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Oblique stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation

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Abstract

An analysis is made of steady two-dimensional oblique stagnation-point flow and radiative heat transfer of an incompressible viscous fluid towards a shrinking sheet which is shrunk in its own plane with a velocity proportional to the distance from a fixed point. Here the axis of the stagnation flow and that of the shrinking sheet are not aligned. A similarity transformation reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations and are solved numerically using a shooting technique. The analysis of the results obtained shows that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity. The effect of non-alignment for the wall shear stress and the horizontal velocity components are discussed. Streamline patterns are also shown for shrinking at the sheet with aligned and non-aligned cases. It is found that the temperature at a point in the fluid decreases with increase in effective Prandtl number (Pr eff ). The results pertaining to the present study indicate that as Pr eff increases, the rate of heat transfer also increases. The reported results are in good agreement with the available published work in the literature.

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Acknowledgements

The authors thank the reviewers for their time and interest as well as constructive suggestions and comments for improving the paper. The work of one of the authors (T.R.M) is supported under SAP (DRS PHASE II) program of UGC, New Delhi, India. One of the authors (A.S.G) acknowledges the financial support of Indian National Science Academy for carrying out this work.

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Correspondence to Samir Kumar Nandy.

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Mahapatra, T.R., Nandy, S.K. & Gupta, A.S. Oblique stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation. Meccanica 47, 1325–1335 (2012). https://doi.org/10.1007/s11012-011-9516-z

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  • DOI: https://doi.org/10.1007/s11012-011-9516-z

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