The analytic solution for the unsteady flow of generalized Oldroyd- B fluid on oscillating rectangular duct is studied. In the absence of the frequency of oscillations, we obtain the problem for the flow of generalized Oldroyd- B fluid in a duct of rectangular cross- section moving parallel to its length. The problem is solved by applying the double finite Fourier sine and discrete Laplace transforms. The solutions for the generalized Maxwell fluids and the ordinary Maxwell fluid appear as limiting cases of the solutions obtained here. Finally, the effect of material parameters on the velocity profile spotlighted by means of the graphical illustrations

            In this paper, several conditions are put in order to compose the sequence of partial sums ,  and  of the fractional operators of analytic univalent functions ,  and   of bounded turning which are bounded turning too.

The possibility of using the magnetic field technique in prevention of forming scales in heat exchangers pipes using
hard water in heat transfer processes, also the studying the effective and controllable parameters on the mechanism of
scale formation.
The new designed heat exchanger experimental system was used after carrying out the basic process designs of the
system. This system was used to study the effect of the temperature (40-90 °C) and water flow rate (0.6-1.2 L/min) on
the total hardness with time as a function of precipitation of hardness salts from water and scale formation.
Different magnetic field designs in the heat exchanger experimental system were used to study the effect of magnetic
field design a

The problem of non-Darcian-Bènard double diffusive magneto-Marangoni convection   is considered in a horizontal infinite two layer system. The system consists of a two-component fluid layer placed above a porous layer, saturated with the same fluid with a constant heat sources/sink in both the layers, in the presence of a vertical magnetic field.   The lower porous layer is bounded by rigid boundary, while the upper boundary of the fluid region is free with the presence of Marangoni effects.  The system of ordinary differential equations obtained after normal mode analysis is solved in a closed form for the eigenvalue and the Thermal Marangoni Number (TMN) for two cases of Thermal Boundary Combinations (TBC); th

In this paper, we define certain subclasses of analytic univalent function associated with quasi-subordination. Some results such as coefficient bounds and Fekete-Szego bounds for the functions belonging to these subclasses are derived.

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

The steady state laminar mixed convection and radiation through inclined rectangular duct with an interior circular tube is investigated numerically for a thermally and hydrodynamicaly fully developed flow. The two heat transfer mechanisms of convection and radiation are treated independently and simultaneously. The governing equations which used are continuity, momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C) methods. The finite difference approach with the Line Successive Over-Relaxation (LSOR) method is used to obtain all the computational results. The (B.F.C) method is used to generate the grid of the problem. A computer program (Fortran

The steady state laminar mixed convection and radiation through inclined rectangular duct with an interior circular tube is investigated numerically for a thermally and hydrodynamicaly fully developed flow. The two heat transfer mechanisms of convection and radiation are treated independently and simultaneously. The governing equations which used are continuity, momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C) methods. The finite difference approach with the Line Successive Over-Relaxation (LSOR) method is used to obtain all the computational results. The (B.F.C) method is used to generate the grid of the problem. A computer program (Fortr

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.