Acta Mechanica

, Volume 138, Issue 1–2, pp 1–11 | Cite as

Forced convection over a continuous sheet with suction or injection moving in a flowing fluid

  • C. -H. Chen
Original Papers
Received:

Summary

The analysis of forced convection flow and heat transfer about a flat sheet with suction or injection continuously moving in a quiescent or flowing fluid has been carried out. This kind of problem finds applications in a variety of manufacturing processes such as hot rolling, extrusion of plastic sheets, continuous casting, and cooling of a metallic plate in a cooling bath. The governing differential equations are reduced to nonlinear ordinary differential equations by similarity transformations. These equations are solved numerically based on a finite difference algorithm. Representative velocity and temperature profiles within the boundary layer are presented at selected values of free stream velocity and injection parameter. The friction factor and Nusselt number are illustrated for a wide range of governing parameters. For the same injection parameter, Prandtl number, and normalized velocity difference |Uw−U∞|, higher values of the Nusselt number and friction factor result fromUw>U∞ than fromUw<U∞. Also, an increase in the velocity ratioU∞/Uw results in an increase in the heat transfer rate, but a decrease in the friction factor. Furthermore, the heat transfer is enhanced due to increasing the values of the free stream velocity, the injection parameter, and Prandtl number; while it is reduced due to increasing the velocity difference.

Keywords

Heat Transfer Nusselt Number Prandtl Number Friction Factor Heat Transfer Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Cf

friction factor, τw/(ϱur2/2)

F

dimensionless stream function

Fw

injection parameter

h

local heat transfer coefficient

k

thermal conductivity

Nu

Nusselt number,hx/k

Pr

Prandtl number, ν/α

qw

wall heat flux

Re

Reynolds number,urx/ν

T

temperature

Tw

temperature at the fluid-sheet interface

T∞

free stream temperature

Uw

normalized velocity of the sheet,uw/ur

U∞

normalized free stream velocity,u∞/ur

u

fluid velocity component inx-direction

ur

reference velocity, Eq. (8)

uw

velocity of the continuous sheet

u∞

free stream velocity

v

fluid velocity component iny-direction

vw

fluid velocity component iny-direction at the fluid-sheet interface

x

streamwise coordinate

y

cross-stream coordinate

Greek symbols

α

thermal diffusivity

σ

boundary-layer thickness

η

dimensionless cross-stream coordinate

ι

dimensionless temperature

ν

kinematic viscosity

τw

wall shear stress

ψ

stream function

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Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • C. -H. Chen
    • 1
  1. 1.Department of Mechanical Design EngineeringNational Huwei Institute of TechnologyHuwei, YunlinTaiwan

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