We study the Darboux integrability of the celebrated Falkner– Skan equation f ′′′+ff ′′+λ(1−f ′2) = 0, where λ is a parameter. When λ = 0 this equation is known as Blasius equation. We show that both differential systems have no first integrals of Darboux type. Additionally we compute all the Darboux polynomials and all the exponential factors of these differential equations.

We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skan-dalis describing finite dimensional unitary solutions of pentagon equation is extended to the non-unitary case. We establish the relation between Hopf-Galois algebras and solutions to modified pentagon equation.

in the age of technology, it is vital to cool down different parts of a device to use it more beneficially. using nanofluids is one of the most common methods which has shown very effective results. in this paper, we have rephrased a classic equation in fluid mechanics, i.e. the falkner-skan boundary layer equation, in order to be used for nanofluid. this nonlinear equation, which was presented...

This paper presents the Adjoint Parabolized Stability Equations (APSE) which are used to predict the receptivity of shear layers to a variety of disturbances. Results from the APSE are first carefully validated against solutions of the Adjoint Navier–Stokes (ANS) equations which demonstrates that APSE is an accurate and effecient means of predicting receptivity. Then APSE is used to document th...

Brucellosis is a disease that generally occurs in animals such as cows, pigs, dogs, cattles and goats. Brucella are gram negative, non-motile, non-spore forming coccobacilli bacteria (Dr Delia Skan, August 2004). The genus Brucella comprises at least 8 species named according to the preferred mammal hosts (Maria-Jesus Grillo, 2012). B.melitensis, B.abortus, B.suis and B.canis are the most impor...

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained re...