Investigation of heat distribution using non-integer order time derivative
This paper presents the analyses of heat distribution based on non-linear order time derivative. The described problem has been demonstrated on a simple rectangular structure made of the silicon. Moreover, the thermal model called Dual-Phase-Lag has been employed to obtain the solution. Furthermore, the new approximation of Dual-Phase-Lag model has been proposed. This modification has been based on Grünwald-Letnikov definition of fractional derivative. The time derivative order, which appears in Fourier-Kirchhoff model, has been modified to non-integer order. Next, received normalized rises of the temperature have been compared with results obtained using Dual-Phase-Lag equation. Then, the orders of the fractional time derivative have been matched to different values of the heat flux and temperature time lags. Eventually, the final formula, which takes into consideration the order of time derivative and both model parameters of Dual-Phase-Lag
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