Analysis of Non-Fourier Heat Conduction Problem with Suddenly Applied Surface Heat Flux

In literature, the well-acknowledged initial condition is generally used when solving the non-Fourier problems. However, in references, some cases with a suddenly applied heat flux boundary under such an initial condition violate the first law of thermodynamics. This unreasonable situation is first demonstrated in the cases of constant heat flux using the Cattaneo–Vernotte model of a one-dimensional finite medium with the other side being isothermal or insulated. Then it is also demonstrated in the cases of arbitrary heat flux by reduction to absurdity. To adjust the unreasonable situation, an innovative definition of initial condition is proposed to obtain accurate solutions. Besides, the modified cases of a constant heat flux boundary are also discussed in this work with different relaxation time. In those cases, this study, for the first time, discovers that the heat wave can be inversely reflected under the isothermal boundary. Then when is extremely big, the heat flux input may result in a cooling response.