtonian heating, exponential heating and variable temperature under the considerations of wall slip boundary condition as well as no-slip boundary condition. For the sake of generalized memory effects, mathematical fractional models are formulated based on Caputo, Caputo-Fabrizio, CPC, Atangana-Baleanu in Caputo sense and Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. These fractional models have been solved analytically and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of special functions by employing the Laplace transformation method. To comprehensively discuss the dynamics of the considered problem, physical impacts of different parameters on momentum, heat and mass profiles are studied and reverberations are graphically highlighted and deliberated. Special cases are investigated of the obtained solutions and it is noticed that some well-known results are achieved, found in the literature from these special cases. Thermophysical investigation of Oldroyd-B fluid with functional effects of permeability along with memory effect study using non-singular kernel derivative approach. Double diffusive magneto-free-convection flow of rate type fluid over a vertical plate with heat and mass flux, special functions based analysis using local and non-local kernels subject to exponential heating. Functional effects of permeability on Oldroyd-B fluid under magnetization, a comparison of slipping and non-slipping solutions. Fractional analysis of MHD Maxwell fluid with ramped boundary conditions and transport phenomena solutions based on special functions. Thermal and concentration diffusion impacts on MHD Maxwell fluid with generalized Fourier’s and Fick’s perspective. Special functions based solutions of unsteady convective flow of a MHD Maxwell fluid for ramped wall temperature and velocity with concentration. Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative. Heat and mass transport impact on MHD second grade fluid together with a comparative analysis of fractional operators. Generalized Mittag-Leffler kernel form solutions of free convection heat and mass transfer flow of Maxwell fluid with Newtonian heating by applying Prabhakar fractional derivative approach. Various fluid models that are mentioned above, exact solutions are derived and the solutions presented in all the fluid models satisfy the imposed initial and boundary conditions. A comprehensive comparative studies between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.