Journal of Mathematics Research; Vol. 4, No. 5; 2012 ISSN 1916-9795 E-ISSN 1916-9809 Published by Canadian Center of Science and Education Comparison of the Exact and Approximate Values of Certain Parameters in Laminar Boundary Layer Flow Using Some Velocity Profiles Asuquo E. Eyo 1 , Nkem Ogbonna 2 & Moses E. Ekpenyong 3 1 Department of Mathematics and Statistics, University of Uyo, Uyo, Nigeria 2 Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria 3 Department of Computer Science, University of Uyo, Uyo, Nigeria Correspondence: Asuquo E. Eyo, Department of Mathematics and Statistics, University of Uyo, Uyo, Nigeria. E-mail: asuquoessieneyo@yahoo.com Received: May 24, 2012 Accepted: June 7, 2012 Online Published: September 11, 2012 doi:10.5539/jmr.v4n5p17 URL: http://dx.doi.org/10.5539/jmr.v4n5p17 Abstract We apply second, third, fourth, fifth and sixth order velocity profiles to discuss laminar boundary layer flow over a flat plate. Inclusion of these velocity profiles in Von Karman-Pohlhausen (1921) momentum integral equa- tion enables us to determine the approximate values of the parameters namely, (i) boundary layer thickness, (ii) displacement thickness, (iii) momentum thickness, (iv) thickness ratio, (v) skin friction coefficient, (vi) drag coef- ficient and (vii) the shear rate relation on the plate. Comparison of the approximate values with the exact Blasius (1908) values leads to the determination of the percentage error for each of the above parameters for the different velocity profiles. From the sixth order velocity profile we can predict that higher order velocity profiles will yield greater percentage errors and hence worse and worse results for these parameters except displacement thickness. Keywords: exact values, approximate values, laminar, boundary layer flow, parameters in the flow, velocity pro- files 1. Introduction Boundary layer is formed whenever there is relative fluid motion between the solid boundary and the fluid. The velocity within the boundary layer increases from zero at the boundary surface to the velocity of the main stream asymptotically. Therefore the thickness of the boundary layer is arbitrary defined as that distance from the bound- ary in which the velocity reaches 99 percent of the velocity of the free stream, Schlichting (1968). Boundary layer flow has been a topic of intensive research by various researchers since the development of the concept by Prandtl (1925). Craft and Lowell (2009) investigated two aspects of oceanic hydrothermal heat flux that are not well understood namely, the relative partitioning of heat flux between high-temperature and low-temperature flows at oceanic spreading ridges and next the hydrothermal behaviour of the near-axis region, where seismic data suggest that a zone of partial melt extends quasi-vertically into the low crust at the East Pacific Rise. They applied steady state boundary layer theory to each system by assuming circulation occurs near a hot isothermal wall that laterally transfers heat to and induces convection within an adjacent fluid-filled medium. In their analysis, they showed that, for the near-axis model, heat transfer in the hydrothermal boundary layer is greater than the input from steady state generation of the oceanic crust by seaflow spreading. Dorfman (2011) presented a review of universal functions widely used in different areas of boundary layer theory for many years up to the present. Thus, he considered different kinds of universal functions, from simple equa- tions of dimensionless numbers in similarity theory to universal parametric boundary layer equations. Finally, he adopted various universal solutions from almost 100 articles published since the famous Howarth study of Blasius series in 1935 to show the breadth of universal aproaches with application in laminar, turbulent and transition boundary layers in solving non-isothermal and conjugate heat transfer problems as well as in planetary boundary layer problems in meteorology. 17