ORIGINAL A fin design employing an inverse approach using simplex search method Ranjan Das • Ashis Mallick • K. T. Ooi Received: 25 August 2012 / Accepted: 18 March 2013 / Published online: 30 March 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract This paper is aimed at estimating unknown parameters in a rectangular fin satisfying a predefined temperature. The differential transformation along with simplex method is used. The study has been done for dif- ferent initial guess, random errors and measurement points. It is observed that, there is unique value of the convection- conduction parameter, but different conductivity and radi- ative parameters exist which will be useful in adjusting the parameters amongst various alternatives. List of symbols A c Cross sectional area of the fin (m 2 ) a Integral constant representing the fin tip temperature b Length of the fin (m) C Variable thermal conductivity parameter (=kT b ) C e Estimated value of C calculated from the inverse method R Radiative parameter ¼ erT 3 b Pb 2 k a A c   R e Estimated value of R calculated from the inverse method e Error in calculating the integral constant e r Random measurement error F Objective function h Convective heat transfer coefficient (W/m 2 K) k Thermal conductivity (W/m K) N Convection-conduction parameter ¼ ffiffiffiffiffiffiffi hPb 2 k a A c q   n Set containing the unknowns to be estimated in the inverse method P Perimeter of the fin (m) Q Heat transfer rate (W) T Temperature (K) t Thickness of the fin (m) w Width of the fin (m) X Non-dimensional location along the fin length (=x/b) x Distance measured from the fin surface (m) Subscripts a Ambient condition b Fin base e Estimated values Superscripts * Exact value Greek symbols v Expansion coefficient e Surface emissivity c Contraction coefficient g Fin efficiency ¼ Q Q ideal   k Variable thermal conductivity coefficient (K -1 ) h Non-dimensional temperature ¼ T T b   q Reflection coefficient R. Das (&) School of Mechanical, Materials and Energy Engineering, Indian Institute of Technology Ropar, Nangal Road, Rupnagar 140001, Punjab, India e-mail: ranjandas81@gmail.com; ranjandas@iitrpr.ac.in; ranjandas@gmail.com A. Mallick Department of Mechanical Engineering, Tezpur University, Naapam 784 028, India e-mail: 123.ashis@gmail.com K. T. Ooi School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50-Nanyang Avenue, Singapore 639 798, Singapore e-mail: mktooi@ntu.edu.sg 123 Heat Mass Transfer (2013) 49:1029–1038 DOI 10.1007/s00231-013-1146-7