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

- Received:

DOI: 10.1007/BF02837706

- Cite this article as:
- 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 in

*x*and*y*directions, respectively- c
ratio of velocity gradients,

*b/a*- Cf
_{x}, Cf_{y} skin-friction coefficients along

*x*and*y*directions, respectively- f, s
dimenionless stream functions such that

*f′*=*u/u*_{e}and*s′*=*v/v*_{e}- f
_{w} mass transfer parameter,-

*(ρw)*_{w}/(ρ_{e}μ_{e}a)^{1/2}- g
dimensionless enthalpy,

*h/h*_{e}- g
_{w} cooling parameter for the wall,

*h*_{w}/h_{e}- h
enthalpy

- Pr
Prandtl number

- q
heat transfer rate

- Re
_{x} local Reynolds number,

*u*_{c}x/v_{e}- St
Stanton number

- T
temperature

- u, v, w
velocity components along

*x, y, z*directions, respectively- x, y, z
principal, transverse and normal directions, respectively

- η
similarity variable, (

*ρ*_{e}/*μ*_{e})^{1/2}∫_{0}^{z}(*ρ*/*ρ*_{e})*dz*- μ
coefficient of viscosity

- ν
kinematic viscosity

- ρ
density

- τ
_{x}, τ_{y} dimensional shear stress functions

- ω
exponent in the power-law variation of viscosity

### Superscript

- ′ (prime)
differentiation with respect to

*η*

### Subscripts

- e
condition at the edge of the boundary layer

- w
condition at the surface

*z=η*=0.