where Qp is the heat capacity of the heating pipe installed digester per meter (W/m), Tw,a (C) is the average temperature of water, Dp (mm) is the diameter of the pipe, Lp,w (mm) is the wall thickness of the pipe, kp (W/m K) is the heat transfer coefficient of the heating pipe material, hi (W/m2 K) is the coefficient of internal convective