TY - JOUR
T1 - Mixed convection above a rotating disk
AU - Arrieta-Sanagustín, J.
AU - Blyth, M.G.
PY - 2013/8/1
Y1 - 2013/8/1
N2 - Mixed convection above a horizontal disk rotating in a semi-infinite fluid is examined when the disk is heated so that its temperature varies quadratically with distance away from its centre. Steady similarity solutions are presented for a range of values of the two dimensionless parameters, a Prandtl number and a Grashof number. The results are corroborated by asymptotic analyses undertaken in the limits of small and large Prandtl number. For finite Prandtl number, the existence of multiple solutions at fixed Grashof number is revealed. The similarity structure for steady solutions fails beyond a critical Grashof number and this is interpreted in terms of a finite-time singularity of the unsteady form of the governing equations.
AB - Mixed convection above a horizontal disk rotating in a semi-infinite fluid is examined when the disk is heated so that its temperature varies quadratically with distance away from its centre. Steady similarity solutions are presented for a range of values of the two dimensionless parameters, a Prandtl number and a Grashof number. The results are corroborated by asymptotic analyses undertaken in the limits of small and large Prandtl number. For finite Prandtl number, the existence of multiple solutions at fixed Grashof number is revealed. The similarity structure for steady solutions fails beyond a critical Grashof number and this is interpreted in terms of a finite-time singularity of the unsteady form of the governing equations.
UR - http://www.scopus.com/inward/record.url?scp=84881447872&partnerID=8YFLogxK
U2 - 10.1093/qjmam/hbt006
DO - 10.1093/qjmam/hbt006
M3 - Article
AN - SCOPUS:84881447872
SN - 0033-5614
VL - 66
SP - 317
EP - 331
JO - Quarterly Journal of Mechanics and Applied Mathematics
JF - Quarterly Journal of Mechanics and Applied Mathematics
IS - 3
ER -