In this work we consider a nonlinear parabolic equation with spherical symmetry, describing drying (shrinkage) effects of grain dehydration. The water removal is described by Fickian diffusion model and the diffusion term is dependent on the moisture content and the temperature. The formulated optimization problem for recovering two parameters in the non-linear diffusion coefficient satisfies the state constraints and minimize the cost functional, with a good accuracy, although not exactly. We develop numerical method for recovering these parameters in the non-linear diffusion term. Such a two-parameter coefficient inverse problem is ill-posed, since small errors in the input data may lead to large errors in the computed solution. The proposed approach is based on Levenberg-Marquardt method. Computational examples with synthetic and real data for chickpeas, obtained experimentally, are discussed.