Boundary layer flow of a dusty fluid over a permeable shrinking surface

Purpose -The purpose of this paper is to numerically study the boundary layer problem for the case of two-dimensional flow of dusty fluid over a shrinking surface in the presence of the fluid suction at the surface. Design/methodology/approach -The governing equations of the problem are reduced to the system of ordinary differential equations using the similarity transformation and then solved using the bvp4c method in the Matlab software. Findings -The effects of the drag coefficient parameter L, the fluid-particle interaction parameter d, the suction parameter s and the particle loading parameter v on the flow of the permeable shrinking sheet are investigated. It is found that the aforementioned parameters have different effects in the shrinking sheet flow. This study has also succeeded in discovering the second solution, and through the stability analysis, it is suggested that the solution is unstable and not physically realizable in practice. Practical implications -The current findings add to a growing body of literature on the boundary layer problem in the dusty fluid. The dusty fluid is significant in various practical applications such as in the transporting suspended powdered materials through pipes, propulsion and combustion in rockets, the flow of blood in arteries, wastewater treatment and as corrosive particles in engine oil flow. Originality/value -Even though the dusty fluid problem has been extensively studied in the flow of the stretching sheet, limited findings can be found over a shrinking flow. In fact, this is the first study to discover the second solution in the dusty fluid problem.