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Unsteady forced convection laminar boundary layer flow over a moving longitudinal cylinder

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Summary

The unsteady nonsimilar forced convection flow over a longitudinal cylinder, which is moving in the same or in the opposite direction to the free stream, has been investigated. The unsteadiness is due to the free stream velocity, cylinder velocity, surface temperature of the cylinder and the mass transfer, and nonsimilarity is due to the transverse curvature. The partial differential equations, governing the flow, have been solved numerically, using an implicit finite-difference scheme in combination with a quasilinearization technique. The results show that both, skin friction and heat-transfer, are appreciably affected by the free stream velocity distributions and by the cylinder velocity. Also, skin friction as well as heat-transfer are found to increase as the transverse curvature or the suction increases, but the effect of injection is just the opposite. The heat-transfer is significantly affected by the viscous dissipation and variation of surface temperature with time. It is observed that results of this problem are crucially dependent on the parameter α, which is the ratio of the velocity of the cylinder to the velocity of the free stream. In particular, it is found that solutions for the upstream moving cylinder exist only for a certain range of this parameter (α), and they are nonunique in a small range of α too.

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Abbreviations

A :

constant

C f :

skin friction coefficient, Eq. (21)

Nu x :

local Nusselt number (heat-transfer coefficient), Eq. (22)

Ec:

Eckert number (dissipation parameter)

c p :

specific heat at constant pressure

k :

thermal conductivity

q :

heat transfer rate per unit area

F, G :

dimensionless velocity and normalized temperature respectively

T :

temperature of the fluid

T w :

surface temperature of the cylinder

μ, ν, ϱ:

coefficient of viscosity, kinematic viscosity and density respectively

Pr:

Prandtl number (Pr=μc p /k)

r, x :

radial and axial co-ordinates

Re x :

local Reynolds number

t *,t :

dimensionless and dimensional times respectively

u, v :

velocity components of the fluid alongx- andr-directions respectively

U :

free stream velocity

η, ξ:

transformed coordinates

τ:

shear stress

R, ϕ:

functions oft *

\(\bar R\) :

radius of the cylinder

ψ,f :

dimensional and dimensionless stream functions

ε, ε1 :

constants

u w (t):

time-dependent cylinder velocity

α:

ratio of the velocity of the cylinder to the velocity of the free stream

F w ′,G w ′:

skin friction and heat-transfer parameter respectively

′:

derivative with respect to η

e, w :

conditions at the edge of the boundary layer and on the surface of the cylinder respectively

w 0 :

conditions on the surface of the cylinder att *=0

i :

initial condition

r, t, t *,x, ξ:

derivatives with respect tor, t, t *,x, ξ respectively

∞:

free stream value

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Author notes

  1. G. Nath

    Present address: Department of Mathematics, Indian Institute of Science, 560012, Bangalore, India

  2. A. T. Eswara

    Present address: Department of Mathematics, Malnad College of Engineering, 573201, Hassan, India

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, 560012, Bangalore, India

    A. T. Eswara

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  1. A. T. Eswara
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  2. G. Nath
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Eswara, A.T., Nath, G. Unsteady forced convection laminar boundary layer flow over a moving longitudinal cylinder. Acta Mechanica 93, 13–28 (1992). https://doi.org/10.1007/BF01182570

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