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Research Papers: Jets, Wakes, and Impingment Cooling

# Axisymmetric Stagnation Flow and Heat Transfer of a Compressible Fluid Impinging on a Cylinder Moving Axially

[+] Author and Article Information
Asghar B. Rahimi

Professor
Faculty of Engineering,
P. O. Box No. 91775-1111,
e-mail: rahimiab@yahoo.com

Assistant Professor
Department of Mechanical Engineering,
Shahrood Branch,
Shahrood 3619633619, Iran.

Assistant Professor
Department of Mechanical Engineering,
Shahrood Branch,
Shahrood 3619633619, Iran

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 2, 2014; final manuscript received July 15, 2015; published online October 6, 2015. Assoc. Editor: William P. Klinzing.

J. Heat Transfer 138(2), 022201 (Oct 06, 2015) (9 pages) Paper No: HT-14-1106; doi: 10.1115/1.4031130 History: Received March 02, 2014; Revised July 15, 2015

## Abstract

The steady-state viscous flow and also heat transfer in the vicinity of an axisymmetric stagnation point on a cylinder moving axially with a constant velocity are investigated. Here, fluid with temperature-dependent density is considered. The impinging freestream is steady and with a constant strain rate (strength) $k¯$. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations. The general self-similar solution is obtained when the wall temperature of the cylinder or its wall heat flux is constant. All the solutions above are presented for Reynolds numbers, $Re=k¯a2/2υ$, ranging from 0.1 to 1000, low Mach number, selected values of compressibility factor, and different values of Prandtl numbers where $a$ is cylinder radius and $υ$ is kinematic viscosity of the fluid. Shear stress is presented as well. Axial movement of the cylinder does not have any effect on heat transfer but its increase increases the axial component of fluid velocity field and the shear stress.

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## Figures

Fig. 1

A schematic mechanism of the radially impinging flow production

Fig. 2

Schematic diagram of an axially moving cylinder

Fig. 3

Schematic diagram of inviscid flow on cylinder

Fig. 4

Variation of dimensionless axial movement function (H/V) in terms of η for Tw = 500 K, T∞ = 300 K, β = 0.0033, Re = 1, and selected values of Prandtl number

Fig. 5

Variations of dimensionless axial movement function (H/V) in terms of η for selected values of Pr for Re = 10, β = 0.0033, and γ = 100

Fig. 6

Variation of θ in terms of η at, Tw = 500 K, T∞ = 300 K, Re = 10.0, β = 0.0033, and for different values of Prandtl numbers

Fig. 7

Variations of dimensionless axial movement function (H/V) in terms of η for selected values of β for Re = 100, Pr = 1, and Tw = 500 K

Fig. 8

Variation of shear stress versus Reynolds number at Pr = 0.7, γ = 50, V  =  5 m/s for selected values of compressibility factor

Fig. 9

Variations of θ in terms of η at Pr = 1.0, Tw = 500 K, T∞ = 500 K, Re = 1.0, and for different values of compressibility factor

Fig. 10

Variations of θ in terms of η at γ = 10.0 and Pr = 0.7, Re = 10 for different values of compressibility factor

Fig. 11

Variation of shear stress against wall temperature at V  =  5 m/s and V  =  10 m/s, Pr = 0.7, β  =  0.0033, and for selected values of Reynolds numbers

Fig. 12

Variation of shear stress against γ for selected values of Reynolds number at V = 5 m/s and V = 10 m/s, Pr = 0.7, β = 0.0033, and for selected values of Reynolds number

Fig. 13

Variation of pressure function in terms of η at, Pr = 0.7, Tw = 500 K, T∞ = 300 K, β = 0.0033, and for different values of Reynolds numbers

Fig. 14

Variation of f in terms of η at Tw = 300 K, β = 0.0033, and Pr = 0.7 for different values of Reynolds numbers

Fig. 15

Variation of shear stress against Reynolds number at V = 5 m/s, Pr = 0.7, β = 0.0033, and for selected values of wall temperature

Fig. 16

Variations of dimensionless axial movement function (H/V) in terms of η for β = 0 and for selected values of Reynolds number

Fig. 17

The normalized stream function ψ̂ = ψ/0.5k¯a3 = 2f(η)(z/a) with, Re = 1, α = 0. Fluid is injected from the outer cylinder at η = 2 toward the inner cylinder.

Fig. 18

The normalized stream function ψ̂ = (ψ/0.5k¯a3) = 2f(η)(z/a)−α∫1ηH/Vdη with Re = 1. Fluid is injected from the outer cylinder at η = 2 toward the inner cylinder.

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