@inproceedings{scholars559,
           pages = {63--72},
         journal = {Proceedings of the ASME Summer Heat Transfer Conference 2009, HT2009},
            year = {2009},
           title = {Effects of mass transfer and free-convection currents on the flow near a moving vertical plate with ramped wall temperature},
         address = {San Francisco, CA},
             doi = {10.1115/HT2009-88045},
            note = {cited By 8; Conference of 2009 ASME Summer Heat Transfer Conference, HT2009 ; Conference Date: 19 July 2009 Through 23 July 2009; Conference Code:80429},
          volume = {2},
        keywords = {Buoyancy forces; Concentration fields; Constant temperature; Convection currents; Coupled boundary conditions; Coupled heat and mass transfer; Critical analysis; Density gradients; Diffusional mass transfer; Enhancing effect; Exact analytical solutions; Free convection; Free convection flows; Free convection heat transfer; Free convections; Governing equations; Heat and mass transfer; Laplace transform techniques; Limiting case; Mass flux; Plate temperature; Schmidt numbers; Surface temperatures; Temperature boundary; Thermal buoyancy; Thermal buoyancy force; Velocity field; Vertical plate; Wall temperatures, Boundary conditions; Buoyancy; Friction; Heat exchangers; Heat transfer; Laplace transforms; Natural convection; Scandium; Skin friction; Tribology, Mass transfer},
             url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-77952967680&doi=10.1115\%2fHT2009-88045&partnerID=40&md5=0e31fc86321f09d52266f786b3885f4f},
        abstract = {A theoretical analysis to the problem of free convection flow induced by an infinite moving vertical plate subject to a ramped surface temperature with simultaneous mass transfer to or from the surface is presented. The plate temperature increases linearly over a specified period of time until it reaches a constant value. Diffusional mass transfer occurs at the surface contributing to the density gradient in the boundary layer. An exact analytical solution to the governing equations for flow, temperature and concentration with coupled boundary conditions in the dimensionless form have been developed using the Laplace transform technique. Heat and mass transfer at the plate are assumed to be purely diffusive in nature. The cases of impulsive start and uniformly accelerating start of the plate are considered and solutions for the flow, temperature and concentration fields are derived. The effects of different system parameters have been studied in terms of relevant dimensionless groups such as Grashof number (Gr ), Prandtl number (Pr), Schmidt number (Sc), time (t) and the mass to thermal buoyancy ratio (N). The possible cases of the last parameter, namely N = O (the buoyancy force is due to thermal diffusion only), N {\ensuremath{>}} 0 (the mass buoyancy force acts in the same direction of thermal buoyancy force) and N {\ensuremath{<}} 0 (the mass buoyancy force acts in the opposite direction of thermal buoyancy force) are investigated and their effects on the velocity field and skin-friction are explicitly determined. The ramped temperature boundary condition predictably has an enhancing effect on the skin friction. The mass flux to the plate influences the velocity and hence the skin friction. A critical analysis of the coupled heat and mass transfer phenomena is provided. The free convection near a ramped temperature plate has also been compared with the flow near a plate with constant temperature as a limiting case. Copyright {\^A}{\copyright} 2009 by ASME.},
          author = {Narahari, M. and Dutta, B. K.},
            isbn = {9780791843574}
}