Micro/nano thermal boundary layer equations with slip creep jump boundary conditions

2007 ◽  
Vol 72 (6) ◽  
pp. 894-911 ◽  
Author(s):  
M. T. Matthews ◽  
J. M. Hill
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Thermal Boundary Layer ◽  
Boundary Layer Equations

On the propagation of disturbances in a laminar boundary layer. I

1973 ◽  
Vol 73 (3) ◽  
pp. 493-503 ◽  
Author(s):  
S. N. Brown ◽  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Asymptotic Formula ◽  
Boundary Conditions ◽  
Laminar Boundary Layer ◽  
Numerical Results ◽  
Boundary Layer Equations ◽  
Displacement Thickness ◽  
Layer I

An analysis is made of the response of a laminar boundary layer to a perturbation, either in the mainstream, or of the boundary conditions at the wall. The disturbance propagates with the mainstream velocity, and the manner in which it decays at large distances downstream is determined by eigensolutions of the boundary-layer equations. The elucidation of the structure of these eigensolutions requires division of the boundary layer into three regions. Comparison of the asymptotic formula obtained for the displacement thickness is made with the numerical results of Ackerberg and Phillips (1).

A singularity in thermal boundary-layer flow on a horizontal surface

1992 ◽  
Vol 242 ◽  
pp. 419-440 ◽  
Author(s):  
P. G. Daniels
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Rational Numbers ◽  
Velocity Fields ◽  
Boundary Layer Equations ◽  
Layer Flow ◽  
Buoyancy Flows ◽  
Temperature And Velocity Fields

A thermal boundary layer, in which the temperature and velocity fields are coupled by buoyancy, flows along a horizontal, insulated wall. For sufficiently low local Froude number the solution terminates in a singularity with rising skin friction and falling pressure. The structure of the singularity is obtained and the results are compared with numerical solutions of the horizontal boundary-layer equations. A novel feature of the analysis is that the powers of the streamwise coordinate involved in the structure of the singularity do not appear to be simple rational numbers and are determined from the solution of a pair of ordinary differential equations which govern the flow in an inner viscous region close to the wall. Modifications of the theory are noted for cases where either the temperature or a non-zero heat transfer are specified at the wall.

Similarity Solution for Unsteady Free Convection From a Vertical Plate at Constant Temperature to Power Law Fluids

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
J. Abolfazli Esfahani ◽  
B. Bagherian
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Free Convection ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Theoretic Approach ◽  
Local Skin ◽  
Power Law Fluids

The transformation group theoretic approach is applied to perform an analysis of unsteady free convection flow over a vertical flat plate immersed in a power law fluid. The thermal boundary layer induced within a vertical semi-infinite layer of Boussinseq fluid. The system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions via two-parameter group theory. The obtained ordinary differential equations are solved numerically for velocity and temperature using the fourth order Runge-Kutta and shooting method. The effect of Prandtl number and viscosity index (n) on the thermal boundary-layer, velocity boundary-layer, local Nusselt number, and local skin-friction were studied.

The thermal boundary layer in the flow between converging plane walls

1963 ◽  
Vol 59 (1) ◽  
pp. 225-229 ◽  
Author(s):  
N. Riley
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Analytical Solutions ◽  
Thermal Boundary Layer ◽  
Parallel Plane ◽  
Boundary Layer Equations ◽  
Converging Flow

AbstractThe thermal boundary layer in the converging flow between non-parallel plane walls is studied. Analytical solutions of the boundary-layer equations are derived and the heat transfer across the wall is obtained from these solutions.

Symmetry Analysis of Boundary Layer Equations of an Upper Convected Maxwell Fluid with Magnetohydrodynamic Flow

2011 ◽  
Vol 66 (5) ◽  
pp. 321-328
Author(s):  
Gözde Deǧer ◽  
Mehmet Pakdemirli ◽  
Yiǧit Aksoy
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Boundary Conditions ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Similarity Solutions ◽  
Variable Magnetic Field ◽  
Physical Parameters ◽  
Boundary Layer Equations

Steady state boundary layer equations of an upper convected Maxwell fluid with magnetohydrodynamic (MHD) flow are considered. The strength of the magnetic field is assumed to be variable with respect to the location. Using Lie group theory, group classification of the equations with respect to the variable magnetic field is performed. General boundary conditions including stretching sheet and injection are taken. Restrictions imposed by the boundary conditions on the symmetries are discussed. Special functional forms of boundary conditions for which similarity solutions may exist are derived. Using the symmetries, similarity solutions are presented for the case of constant strength magnetic field. Stretching sheet solutions with or without injection are presented. Effects of physical parameters on the solutions are depicted.

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