Investigation of Thermal Diffusivity–microhardness Correlation Extended to Surface-Nitrured Steel Using Boubaker Polynomials Expansion

Abstract

This study sums up the authors recent works1–6 on steel regarding non-destructive testing and evaluation achieved between 2000 and 2008. The main related items are the establishment of a polynomial correlation4 between the thermal diffusivity and the Vickers' hardness HV using the recently established Boubaker polynomial expansion. This correlation is undoubtedly an efficient guide to set an NDT protocol to investigate steel-strengthened surface performance. Special attention is given to carburized steel material,6 as the existence of any appropriated NDT photothermal technique is demonstrated2,5,6 to be unavoidably subjected to some restrictive conditions. The perspectives of the new features of this recent technique are discussed, with special concern with differently treated material like nitrured and nitrocarburized quenched steel.

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

“…The Boubaker polynomials expansion scheme (BPES) [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] is a resolution protocol which has been successfully applied to several applied-physics and mathematics problems. The BPES protocol ensures the validity of the related boundary conditions regardless of main equation features.…”

“…Several solutions have been proposed through the BPES in many fields such as numerical analysis [34][35][36][37], theoretical physics [38][39][40][41], mathematical algorithms [42], heat transfer [43], homodynamic [44,45], material characterization [46], fuzzy systems modeling [47][48][49][50], and biology [51,52].…”

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

“…where B 4k are the 4k-order Boubaker polynomials [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], r k are B 4k minimal positive roots, N 0 is a prefixed integer, and ξ k | k=1,...,N0 are unknown pondering real coefficients. This expression refers to the Boubaker polynomials expansion scheme (BPES) [29][30][31].…”

“…This expression refers to the Boubaker polynomials expansion scheme (BPES) [29][30][31]. This scheme is a resolution protocol which has been successfully applied to several applied-physics and mathematics problems.…”

“…Several solutions have been proposed through the BPES in many fields such as numerical analysis [28][29][30][31], theoretical physics [31][32][33][34], mathematical algorithms [35], heat transfer [36], homodynamic [37,38], material characterization [39], fuzzy systems modeling [40][41][42], and biology [43,44]. The main advantage of this formulation (9) is the verification of boundary conditions, expressed in (4), in advance to resolution process, along with affording controllable and easy-to-access first derivatives of E(η).…”