## "Babes-Bolyai" University of Cluj-Napoca Faculty of Mathematics and Computer Science

 Special topics of fluid mechanics
 Code Semes-ter Hours: C+S+L Credits Type Section MM270 1 2+2+0 8 compulsory Matematică Aplicată MM270 1 2+2+0 8 compulsory Modele matematice in Mecanica si Astronomie
 Teaching Staff in Charge
 Prof. POP Ioan, Ph.D., popi@math.ubbcluj.ro
 Aims Teaching of fundamental notions of the mechanics of the continuum deformable media. Establishing of Euler and Navier-Stokes equations. Their applicability for the study of some planar potential motions of viscid, incompressible fluids and of the motions along different profiles.
 Content 1. Elements of theory of deformable continuous media: the small deformation, the deformation tensor, the volume deformation, the small displacement of a fluid particle, the linear deformation in curvilinear coordinates. The deformation surface (the deformation quadric). General notions about stresses, Cauchy equations of motions, the symmetry of the stress tensor, the equation of the stress quadric, principal stresses. 2.Equations of fluid mechanics: the equations of viscous fluid flows (Navier-Stokes equations), the equations of ideal fluid flows (Euler's equations). Applications of Bernoully's integrals. The methods of fluid mechanics: the general equations and formulas for the plane potential flow. Complex potential, complex velocity, hydrodynamic flux, the velocity circulation, the formulas of Blasius and Ciaplygin for the steady motion, the determination of the complex potential. Certain plane motions (the translational fluid flow, doublet, vortex). The fluid flow around a circular cylinder, the detremination of the hydrodinamic force on the circular obstacle, the motion without circulation. The motion around of an elyptical cylinder and of a plane flat. 4. Methods of viscous fluid mechanics: exact solutions of the Navier-Stokes equations: the one-dimensional motion, Couette flow, Hagen-Poiseuille flow, the ecuation of the stream function for the plane axial-symmetric flow.
 References 1. Bradeanu, P. - Mecanica fluidelor, Ed. Tehnica, Bucuresti, 1973. 2. Dragos, L. - Principiile mecanicii mediilor continue, Ed. Tehnica, Bucuresti, 1982. 3. Iacob, C. - Introducere matematica in mecanica fluidelor, Ed. Acad. R.P.R., Bucuresti, 1952. 4. Loisianski, L. G. - Mehanika jidkosti i gaza (in limba rusa), Ed. Nauka, Moscova, 1970. 5. Aziz, A., Na, T. Y. - Perturbation methods in heat transfer, Springer, New York, 1984. 6. Bradeanu, P., Pop, I., Bradeanu, D. - Probleme si exercitii de mecanica teoretica, Ed. Tehnica, Bucuresti, 1979. 7. Pop, - Teoria stratului limita laminar nestationar, Ed. Stiintifica si Enciclopedica, Bucuresti, 1983. 8. Bejan, A. - Convection Heat Transfer (second edition). Wiley, New York, 1995. 9. Nakayama, A. - PC - Aided Numerical Heat Transfer and Convective Flow, CRC Press, Tokyo, 1995. 10. Kohr, M.- Probleme Moderne ale Mecanicii Fluidelor vascoase, Presa Universitara Clujeana, Cluj-Napoca, 2000.
 Assessment Exam at the end of the term.