Direct methods to manipulate internal heat conduction in solids remain nearly elusive. In this work, we propose a two-dimensional (2D) gradient thermal metamaterial lens designed to control the internal non-Fourier heat conduction. This gradient thermal metamaterial comprises cylindrical structures made of dermis immersed in a stratum background with an effective refractive index adhering to the hyperbolic secant profile rule. Subsequently, the effective refractive index of the thermal metamaterial is defined and numerically assessed using the extended plane wave expansion method. Thereafter, the non-Fourier heat conduction is analyzed numerically via the finite element method in the time-domain. Our findings indicate that the proposed gradient thermal metamaterial can focus the heat effectively and is akin to a flat thermal lens. The proposed flat thermal lens offers promising avenues for enhancing the material properties by laser-based technologies.

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