Thermal boundary layers over a shrinking sheet: an analytical solution
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In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word.
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- 1.Altan, T., Oh, S., Gegel, H.: Metal Forming Fundamentals and Applications. American Society of Metals, Metals Park (1979)Google Scholar
- 2.Fisher E.G.: Extrusion of Plastics. Wiley, New York (1976)Google Scholar
- 3.Tadmor, Z., Klei, I.: Engineering Principles of Plasticating Extrusion. Polymer Science and Engineering Series. Van Nostrand Reinhold, New York (1970)Google Scholar
- 32.White F.M.: Viscous Fluid Flow, 2nd edn. McGraw-Hill, New York (1991)Google Scholar
- 33.Wolfram S.: Mathematica—A System for Doing Mathematics by Computer, 2nd edn. Addison-Wesley, New York (1993)Google Scholar