SOME EXACT SOLUTIONS OF THE SECOND GRADE FLUID IN DIFFERENT GEOMETRIES
T. HAROON
COMSATS Institute of Information Technology, Chak Shehzad, Islamabad, Pakistan.
A. M. SIDDIQUI
Pennsylvania State University, York Campus, York, PA 17403, USA.
WAQAR KHAN
School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, PR China.
T. ALLISON
Pennsylvania State University, York Campus, York, PA 17403, USA.
*Author to whom correspondence should be addressed.
Abstract
Some exact solutions of the equations of motion for second grade fluid are obtained using different geometries. Two-dimensional momentum equations are transformed into a highly non-linear compatibility equation using stream function which are then linearised by using the relationship between stream function and vorticity. The stream function, velocity and pressure distributions are obtained for flow behind a grid; rotational diverging counterflow above a plate with suction; flow due to stretching of plate; corner flow and flow due to asymptotic suction. Results are retrieved for viscous case by putting material constant α1 = 0. Solutions are also presented graphically.
Keywords: Second grade fluid, exact solutions, two-dimensional grid flow, suction, stretching plate, corner flow