Latin American Applied Research 50(3): 229-234 (2020) 229 A TECHNIQUE TO ESTIMATE THE TRANSIENT COEFFICIENT OF HEAT TRANSFER BY CONVECTION G. UMBRICHT †§‡ , D. RUBIO † , R. ECHARRI § and C. EL HASI ‡ † Centro de Matemática Aplicada. ECyT- Univ. Nac. de San Martin. C.P. 1650. Buenos Aires, Argentina. guilleungs@yahoo.com.ar, diana.rubio@unsam.edu.ar § Instituto de Desarrollo Humano. Univ. Nac. de General Sarmiento. CP.1613. Buenos Aires, Argentina. recharri@ungs.edu.ar ‡ Instituto de Ciencias. Univ. Nac. de General Sarmiento. CP.1613. Buenos Aires, Argentina. cdelhasi@gmail.com Abstract−− This work aims to the study of the characteristics of the dissipation by convection of a solid circular section of a diameter d in a fluid. Specif- ically, it focuses on the estimation of the transient heat transfer coefficient. It is assumed that the circular section increases its temperature homogeneously over its whole surface from an initial temperature value   to the asymptotic temperature value   . A new ap- proach is proposed to estimate the heat transfer coef- ficient in the transient state. Temperature and elastic- ity analysis were made on several numerical experi- ments to study the performance of the proposed esti- mation. Numerical research indicates that the pro- posed technique allows to obtain a more precise heat transfer coefficient than the usual one, which leads to a better estimate of the temperature profile in the transient state. Keywords−− Dissipation. Convection. Elasticity, Modeling. I. INTRODUCTION The results of several experiments that have been carried out by different researchers show that the mechanism of convection is a complex process of heat transfer mainly due to its non-linear nature and the large number of vari- ables involved. Besides the geometrical configuration and the roughness of the surface, the transient heat trans- fer strongly depends upon the thermophysical properties of the fluid like the type of flow (laminar or turbulent), the dynamic viscosity (), the thermal conductivity (  ), the density (  ) and the specific heat (   ) (Cengel, 2007). Heat transfer by convection is composed of two distinct mechanisms, the transfer due to random molecu- lar motion and the energy transferred by the total or mac- roscopic movement of the fluid (Cengel, 2007). The movement of the fluid is directly associated with a large number of molecules that move collectively, such move- ment in the presence of a temperature gradient contrib- utes to heat transfer. Despite this complexity, the heat transfer rate is usu- ally considered to be proportional to the temperature dif- ference between the solid surface and the surrounding fluid, described by the Newton's cooling law, where the heat transfer coefficient, denoted by ℎ, is the proportion- ality constant. Typical values of ℎ for some common flu- ids vary between 0.5 and 1000 (  2 ° ⁄ ) for air, gases and dry vapors; and from 50 to 3000 (  2 ° ⁄ ) for wa- ter and liquids (Incropera et al., 1996). The expressions that govern the natural convection are the continuity equation, the momentum conservation equation and the energy conservation equation. These equations are used to determine the Grashof number (  ). This number represents the effect of the phenome- non of natural convection and it is given by the ratio be- tween the buoyancy force and the viscous force acting on the fluid. Moreover, the calculation of ℎ involves other characteristic dimensionless numbers, including the Nusselt number (  ) and the Prandlt number (  ). The first one is the ratio between conduction velocity and convection heat transfer velocity while the latter one is the ratio between momentum and heat diffusivity. Usu- ally, the natural convection process is modeled using a constant convection coefficient ℎ calculated by means of the steady-state temperature. However, for a transient process the coefficient ℎ changes with the temperature at the wall surface, then a constant h would lead to dubious results. During the last decades, some articles were published that aimed to experimentally determine the coefficient of heat transfer by convection in the transient state and its dependence on time (Churchill, 1983; Mcadams, 1964). In more recent works the problem of determining the heat transfer coefficient was formulated as an inverse problem where different mathematical tools were considered (Chantasiriwanc, 1999; Osman and Beck, 1990). Lately, some researchers have addressed related problems fo- cused on the characteristic length and the shape of the dissipative surface (Baïri et al., 2014; Das et al., 2017) characteristics of the flow including nanofluids (Rashad, 2014; Silin et al., 2010), edge conditions, thermophysical properties of the surface (Sharma, 2005) and the porosity of the medium (Loganathan and Dhivya, 2018; Makinde, 2011). Other considerations were made in Kozanoglu and Cruz, 2003; Srinivasacharya and Kaladhar, 2010. This work is concerned with the estimation of the time-dependent natural convection function ℎ() for a circular section of diameter  that increases its tempera- ture homogeneously over the whole surface from an ini- tial temperature   to the asymptotic value   . A new