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Laminar boundary layers on rotating axisymmetric surfaces with suction or injection

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Abstract

Steady laminar boundary layer flow and heat transfer over rotating axisymmetric bodies with uniform suction or injection have been studied theoretically. Upon introducing suitable new variables, the governing boundary layer equations for an isothermal body are first reduced to a set of coupled nonlinear partial differential equations, simplifying the numerical solution procedure. By using the difference-differential method, the partial differential equations are reduced to ordinary differential ones. The solutions of the resulting differential equestions have been expressed in the form of integral equations, and numerical calculations were performed solving the integral equations by iterative quadratures. As illustrations, the cases of rotating discs and other axisymmetric surfaces are considered. The effects of suction on the velocity and temperature profiles, as well as on the local skin friction coefficient and the local Nusselt number, are discussed. Also the effect of the Prandtl number on the local Nusselt number for an impermeable surface is determined. The agreement of the results obtained by the present method with available results is found to be very good.

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Abbreviations

A :

constant, equation (6)

C fx , Cfz :

local skin friction coefficients, equation (30)

f, g :

reduced stream functions, equation (7)

h :

uniform step size

E, F, G, H :

functions, equations (23–26)

k :

thermal conductivity

m :

exponent (constant), equation (6)

Nu:

local Nusselt number

Pr:

Prandtl number

q :

local heat flux

r :

function representing a body shape

P, Q, R :

functions, equations (27–29)

Re:

local Reynolds number

s :

suction or injection parameter, equation (10)

T :

temperature

u :

velocity component inx direction

v :

velocity component iny direction

v 0 :

suction velocity

w :

velocity component inz direction

x :

coordinate along the generating line

x*:

transformed independent variable

y :

coordinate normal to the body surface

z :

transversal coordinate

η :

transformed variable, equation (7c)

ϑ :

dimensionless temperature, equation (7b)

μ :

dynamic viscosity

ν :

kinematic viscosity

τ :

local skin friction

ρ :

density

ψ :

stream function

ω :

angular velocity

w :

wall condition

∞:

ambient condition

′:

differentiation with respect toη

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Iwate University, 020, Morioka, Japan

    T. Watanabe

  2. Faculty of Mathematics, University of Cluj, R-3400, Cluj CP 253, Romania

    I. Pop

Authors
  1. T. Watanabe
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  2. I. Pop
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Watanabe, T., Pop, I. Laminar boundary layers on rotating axisymmetric surfaces with suction or injection. Appl. Sci. Res. 52, 101–114 (1994). https://doi.org/10.1007/BF00868053

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  • DOI: https://doi.org/10.1007/BF00868053

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