Optimal Estimation of Thermal Diffusivity in a Thermal Energy Transfer Problem with Heat Generation, Convection Dissipation and Lateral Heat Flow

Abstract

This work focuses on determining the coefficient of thermal diffusivity in a one-dimensional heat transfer process along a homogeneous and isotropic bar, embedded in a moving fluid with heat generation. A first type (Dirichlet) condition is imposed on one boundary and a third type (Robin) condition is considered at the other one. The parameter is estimated by minimizing the squared errors where noisy observations are numerically simulated at different positions and instants. The results are evaluated by means of the relative errors for different levels of noise. In order to enhance the estimation performance, an optimal design technique is chosen to select the most informative data. Finally, the improvement of the estimate is discussed when an optimal design is used.

Thermal Characteristics of Bioconvective Flow of a Shear-thinning Fluid Conveying Nanoparticles and Gyrotactic Cells within a Stratified Region

“…Their result showed that as stratification increases the temperature gradient between the surface and the free stream is reduced, which lowers both fluid velocity and temperature. By using the hottest water first, the system's efficiency is improved, [17], and similar researches on stratification were done by [18], [19], [20], while an analytical approach to examine the effects of double stratification and variable fluid properties on an upper convected Maxwell fluid chemical reaction was done by [21] and [22], discussed the impact of bioconvection flow of nanofluid over a medium, among others, [23], [24], [25], [26], [27].…”