Boundary layer flow of Reiner-Philippoff fluids

An analysis is made of the boundary layer flow of Reiner-Philippoff fluids. This work is an extension of a previous analysis by Hansen and Na [A.G. Hansen and T.Y. Na, Similarity solutions of laminar, incompressible boundary layer equations of non-Newtonian fluids. ASME 67-WA/FE-2, presented at the ASME Winter Annual Meeting, November (1967)], where the existence of similar solutions of the boundary layer equations of a class of general non-Newtonian fluids were investigated. It was found that similarity solutions exist only for the case of flow over a 90[deg] wedge and, being similar, the solution of the non-linear boundary layer equations can be reduced to the solution of non-linear ordinary differential equations. In this paper, the more general case of the boundary layer flow of Reiner-Philippoff fluids over other body shapes will be considered. A general formulation is given which makes it possible to solve the boundary layer equations for any body shape by a finite-difference technique. As an example, the classical solution of the boundary layer flow over a flat plate, known as the Blasius solution, will be considered. Numerical results are generated for a series of values of the parameters in the Reiner-Philippoff model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31231/1/0000134.pd

An initial-value method for the solution of certain nonlinear diffusion equations in biology

The steady-state one-dimensional diffusion equation with a nonlinear source term is a class of differential equations governing the behavior of many biological systems. As with other types of nonlinear differential equations, exact analytical solutions exist only in some very special cases. Previously, analytical solutions could be obtained only by a linearization process; moreover, the analytical solutions thus obtained approach the exact solution in a very limited range of some physical parameters. On the other hand, numerical solutions obtained by using digital computers, although exact, usually require an iteration process due to the two-point nature of the boundary conditions in such problems.In this article a method of transformation is introduced that makes it possible to transform the governing differential equation from a boundary-value to an initial-value problem. As a result, exact numerical solutions to this class of equations can be obtained in a single step. Numerical solutions of the concentration profiles in an enzyme system are presented as an illustration of the method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32827/1/0000202.pd

Naturnal convection of a Darcian fluid about a wavy cone

The results of a study of natural convection along an isothermal wavy cone embedded in a fluid-saturated porous medium are presented. The boundary layer under consideration is cencerned with the regime where the Darcy-Rayleigh number Ra is very large. It is assumed that the surface waves have O(1) amplitude and wavelength. The boundary layer equations are solved numerically using the Keller-box method. Detailed results of the effect of the sinusoidal waves on the heat flux on the wall are given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31232/1/0000135.pd

Free convection flow on a nonisothermal flat plate under nonuniform gravity

In this paper, we present results obtained by using a numerical procedure for the free convection flow along a rotating nonisothermal plate subject to a nonuniform gravity field. Several specific forms for the temperature distributions of the plate are considered. For these instances the skin-friction and heat transfer rate on the wall at selected values of the distance from the leading edge and for some values of Prandtl numbers are presented. The method employed is shown to be very accurate in comparison with previous solutions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25260/1/0000703.pd

Free convection flow past a vertical flat plate embedded in a saturated porous medium

A numerical solution for the free convection flow past a vertical semi-infinite flat plate embedded in a highly saturated porous medium by allowing the plate to have a non-uniform temperature or a non-uniform heat flux distributions has been developed. Both local heat transfer rate and excess surface temperature as a function of the distance along the plate are tabulated for a few cases of prescribed wall temperature and heat flux distributions. Such tabulations serve as a reference against which other approximate solutions can be compared in the future.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25424/1/0000873.pd

A numerical scheme for unsteady flow of a viscous fluid between elliptic plates

A new continuation method has been developed to solve the nonlinear eigenvalue problem describing the unsteady, squeezing flow of a viscous fluid between elliptic plates. Unlike the numerical schemes previously used (e.g. homotopy algorithm), the present scheme is conceptually simple, noniterative, insensitive to the first approximation and works for all values of squeeze number S characterizing the flow. The numerical results compare extremely well with those obtained with sophisticated schemes. Since existing numerical data are limited to three sparsely spaced values of S, additional data are reported for systematically spaced values of squeeze number S and ellipticity parameter [beta]. Although the scheme has been applied to a specific problem, it appears potentially capable of handling a variety of nonlinear eigenvalue problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24355/1/0000624.pd

A noniterative numerical solution for step-heated semi-infinite solid with temperature dependent thermal properties

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24513/1/0000791.pd

Flow and heat transfer over a longitudinal circular cylinder moving in parallel or reversely to a free stream

Steady laminar boundary layer flow and heat transfer over a thin longitudinal isothermal circular cylinder moving in a flowing stream has been studied in this paper. The cases in which the cylinder is moving in the same (parallel) or in the opposite (reverse) direction to the free stream are considered. The transformed nonsimilar boundary layer equations are solved numerically using the Keller-box method for some values of the curvature parameter, the Prandtl number and relative velocity parameter. The results show that the velocity and temperature distributions as well as the coefficients of skin friction and the local Nusselt number are appreciably affected by the relative velocity parameter.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41698/1/707_2005_Article_BF01410516.pd

Periodic heat transfer in fins with variable thermal parameters

Periodic heat transfer in a convecting fin with temperature dependent thermal conductivity and coordinate dependent heat transfer coefficient, is analyzed using a perturbation analysis. The zero-order problem, which corresponds to steady-state fin behaviour, is solved by quasilinearization. A method of complex combination is used, in conjunction with a noniterative numerical scheme, to solve the first-order and the second-order problems. The nonlinear nature of the problem gives rise to a nonoscillatory component in the second-order term, which causes a net change in the mean values of temperature and heat transfer rate. The direction of change depends on the thermal conductivity parameter [alpha]. For [alpha] [mu] 0, the mean temperature is increased, while the mean heat transfer rate is decreased. For [alpha] < 0, the effect is opposite. Detailed results showing the effects of various parameters on temperature distribution, heat transfer rate and time-averaging fin efficiency are presented and discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24300/1/0000566.pd

Boundary-layer flow of a micropolar fluid due to a stretching wall

 A Theoretical analysis is carried out to study the boundary-layer flow over a continuously moving surface through an otherwise quiescent micropolar fluid. The transformed boundary-layer equations are solved numerically for a power-law surface velocity using the Keller-box method. The effects of the micropolar K and exponent m parameters on the velocity and microrotation field as well as on the skin-friction group are discussed in a detailed manner. It is shown that there is a near-similarity solution of this problem. The accuracy of the present solution is also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42236/1/419-67-4-229_70670229.pd