The effect and correction of concave surfaces on heat transfer in the transient TLC technique

Abstract This paper focuses on the effect of concave surfaces on heat transfer. Heat transfer coefficients are solved by variation-adjoining assimilation with the Newton descent method in one-dimensional Cartesian coordinates and cylindrical coordinates. Dimensionless numbers are used to analyze the heat transfer relation of a concave wall and a flat wall satisfying the semi-infinite assumption. It is found that the Bi (Biot number) discrepancy of concave and flat walls, Δ B i , is less affected by Fo . However, the dimensionless boundary temperature and dimensionless curvature radius have great influence on Δ B i . In addition, Δ B i is inversely proportional to the dimensionless curvature radius under the condition of the same dimensionless boundary temperature, and Δ B i increases with the increase of the dimensionless boundary temperature. Therefore, an empirical correction is introduced by fitting these relations. A transient TLC experiment on a concave wall is conducted to prove the relations, and the results of heat transfer coefficients over a flat surface, a concave surface and a concave correction are compared. It is proven that the correction introduced by this paper is very suitable for the transient TLC measurements and is more accurate in a larger application range than the previous correction.