M. Dada et al. Nano Biomedicine And Engineering 2009, 2, 10-18 nanobe.org 10 Nano Biomed Eng ISSN 2150-5578 http:// nanobe.org Investigation of Nano-keyhole Cooling Evolution using Boubaker Polynomials Expansion Scheme (BPES) M. Dada * , Olufemi Folorunsho Moses ++ , O. B. Awojoyogbe * , K. Boubaker + and K. Isah*, * Department of Physics, Federal University of Technology, Minna, Niger-State , Nigeria . + ESSTT/ 63 Rue Sidi Jabeur 5100 Mahdia, Tunisia. ++ P.O. Box 9352, GDP. Marina Lagos-State, Nigeria. *Corresponding authors. Email: boubaker_karem@yahoo.com Abstract This study proposes an analytical expression for temperature evolution inside a nano-keyhole modeled device. Several assumptions have been taken into account. The validity of the model has been tested through compatibility with experiment and Newtonian cooling laws. Keywords: Keyhole, Heat equation, Newtonian cooling, Boubaker Polynomials. Citation: M. Dada, et al. Investigation of Nano-Keyhole Cooling Evolution using Boubaker Polynomials Expansion Scheme (BPES). Nano Biomed Eng. 2010, 2(1), 10-18. 1. Introduction: In recent years, numerical modeling has become a realistic method in many applied physics fields [1-5] as for the prediction of weld geometries and time dependent evolution. A schematic illustration of the geometrical features of the keyhole weld is provided in Fig. (1). In this model tree main assumption are taken into account:  The keyhole wall temperature corresponds to the metal boiling point.  The exciting beam thermal and optical profiles are coherent..  The absorption coefficient is constant on keyhole wall. OPEN ACCESS Article