Prof. Dr. M. H. Hamdan, Fellow, I.M.A.
Department of Mathematics and Statistics
University of New Brunswick, Saint John, NB, Canada E2L 4L5
[email protected]

Title: Flow over Porous Layers: Modelling Aspects of Flow in the Transition Layer

Abstract: Recent advances in the study of the mechanics of the transition layer between a Darcy porous layer and a Navier-Stokes’ channel employ a Brinkman’s porous layer with variable permeability, sandwiched between the two flow regiments. Flow in the Brinkman’s layer is governed by the well-known Brinkman’s equation which has been shown to give rise to Airy’s differential equation. Exact solutions of the flow in the transition layer are then given in terms Airy’s functions. This approach continues to be implemented in the study of flow through and over porous layers, and has provided an impetus to the transition zone approach, which initiated a number of novel ideas that include:

1) Introducing and reviving the implementation of classical integral functions in the porous media literature (as witnessed by the use of Airy’s differential equation and the Airy functions in providing an analytical solution to the flow in the transition zone);

2) Introducing new integral functions to facilitate solution to the inhomogeneous Airy’s differential equation. This, in turn, facilitates analysis of other related problems governed by the inhomogeneous Airy’s equation.

3) Initiating non-traditional models of permeability variations in porous media. These complement classical models that use elementary mathematical functions and have served the subject matter well.

The use of special functions in advancing the topic represents a new generation of models the computations of which is no longer a formidable task.

In the current work, modelling aspects of flow through and over porous layers with an embedded transition layer are discussed in order to provide alternative variable permeability models that reduce Brinkman’s equation in the transition zone to equations that complement Airy’s equation. In particular, the interest is to model the flow using generalized Airy’s equation and Weber’s inhomogeneous differential equation, and to provide efficient algorithms for their computations.

Bio: Dr. M. H. Hamdan received an Ordinary National Diploma in Technology-Engineering from Swindon College, U.K.; a Certificate in Negotiation, Mediation and Conflict Resolution from St. Mary’s University, Canada; a B.Sc, M.Sc., and a Ph.D in Applied Mathematics from the University of Windsor, Canada. He taught at a number of universities both as a regular faculty member and as a visiting professor, in Canada, China and the Middle East. He has been teaching at the University of New Brunswick, Canada, for 34 years, and is a previous Chair of the Department of Mathematics, Statistics and Computer Science. His teachable areas span the areas of Mathematics, Fluid Mechanics, Decision Sciences and Management Science, Mathematical Economics, and Negotiations. His research areas include computational fluid dynamics, single-phase flow through porous media, and modeling dusty gas flow through porous media. He is an International Consultant in Science and Technology Planning and in School Mathematics Curricular Development. He is the recipient of a number of teaching and research awards, and is listed among American Men and Women of Science; Who’s Who in Science and Engineering; and Who’s Who in the World.