We consider a saturated Darcy porous medium with an exothermic chemical reaction on the lower boundary. The Dufour effect is neglected, however the influence of the Soret effect is studied. It is found that increasing the Soret coefficient may be either l

In the present paper we introduce a new approximation method, called the squared remainder minimization method (SRMM), which allows us to compute analytical approximate polynomial solutions for several nonlinear heat transfer problems. The applications illustrate the validity of the method and a comparison with previous results emphasizes the accuracy of the method.