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Research Papers: Natural and Mixed Convection

# Mixed Convection Along a Semi-Infinite Vertical Flat Plate With Uniform Surface Heat Flux

[+] Author and Article Information
S. Ghosh Moulic

Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, Kharagpur 721302, India

L. S. Yao

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106

J. Heat Transfer 131(2), 022502 (Jan 05, 2009) (8 pages) doi:10.1115/1.2995725 History: Received March 19, 2008; Revised July 26, 2008; Published January 05, 2009

## Abstract

Mixed-convection boundary-layer flow over a heated semi-infinite vertical flat plate with uniform surface heat flux, placed in a uniform isothermal upward freestream, has been investigated. Near the leading edge, the effect of natural convection can be treated as a small perturbation term. The effects of natural convection are accumulative and increase downstream. In the second region, downstream of the leading-edge region, natural convection eventually becomes as important as forced convection. The boundary-layer equations have been solved by an adaptive finite-difference marching technique. The numerical solution indicates that the series solution of the leading-edge region is included in that of the second region. This property is shared by many developing flows. However, the series solutions of local similarity or local nonsimilarity are only valid for very small distances from the leading edge. Numerical results for the local skin-friction factor, wall temperature, and local Nusselt number are presented for $Pr=1$ for a wide range of $Grx*∕Rex5∕2$, where $Grx*$ is a local modified Grashof number and $Rex$ is a local Reynolds number. The results indicate that $cfxRex1∕2$ and $NuxRex–1∕2$ increase monotonically with distance from the leading edge, where $cfx$ is the local skin-friction factor and $Nux$ is the local Nusselt number, and approach the free-convection limit at large values of $Grx*∕Rex5∕2$, although the velocity distribution differs from the velocity distribution in a free-convection boundary layer.

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## Figures

Figure 1

Coordinates

Figure 2

Axial velocity profiles at selected locations

Figure 3

Temperature distribution at selected locations

Figure 4

Axial variation in cfx(Rex∕2)1∕2

Figure 5

Axial variation in wall temperature (a) on forced-convection scale and (b) on free-convection scale

Figure 6

Axial variation in Nux(2∕Rex)1∕2

## Errata

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