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Muhammad ASHRAF Robina YASMEENand Masud AHMAD


The characteristics of radiative mixed convection boundary layer flow generated close to the inner walls of tightly coiled curved pipe for full range of Richardson number λ is investigated. In order to find numerical solutions the governing coupled, nonlinear partial differential equations are transformed into convenient form for integration by using Primitive Variable Formulation. From this transformation the terms highest powers of Dean Number (D = δ1/ 2 Re) are retained into boundary layer form and then solved numerically by using Finite Difference Method. Expressions for the axial and transverse components of skin friction, heat transfer coefficient and flux thicknesses for various values of Richardson Number λ, angle α , curvature of the pipe (tightly coiled pipe in which    0<δ<1), Plank Number Rd and Prandtl Number Pr are obtained and given graphically.

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ASHRAF, Muhammad; YASMEENAND, Robina; AHMAD, Masud. THERMAL RADIATION MIXED CONVECTION BOUNDARY LAYER FLOW IN TIGHTLY COILED CURVED PIPE FOR LARGE RICHARDSON NUMBER. Thermal Science, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <>. Date accessed: 14 dec. 2017. doi:
Received 2017-03-03
Accepted 2017-03-13
Published 2017-03-13


[1] Cumming, H. G., The Secondary Flow in Curved Pipes, Report No. 2880, Aeronautical Research Council, London, Great Britain, 1952
[2] Bootorff, M. R., Rogers, K. W., Theoretical And Experimental Investigation of Boundary Layer Control in Low-Density Nozzles by Wall Suction and Cooling, NASA Technical Memorandum X-53008, University of Southern California, Alabama, 1964
[3] Srivastava, R. S., Laxman, D., Heat Transfer Effects for a Laminar Flow in a Curved Annulus, F. C. Auluck, F. N. A, 5 (1972), 8, pp. 758-773
[4] Yao, L. S., Entry Flow in Heated Tubes, Report No. 2111, Defense Advanced Research Projects Agency, 1977
[5] Stewartson, K., et al., A Boundary Layer Collision in a Curved Duct, Q. J. Mech. appl. Math.,33 (1980), 1, pp. 59-75
[6] Berger, S. A., et al., Flow In Curved Pipes, Ann. Rev. Fluid Mech., 15 (1983), pp.461-512
[7] Narasimha, A., et al., Analysis of Heat Transfer Enhancement in Coiled Tube Heat Exchangers, Heat and Mass Transfer, 44 (2001), pp. 3189-3199
[8] Paisran, N., Somchai, W., A Review of Flow and Heat Transfer Characteristics in Curved Tubes, Renewable and Sustainable Energy Reviews, 10 (2006), pp. 463-490
[9] Petrakis, M. A., et al., Steady Flow in a Curved Pipe with Circular Cross-Section, The Open Fuels and Energy Science Journals, 2 (2009), pp. 20-26
[10] Castiglia, F., et al., Modeling Flow and Heat Transfer in Helically Coiled Pipes, CIRTEN- UNIPA RL- 1205, 2010
[11] Chauhan, D. S., Kumar, V., Radiation Effects on Mixed Convection Flow and Viscous Heating in a Vertical Channel Partially Filled With a Porous Medium, Tamkang J.Science and Engineering, 14 (2011), 2, pp. 97-106
[12] Mahmoodi, M., Mixed Convection Inside Nano-Fluid Filled Rectangular Enclosures with Moving Bottom Wall, Thermal Sciences, 15 (2011), 3, pp. 889-903
[13] Elazym, M. A., et al., Computational Analysis for The Effect of The Taper Angle and Helical Pitch on The Heat Transfer Characteristics of The Helical Cone Coils, The Archive Of Mechanical Engineering, (2012), 3, pp. 361-375
[14] Poplay, V., et al., Analysis of Laminar Boundary Layer Flow Along a Stretching Cylinder in the Presence of Thermal Radiation, WSEAS Trans. Fluid Mech., 8 (2013), 4, pp. 159-164