Applied Scientific Research

, 10:173

Estimation of the critical viscous sublayer in heat transfer problems

Authors

  • Ajit Kumar Ray
    • Department of Aeronautical Engineering Indian Institute of Science
Article

DOI: 10.1007/BF00411910

Cite this article as:
Ray, A.K. Appl. sci. Res. (1961) 10: 173. doi:10.1007/BF00411910

Summary

Imagining a disturbance made on a compressible boundary layer with the help of a heat source, the critical viscous sublayer, through which the skin friction at any point on a surface is connected with the heat transferred from a heated element embedded in it, has been estimated. Under similar conditions of external flow (Ray1)) the ratio of the critical viscous sublayer to the undisturbed boundary layer thickness is about one-tenth in the laminar case and one hundredth in the turbulent case. These results are similar to those (cf.1)) found in shock wave boundary layer interaction problems.

Symbols

cf

skin-friction coefficient

Cp

specific heat at constant pressure (=0.24 BTU/lb °F)

L

streamwise dimension of the heated element

Qw

total heat flux per unit time from the element per unit cross-stream width

qw

heat flux per unit time per unit area of the element

Re

Reynold's number based on length

T

temperature

t

time

u

velocity in the x-direction

U

free stream value of u

x

downstream coordinate; origin at the leading edge of the flat plate

y

coordinate normal to the plate

δT

thickness of the thermal boundary layer (critical viscous sublayer)

δ

thickness of the velocity boundary layer

λ

thermal conductivity (=4.16×10−4 BTU/ft s °F)

μ

coefficient of viscosity (=0.1224×10−6 lb/ft s), kinematic viscosity

ξ

x-coordinate of the up-stream edge of the heated element (up-stream distance of the disturbance)

ρ

density (=0.06625 lb/ft3)

τ

sheering stress

Subscripts

1

values at the outer edge of the boundary layer

w

values at the wall

Copyright information

© Martinus Nijhoff 1961