Abstract
The problem of steady laminar forced convection boundary layer flow of an incompressible viscous fluid over a moving thin needle with variable heat flux is considered. The governing boundary layer equations are first transformed into non-dimensional forms. These equations are then transformed into similarity equations using the similarity variables, which are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for a blunt-nosed needle (m=0). Numerical computations are carried out for various values of the dimensionless parameters of the problem, which include the Prandtl number Pr and the parameter a representing the needle size. It has been found that the wall temperature is significantly influenced by both parameter a and Prandtl number Pr. However, the Prandtl number has no effect on the flow characteristics due to the decoupled boundary layer equations.
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References
Abraham JP, Sparrow EM (2005) Friction drag resulting from the simultaneous imposed motions of a freestream and its bounding surface. Int J Heat Fluid Flow 26:289–295
Agarwal M, Chhabra RP, Eswaran V (2002) Laminar momentum and thermal boundary layers of power-law fluids over a slender cylinder. Chem Engng Sci 57:1331–1341
Ahmad S, Arifin NM, Nazar R, Pop I (2008a) Mixed convection boundary layer flow along vertical moving thin needles with variable heat flux. Heat Mass Transf 44:473–479
Ahmad S, Arifin NM, Nazar R, Pop I (2008b) Mixed convection boundary layer flow along vertical thin needles: assisting and opposing flows. Int Comm Heat Mass Transf 35:157–162
Chen JLS (1987) Mixed convection flow about slender bodies of revolution. J Heat Transf 109:1033–1036
Chen JLS, Smith TN (1978) Forced convection heat transfer from nonisothermal thin needles. J Heat Transf 100:358–362
Cebeci T, Bradshaw P (1988) Physical and computational aspects of convective heat transfer. Springer, New York
Gorla RSR (1979) Unsteady viscous flow in the vicinity of an axisymmetric stagnation point on a circular cylinder. Int J Engng Sci 17:87–93
Gorla RSR (1990) Boundary layer flow of a micropolar fluid in the vicinity of an axisymmetric stagnation point on a cylinder. Int J Engng Sci 28:145–152
Gorla RSR (1993) Mixed convection in an axisymmetric stagnation flow on a vertical cylinder. Acta Mech 99:113–123
Lee LL (1967) Boundary layer over a thin needle. Phys Fluids 10:820–822
Lee SL, Chen TS, Armaly BF (1987) Mixed convection along vertical cylinders and needles with uniform surface heat flux. J Heat Transf 109:711–716
Narain JP, Uberoi MS (1972) Combined forced and free-convection heat transfer from vertical thin needles in a uniform stream. Phys Fluids 15:1879–1882
Narain JP, Uberoi MS (1973) Combined forced and free-convection over thin needles. Int J Heat Mass Transf 16:1505–1511
Sadeghy K, Sharifi M (2004) Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate. Int J Non-Linear Mech 39:1265–1273
Sparrow EM, Abraham JP (2005) Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid. Int J Heat Mass Transf 48:3047–3056
Wang CY (1990) Mixed convection on a vertical needle with heated tip. Phys Fluids A 2:622–625
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Ahmad, S., Arifin, N.M., Nazar, R., Pop, I. (2009). Mathematical modeling of boundary layer flow over a moving thin needle with variable heat flux. In: Mastorakis, N., Sakellaris, J. (eds) Advances in Numerical Methods. Lecture Notes in Electrical Engineering, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76483-2_4
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DOI: https://doi.org/10.1007/978-0-387-76483-2_4
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