A Note on New Exact Solutions for Some Unsteady Flows of Brinkman-Type Fluids over a Plane Wall

Among the motions of a fluid over a plane wall, the Stokes’ problems as well as the motion induced by a constantly accelerating plate have been extensively studied in the literature. However, the first closed-form solutions for the motion of a viscous fluid over an oscillating plate have been late enough obtained by Erdogan [1]. These solutions, as well as those corresponding to the fluid motion due to a constantly or highly accelerating plate have been recently extended by Fetecau et al. [2] to fluids of Brinkman type [3 – 5]. The purpose of this note is to provide new exact solutions for the motion of a Brinkman fluid induced by a constantly or highly accelerating plate or due to an infinite oscillating plate. These dimensionless solutions, unlike those obtained in [2], are fully presented in analytical forms in terms of exponential and complementary error functions. They satisfy all imposed initial and boundary conditions and can easily be reduced to the similar solutions for Newtonian fluids.