The solution of Pennes' bio-heat equation with a convection term and nonlinear specific heat capacity using Adomian decomposition

Abstract Pennes' bio-heat equation is the most widely used to analyze heat transfer phenomenon associated with hyperthermia and cryoablation treatments of cancer. In this study, semi-analytical numerical solutions in a highly nonlinear form derived from renal cell carcinoma tissue's specific capacity along freezing convection term were obtained analyzed for first time. Here, governing was reduced lumped simplification exerted on solid spherical tumor. following, two techniques, adomian decomposition method (ADM) Akbari–Ganji's (AGM) evaluated solving ODE. The comparison revealed full conformity between ADM AGM, addition an excellent agreement results before phase transition. analysis highlighted deviation limited convergence power-series-based methods throughout change beyond. For investigated case $$D_{t} = 0.025,\quad {\text{Biot}} 0.075$$ D t = 0.025 , Biot 0.075 , occurred while $$\tau \in [0,0.7]$$ ? ? [ 0 0.7 ] both methods. Consequently, techniques are applicable find solution change, there no superiority favor one accuracy. contrast, reliable during transition after that. showed that growth tumor, achieving necrosis malignant tissue takes longer, large tumors' temperature may not decrease temperature. interpretation indicated could be considered effective thermal treatment tumors diameter lower than 2.0 cm.