A closed‐form solution of DPL bioheat transfer problem with time‐periodic boundary conditions

Abstract

AbstractA closed‐form (long‐time) solution of one‐dimensional dual‐phase lag bioheat transfer problem with consistent time‐periodic boundary conditions (BCs) is presented in this paper for planar, cylindrical, and spherical skin tissue for a newly developed solution methodology. The steady‐periodic solution is composed of a steady‐state part and an oscillating part; corresponding to the constant and oscillating parts of BCs, respectively. Using the superposition principle, these two parts are split into two problems, which are solved separately. The steady‐state part is fairly straightforward to obtain, while for the oscillating part, an alternate Laplace transform (LT) approach is proposed in this work. It is demonstrated that for sinusoidal BCs, a closed‐form solution in the time domain can be obtained by evaluating an approximate convolution integral, which emulates the effect of the inverse LT. The obtained closed‐form solution is free of any series summation or numerical inversion, thereby, making it computationally very efficient compared with conventional LT and eigenfunctions‐based approaches. The current methodology is verified with the established eigenfunctions expansion‐based methodology. It can be seen that the long‐time solutions obtained by these two approaches are almost identical. The verified methodology is further extended for the time‐periodic nonsinusoidal BCs. The ease of implementation and simplicity of the new methodology for both sinusoidal and nonsinusoidal BCs is demonstrated using a few test cases. It is evident from the results that the developed methodology leads to an efficient and accurate solution.