Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a generalized Maxwell fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and after some time both cylinders suddenly begin to oscillate around their common axis with different angular frequencies of their velocities. The solutions that have been obtained are presented under integral and series forms in terms of generalized G and R functions. Moreover, these solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary Maxwell fluid are also obtained as limiting cases of our general solutions. At the end, flows corresponding to the ordinary Maxwell and generalized Maxwell fluids are shown and compared graphically by plotting velocity profiles at different values of time and some important results are remarked.     

Visible Light Promoted Iron-Catalyzed One-Pot Synthesis of 2-Arylimino-2H-Chromenes from 2-Hydroxybenzyl Alcohols and β- Ketothioamides at Room Temperature

An efficient, environmentally benign and one-pot approach for the synthesis of 2-arylimino-2H-chromenes from 2-hydroxybenzyl alcohols and β-ketothioamides at room temperature under visible light has been developed. The reported reaction conditions were favorable for a wide range of β-ketothioamides afforded good to excellent yields of the respective products. The low cost and air stable Knölker iron catalyst has been employed for the dehydrogenation of 2-hydroxybenzyl alcohols under photolysis that would usually require a higher temperature.