Applications Of Fractional Calculus In Magnetohydrodynamic Flow And Anomalous Heat And Mass Transfer

In recent years,fractional calculus theory has been widely used in viscoelastic fluid flow problems.Different types of fractional order constitutive relations are proposed.Among them,the generalized Maxwell fluid flow model has been widely used because of its consistent results with the experimental data.Based on this,in Chapter 2,we study the natural-convection magnetic flow of generalized Maxwell fluid through a canted plate under the influence of the canted magnetic field.Natural-convection magnetic fluid flow usually occurs in many industrial processes,such as nuclear reactor cooling,geothermal energy extraction,oil exploration and heat recovery.Considering the effects of thermal absorption,thermal radiation,first-order chemical reaction and radiation absorption,we consider the magnetic flow characteristics and thermal behavior of the generalized Maxwell fluid passing through a porous plate under the action of the canted magnetic field.In terms of temperature and concentration,we have established the single-phase lag model to describe the anomalous transport process.Using Laplace transform and Fourier transform,the analytical solutions of velocity,temperature and concentration in the transform domain are given.Then the semi-analytical solutions of velocity,temperature and concentration can be expressed by inverse Fourier transform and numerical inverse Laplace transform.Further,the influence of relevant parameters on the distribution of velocity,temperature and concentration is given,and the influence of each parameter on the distribution of velocity,temperature and concentration as well as the complex dynamic behavior of fluid are analyzed in detail.In order to describe the influence of the heterogeneity of complex viscoelastic materials on the fluid flow and transport process,the spatial fractional operator is introduced.In the third chapter,we analyze the application of unsteady radiation magnetohydrodynamic flow and heat transfer of viscoelastic fluid driven by constant pressure gradient between parallel plates.Firstly,the variable/distributed order space fractional model is introduced and established to characterize the mechanism of viscoelastic fluid flow and heat transfer.Then,using the central difference approximation of the Riesz space fractional derivative,the Crank-Nicholson central difference scheme of the governing equation is established.The effectiveness of the algorithm is verified by two numerical examples.Finally,we discuss the effect of fractional order parameters on velocity and temperature.The numerical results of these different fractional order models are compared and discussed.