An exact solution is obtained for the unsteady flow of an electrically conducting visco-elastic incompressible fluid through a porous medium on an infinite flat plate. The fluid under consideration obeys the rheological equations of state due to the Walters stress-strain relation. The plate is accelerated in the presence of a uniform magnetic field. The analysis includes the case of a solid plate as well as a porous one. The solution of the equations of motion is obtained by the use of a Laplace transform. The effects of the elasticity, magnetic field, permeability of the porous medium, and the suction of the plate on the velocity distribution, as well as on skin friction, are discussed. The analytical results are confirmed numerically. It is found that the velocity distribution increases with an increase of both elasticity and permeability, while it decreases as the magnetic parameter increases. It is also found that the skin friction decreases with an increase in the magnetic field and elasticity parameters, while it increases with an increase of both the permeability of the porous medium and the suction of the plate. PACS Nos.: 47.50.+d, 47.55.Mh, 47.85.Dh Résumé : Nous obtenons une solution exacte pour le problème de l'écoulement instable d'un fluide conducteur, viscoélastique et incompressible à travers un milieu poreux sur une surface plane infinie. Ce fluide obéit aux équations d'état rhéologiques dues à la relation effort-déformation de Walters. La plaque est accélérée et un champ magnétique est présent.L'analyse inclut aussi bien une plaque solide que poreuse. La solution des équations de mouvement est obtenue par transformation de Laplace. Nous analysons les effets de l'élasticité, du champ magnétique, de la perméabilité du milieu poreux et de la succion de la plaque sur la distribution de vitesse et sur la friction de surface. Les résultats analytiques sont confirmés par calcul numérique. Nous trouvons que la distribution de vitesse augmente avec l'élasticité et la perméabilité et décroît lorsque le champ magnétique croît. Nous trouvons aussi que la friction de surface diminue lorsque le champ magnétique et les paramètres d'élasticité augmentent.[Traduit par la Rédaction]

Usually, the temperature distribution of nanofluids and the nanoparticles' concentration are finally governed by second-order ordinary differential equations with polynomial coefficients. In this work, a class of second-order boundary value problems with applications on nanofluids has been theoretically solved in terms of the Kummer function. Several lemmas have been presented to relate the Kummer function with the generalized incomplete gamma function. Accordingly, the current solutions reduce to those in the literature at certain values of the coefficients as special cases. Furthermore, the present results are very useful in obtaining the solutions for any future similar problems without any need to perform further calculations.

Recently, it was observed that the concentration/heat transfer of pure/nano fluids are finally governed by singular second-order boundary value problems with exponential coefficients. These coefficients were transformed into polynomials and therefore the governing equations become singular in a new independent variable. Unfortunately, the published approximate solutions in the literature suffer from some weaknesses as showed by one of the present coauthors. Hence, the exact solution for such types of problems becomes a challenge. In this paper, a straightforward approach is presented to obtaining the exact solution for such class of singular second-order boundary value problems. The results are also applied to some selected problems within the literature. Accordingly, the published solutions are recovered as special cases of the present ones.

In this paper, the problem of heat and mass transfer due to the steady motion of a Rivlin- Ericksen fluid in tubes of varying cross-section is considered. Suction at tube walls is taken into account. Under the assumption that the deformations of the boundaries are small, the equations of motion have been solved by using a perturbation technique. The temperature and concentration distributions are obtained. The effects of various physical parameters are discussed. The Nusselt and Sherwood numbers are obtained. A set of figures for a quantitative illustration is presented.

The present work aimed at improving pineapple (Ananas comosus (L.) Merrill) cv. Smooth Cayenne production throughout the tissue culture technique. Some factors affect this process were studied. The method of surface sterilization, the adventitious and axillary bud formation versus N 6 -Benzyladenine (BA) concentration, type of medium (liquid or solidified), rooting and acclimatization were evaluated. Explants have been surface sterilized with sodium hypochlorite (NaOCl) at 0.5 %, then with mercuric chloride (Hg Cl 2 ) at 0.1 % both for 5 minutes, with survival percentage of 95%. All explants were cultured onto MS basal medium supplemented with different concentrations of BA and 1.0 mg l -1 Kinetin (Kin). All cultures were maintained in a growth room at a 16 h photoperiod (40 mmol.m -2 s -1 ), 27 ± 2°C. After eight weeks, number of initiated shoots was counted and the cultures were transferred for multiplication on the best treatment, 2.0 mg l -1 BA and 1.0 mg l -1 Kin. Therefore, using the liquid medium during multiplication stage speed up the growth of proliferated shoots compared to solidified medium. Utilizing 1.0 -3.0 mg l -1 α-Naphthaleneacetic acid (NAA) or Indole-3-butyric acid (IBA) enhanced the root formation of individual shoots. Finally, the well rooted plantlets, around 12 cm in length, were transplanted onto the Peat moss as a soil bed under the greenhouse. After 4 weeks, the survival percentage was 100 %. By this improved protocol, more than 10000 pineapple plants were produced from one initial plant in less than 9 months.