The convective flow inside polymer solution droplets drying on a lyophobic substrate is numerically studied. The evaporating droplet is presumed as a hemisphere shrinking with time at the constant contact angle. The thermal and solutal effects are simultaneously considered in the computation. The thermal Marangoni convection is induced due to the quick thermal diffusion, and this convection transports the solute resulting in the solutal Marangoni flow. The solutal dependence corresponds to our previous experimental work, but the flow pattern does not. Consideration of the pseudo evaporation rate distribution depending on the contact angle yields to the flow pattern correspondence. (C) 2010 Elsevier Ltd. All rights reserved.