Separation in the mixed convection boundary-layer radial flow over a constant temperature horizontal plate

The boundary-layer flow of a horizontal current emerging radially from a cylindrical vertical surface of radius r(0) with a constant velocity over a heated horizontal wall at constant temperature is analyzed. The boundary-layer equations are made dimensionless with a radial characteristic length in which natural and forced convection become of the same order of magnitude, so that the Prandtl (Pr) number and Gr(2)/Re-5 are the only nondimensional parameters governing the problem, where Gr and Re are the Grashof and Reynolds numbers based on r(0), respectively. A similarity solution valid at the leading edge of the boundary-layer flow is obtained. It contains, as the first order correction to Blasius' thermal boundary layer solution, the effect of buoyancy, and as the second order correction the effect of the radial divergence of the flow. This solution is used to start the numerical integration of the equations to provide a criterion for when separation occurs. It is found that separation, based on the boundary layer model, occurs for Gr < B(Pr)Re-5/2, where the Prandtl's number function B is characterized numerically and found to be almost constant. This separation location law is compared with experimental results for air flowing over a heated horizontal plate at constant temperature, finding a qualitative good agreement. (C) 2014 AIP Publishing LLC.