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Momentum and heat transfer of a special case of the unsteady stagnation-point flow

Applied Mathematics and Mechanics(English Edition) 2020年第1期41卷 51-82页

作者： T.G.FANG F.J.WANG Mechanical and Aerospace Engineering Department North Carolina State University

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)*** boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux *** wall temperature and heat flux have power dependence on both time and spatial *** solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling *** parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power *** is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer *** heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special *** wall heat flux and temperature profiles show very complicated variation *** wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary *** relationship between the number of poles in the wall heat flux and the number of zero-crossing points is *** difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is *** given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.

关键词： unsteady stagnation point flow Navier-Stokes(NS)equations analytical solution heat transfer

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