Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, Volume 87, Issue 5, pp 113–123

# Laminar compressible boundary layer flow at a three-dimensional stagnation point with vectored mass transfer

• M. Muthanna
• G. Nath
Article

DOI: 10.1007/BF02837706

Muthanna, M. & Nath, G. Proc. Indian Acad. Sci. (Math. Sci.) (1978) 87: 113. doi:10.1007/BF02837706

## Abstract

The effect of surface mass transfer velocities having normal, principal and transverse direction components (‘vectored’ suction and injection) on the steady, laminar, compressible boundary layer at a three-dimensional stagnation point has been investigated both for nodal and saddle points of attachment. The similarity solutions of the boundary layer equations were obtained numerically by the method of parametric differentiation. The principal and transverse direction surface mass transfer velocities significantly affect the skin friction (both in the principal and transverse directions) and the heat transfer. Also the inadequacy of assuming a linear viscosity-temperature relation at low-wall temperatures is shown.

### Keywords

Skin frictionheat transfervectored mass transfernoddle and saddle pointsvariable fluid properties: parametric differentiation

### List of Symbols

a, b

velocity gradients inx andy directions, respectively

c

Cfx, Cfy

skin-friction coefficients alongx andy directions, respectively

f, s

dimenionless stream functions such thatf′=u/ue ands′=v/ve

fw

mass transfer parameter,-(ρw)w/(ρeμea)1/2

g

dimensionless enthalpy,h/he

gw

cooling parameter for the wall,hw/he

h

enthalpy

Pr

Prandtl number

q

heat transfer rate

Rex

local Reynolds number,ucx/ve

St

Stanton number

T

temperature

u, v, w

velocity components alongx, y, z directions, respectively

x, y, z

principal, transverse and normal directions, respectively

η

similarity variable, (ρe/μe)1/20z (ρ/ρe)dz

μ

coefficient of viscosity

ν

kinematic viscosity

ρ

density

τx, τy

dimensional shear stress functions

ω

exponent in the power-law variation of viscosity

### Superscript

′ (prime)

differentiation with respect toη

### Subscripts

e

condition at the edge of the boundary layer

w

condition at the surfacez=η=0.