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In this paper, we show that the fractional transport equation can be reduced to a fractional linear differential equation system by using Chebyshev polynomials. We give the analytical solution of this system followed by the spectral approximation. [ABSTRACT FROM AUTHOR]

This study numerically simulates the transport phenomena in steady, two-dimensional, and laminar flow accompanied by heat transfer in a partially heated and partially cooled cavity in the presence of radiatively absorbing, emitting, and scattering gray medium. A portion of the left and right vertical walls is considered as the heater and cooler with constant temperature, respectively, whereas the rest of respective vertical wall is considered to be adiabatic. The horizontal walls are considered adiabatic, too. The discrete ordinate method has been used in modelling the radiative transfer equation followed with finite-volume method as discretization technique. The walls are considered opaque, diffusive, and gray. The effect of radiation, locations of both heater and cooler on fluid flow, and heat transfer has been studied. [ABSTRACT FROM AUTHOR]

The time-evolution of polymer spherulite formation in the melt was investigated by Hv light scattering. The Hv scattering gives both the 'four-leaf clover pattern' and isotropic scattering independent of azimuthal angle. The isotropic scattering from spherulites of isotactic polystyrene is measured over a wide range of crystallization: from bundles to a matured spherulite. Correlation length is obtained from the isotropic scattering. In the early stage of spherulite growth, the correlation length increases in proportion to crystallization time and reaches maximum value of about 1 µm. Hence, the isotropic scattering is attributed to the bundles. The correlation length is the size of the bundles. The bundles grow and successively evolve to spherulites by branching. In the late stage, a matured spherulite grows. However, the correlation length decreases to a value of about 0.6 µm and remains unchanged. By re-examination of the lattice model of Yoon and Stein, the model is found applicable to matured spherulites. The correlation length in matured spherulites is suggested to be the distance between branches of a bundle. The length agrees to a distance between screw dislocations in a crystal grown from the polymer melt. [ABSTRACT FROM AUTHOR]