In non-equilibrium thermodynamics, the rate of heat transfer through a material is determined by the temperature difference across the material and its thermal conductivity. When the temperature difference varies over time, the rate of heat transfer will also change accordingly. This phenomenon can be explained using the concept of irreversible processes and non-equilibrium thermodynamics.The rate of heat transfer Q through a material can be described by Fourier's law:Q = -k * A * dT/dx where k is the thermal conductivity of the material, A is the cross-sectional area through which heat is transferred, and dT/dx is the temperature gradient across the material.In a non-equilibrium state, the temperature difference across the material changes over time, which means that the temperature gradient dT/dx is not constant. This leads to a time-dependent rate of heat transfer. The time dependence of the temperature gradient can be described by a partial differential equation, known as the heat equation:T/t = * Twhere T/t is the rate of change of temperature with respect to time, is the thermal diffusivity of the material = k / * c_p , where is the density and c_p is the specific heat capacity , and T is the Laplacian of the temperature field the second spatial derivative of the temperature .The heat equation is a fundamental equation in non-equilibrium thermodynamics and describes the irreversible process of heat conduction. When the temperature difference across a material varies over time, the heat equation can be used to determine the time-dependent temperature gradient, which in turn affects the rate of heat transfer through the material.In summary, when the temperature difference across a material varies over time, the rate of heat transfer through the material changes as well. This phenomenon can be explained using non-equilibrium thermodynamics and the concept of irreversible processes, specifically by considering the heat equation and Fourier's law. The time-dependent temperature gradient affects the rate of heat transfer, leading to a dynamic heat transfer process that depends on both the material properties and the time-varying temperature difference.