Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body

An analytic approach based on the homotopy analysis method is proposed to solve a nonlinear model of combined convective and radiative cooling of a spherical body. An explicit series solution is given, which agrees well with the exact or numerical solutions. Our series solutions indicate that, for the nonlinear model of combined convective and radiative cooling of a spherical body, the temperature on the surface of the body decays more quickly for larger values of the Biot number Bi and/or the radiation–conduction parameter Nrc. Different from traditional analytic techniques based on eigenfunctions and eigenvalues for linear problems, our approach is independent of the concepts of eigenfunctions and eigenvalues, and besides is valid for nonlinear problems in general. This analytic method provides us with a new way to obtain series solutions of unsteady nonlinear heat conduction problems, which are valid for all dimensionless times 0 ⩽ τ < +∞.