The free convective heat transfer to the power-law non-Newtonian flow from a vertical plate in a porous medium saturated with nanofluid under laminar conditions is investigated. It is considered that the non-Newtonian nanofluid obeys the mathematical model of power-law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The partial differential system governing the problem is transformed into an ordinary system via a usual similarity transformation. The numerical solutions of the resulting ordinary system are obtained. These solutions depend on the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion number Nb, and thermophoresis number Nt. For various values of n and Le, the effects of the influence parameters on the fluid behavior as well as the reduced Nusselt number are presented and discussed.

The free convective heat transfer to the power-law non-Newtonian flow from a vertical plate in a porous medium saturated with nanofluid under laminar conditions is investigated. It is considered that the non-Newtonian nanofluid obeys the mathematical model of power-law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The partial differential system governing the problem is transformed into an ordinary system via a usual similarity transformation. The numerical solutions of the resulting ordinary system are obtained. These solutions depend on the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion number Nb, and thermophoresis number Nt. For various values of n and Le, the effects of the influence parameters on the fluid behavior as well as the reduced Nusselt number are presented and discussed.

The free convective heat transfer to the power-law non-Newtonian flow from a vertical plate in a porous medium saturated with nanofluid under laminar conditions is investigated. It is considered that the non-Newtonian nanofluid obeys the mathematical model of power-law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The partial differential system governing the problem is transformed into an ordinary system via a usual similarity transformation. The numerical solutions of the resulting ordinary system are obtained. These solutions depend on the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion number Nb, and thermophoresis number Nt. For various values of n and Le, the effects of the influence parameters on the fluid behavior as well as the reduced Nusselt number are presented and discussed.

The free convective heat transfer to the power-law non-Newtonian flow from a vertical plate in a porous medium saturated with nanofluid under laminar conditions is investigated. It is considered that the non-Newtonian nanofluid obeys the mathematical model of power-law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The partial differential system governing the problem is transformed into an ordinary system via a usual similarity transformation. The numerical solutions of the resulting ordinary system are obtained. These solutions depend on the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion number Nb, and thermophoresis number Nt. For various values of n and Le, the effects of the influence parameters on the fluid behavior as well as the reduced Nusselt number are presented and discussed.

This work is focused on the study of the natural convection boundary-layer flow over a downward-pointing vertical cone in a porous medium saturated with a non-Newtonian nanofluid in the presence of heat generation or absorption. The transformed boundary layer governing equations are solved numerically. The influences of pertinent parameters such as the heat generation or absorption, the solid volume fraction of nanoparticles and the type of nanofluid on the flow and heat transfer rate in terms of Nusselt number are discussed. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. The generalized governing equations derived in this work can be applied to different cases of non-Newtonian fluids with different values of the power-law viscosity index. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.

This work is focused on the study of the natural convection boundary-layer flow over a downward-pointing vertical cone in a porous medium saturated with a non-Newtonian nanofluid in the presence of heat generation or absorption. The transformed boundary layer governing equations are solved numerically. The influences of pertinent parameters such as the heat generation or absorption, the solid volume fraction of nanoparticles and the type of nanofluid on the flow and heat transfer rate in terms of Nusselt number are discussed. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. The generalized governing equations derived in this work can be applied to different cases of non-Newtonian fluids with different values of the power-law viscosity index. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.

This work is focused on the study of the natural convection boundary-layer flow over a downward-pointing vertical cone in a porous medium saturated with a non-Newtonian nanofluid in the presence of heat generation or absorption. The transformed boundary layer governing equations are solved numerically. The influences of pertinent parameters such as the heat generation or absorption, the solid volume fraction of nanoparticles and the type of nanofluid on the flow and heat transfer rate in terms of Nusselt number are discussed. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. The generalized governing equations derived in this work can be applied to different cases of non-Newtonian fluids with different values of the power-law viscosity index. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.

This work is focused on the study of the natural convection boundary-layer flow over a downward-pointing vertical cone in a porous medium saturated with a non-Newtonian nanofluid in the presence of heat generation or absorption. The transformed boundary layer governing equations are solved numerically. The influences of pertinent parameters such as the heat generation or absorption, the solid volume fraction of nanoparticles and the type of nanofluid on the flow and heat transfer rate in terms of Nusselt number are discussed. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. The generalized governing equations derived in this work can be applied to different cases of non-Newtonian fluids with different values of the power-law viscosity index. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.

The effect of yield stress on the free convective heat transfer of dilute liquid suspensions of nanofluids flowing on a vertical plate saturated in porous medium under laminar conditions is investigated considering the nanofluid obeys the mathematical model of power-law. The model used for non-Newtonian nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing boundary- layer equations are cast into dimensionless system which is solved numerically using a deferred correction technique and Newton iteration. This solution depends on yield stress parameter Ω, a power-law index n, Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb, and a thermophoresis number Nt. Analyses of the results found that the reduced Nusselt and Sherwood numbers are decreasing functions of the higher yield stress parameter for each dimensionless numbers, n and Le, except the reduced Sherwood number is an increasing function of higher Nb for different values of yield stress parameter.

Seed and trichome morphology of 13 taxa representing the genus Fagonia in Egypt have been studied using light (LM) and scanning electron microscopy (SEM). Macro- and micro-morphological characters, including seed shape, seed size, seed coat sculpture, trichome density and structure were studied to evaluate their systematic signifi cance. Seed shape and trichome density were found to have only minor taxonomic value, but seed coat sculpturing and trichome structure proved to be valuable characters. Th ese characters off er evidence to combine certain species, e.g. Fagonia kassasii and F. schimperi in F. bruguieri , Fagonia microphylla in F. scabra and Fagonia thebaica in F. arabica . However, F. sinaica , F. tristis, F. boveana and F. isotricha should be maintained as separate species. Generally, the diff erent patterns of seed and trichome morphology are useful in delimitation of species within the genus Fagonia, but they could not be used to characterize groups of related species.