Generalized Crane flow induced by continuous surfaces stretching with arbitrary velocities
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- Weidman, P.D. & Magyari, E. Acta Mech (2010) 209: 353. doi:10.1007/s00707-009-0186-z
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The boundary-layer flow induced by a permeable sheet stretching with general polynomial velocity distribution is considered. This generalizes the work of Kumaran and Ramanaiah (Acta Mech. 116: 229–233, 1996) who were the first to observe that a Crane-type solution exists for wall motion composed of arbitrary linear and quadratic stretching terms, as long as an appropriate lateral transpiration is applied. We solve explicitly the problem to an arbitrarily high degree of the polynomial stretching. This motivates the second part of our study which provides explicit boundary-layer solutions for arbitrary wall stretching, with suitable transpiration. These solutions describe generalized Crane flows whose reciprocal (dimensionless) thicknesses always coincide with the negative of their (dimensionless) entrainment velocities. The associated heat transfer problem is solved explicitly for arbitrary stretching when an appropriate surface temperature distribution is prescribed.