Design of non-circular nanoinhomogeneities with uniform heat flux in two-dimensional heat conduction. (February 2021) - Song, Kun; Yin, Deshun; Dai, Ming; Schiavone, Peter
Abstract: It is known that the heat flux inside a circular nanoinhomogeneity remains uniform when taking interface phonon scattering into account. We use a combination of complex variable methods and numerical techniques to design a non-circular nanoinhomogeneity with internal uniform heat flux embedded in an infinite plate subjected to uniform remote heat loading. Our results clearly demonstrate that the shape of the nanoinhomogeneity remains independent of certain specific remote loadings but depends firmly on the corresponding thermal conductivities, interface parameter and the size of the inhomogeneity itself. Moreover, we find that the magnitude and direction of the uniform heat flux within the nanoinhomogeneity can be controlled independently by adjusting the shape of the inhomogeneity. Central to our analysis is the use of a conformal mapping function obtained via Newton-Raphson iteration. The accuracy of this conformal mapping function is verified using the corresponding actual heat flux around the nanoinhomogeneity. Our results illustrate that the error in our iterative procedure to obtain the mapping function is negligible in most cases of practical interest.