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An improved boundary layer scaling with ramp heating on a sloping plate

By Suvash C. Saha and M.M.K. Khan


A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the boundary layer flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the startup had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same

Topics: 010300 NUMERICAL AND COMPUTATIONAL MATHEMATICS, 091307 Numerical Modelling and Mechanical Characterisation, Natural convection, Ramp heating, Boundary layer, Unsteady flow, Prandtl number
Publisher: Elsevier
Year: 2012
DOI identifier: 10.1016/j.ijheatmasstransfer.2012.01.038
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