Convection-radiation from a continuously moving fin of variable thermal conductivity

Abstract The homotopy analysis method (HAM) is applied to generate an analytic solution for heat transfer in a moving fin of variable thermal conductivity which is losing heat by simultaneous convection and radiation to its surroundings. The accuracy of the analytic solution is validated by comparing it with the direct numerical solution of the problem. The analytic solution is found to be accurate to at least three places of decimal for a wide range of values of the parameters that are commonly encountered in thermal processing application. Graphs displaying the results are interpreted in physical terms.

[1]  M. Char,et al.  Conjugate forced convection heat transfer from a continuous, moving flat sheet , 1990 .

[2]  J. P. Hartnett,et al.  Advances in Heat Transfer , 2003 .

[3]  Mukund V. Karwe,et al.  Numerical simulation of thermal transport associated with a continuously moving flat sheet in materials processing , 1991 .

[4]  Mukund V. Karwe,et al.  Fluid Flow and Mixed Convection Transport From a Moving Plate in Rolling and Extrusion Processes , 1988 .

[5]  Y. Jaluria.  TRANSPORT FROM CONTINUOUSLY MOVING MATERIALS UNDERGOING THERMAL PROCESSING , 1992 .

[6]  Ephraim M Sparrow,et al.  Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid , 2005 .

[7]  Guy Jacobsohn,et al.  A discrete Taylor series method for the solution of two-point boundary-value problems , 2001, J. Frankl. Inst..

[8]  H. Keller.  Numerical Methods for Two-Point Boundary-Value Problems , 1993 .

[9]  J. Biazar,et al.  Variational iteration method for solving Fokker-Planck equation , 2010, J. Frankl. Inst..

[10]  R. Cortell.  Flow and heat transfer in a moving fluid over a moving flat surface , 2007 .

[11]  F. Méndez,et al.  Heat Transfer Analysis on a Moving Flat Sheet Emerging into Quiescent Fluid , 2002 .

[12]  Peng Wu,et al.  An efficient method for solving Emden-Fowler equations , 2009, J. Frankl. Inst..

[13]  Julian Szekely,et al.  Fluid flow phenomena in metals processing , 1979 .

[14]  Aydin Kurnaz,et al.  The solution of the Bagley-Torvik equation with the generalized Taylor collocation method , 2010, J. Frankl. Inst..

[15]  Anjan Biswas,et al.  Application of the G′/G-expansion method for nonlinear diffusion equations with nonlinear source , 2010, J. Frankl. Inst..

[16]  J. Tsai,et al.  Cooling of a continuous moving sheet of finite thickness in the presence of natural convection , 1990 .

[17]  Y. Jaluria,et al.  Temperature distribution in a moving material subjected to surface energy transfer , 1983 .

[18]  Yogesh Jaluria,et al.  Thermal Processing of Materials: From Basic Research to Engineering , 2003 .

[19]  Steven R Schmid Kalpakjian,et al.  Manufacturing Engineering and Technology , 1989 .

[20]  Chien-Hsin Chen,et al.  Convection cooling of a continuously moving surface in manufacturing processes , 2003 .

[21]  Y. Jaluria,et al.  Thermal transport from a heated moving surface , 1986 .

[22]  S. Liao.  Notes on the homotopy analysis method: Some definitions and theorems , 2009 .

[23]  S. R. Choudhury,et al.  Analytical solution for the transient temperature distribution in a moving rod or plate of finite length with surface heat transfer , 1994 .

[24]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[25]  Taylan Altan,et al.  Metal Forming : Fundamentals and Applications , 1983 .

[26]  E. G. Fisher,et al.  Extrusion of plastics , 1976 .

[27]  Antonio Marquina,et al.  Diffusion front capturing schemes for a class of Fokker-Planck equations: Application to the relativistic heat equation , 2010, J. Comput. Phys..