The finite difference method was used to simulate the unsteady state cooling of spheres, infinite slabs and infinite cylinders of food materials subject to both convection and evaporation at the product surface. Simulations were conducted across wide ranges of air temperature, surface heat transfer coefficient, product initial temperature, surface water activity and air relative humidity Algebraic equations are proposed for finding three parameters-the product equilibrium temperature as time-->infinity, a slope parameter of semi-log plots relating unaccomplished temperature change to time and an intercept parameter of the same plots. The first of these equations is based on psychrometric theory and the other two were derived by using Mon-linear regression to curve-fit the numerically simulated cooling rates. These equations allow the numerically simulated cooling times to be predicted within about +/-5%. In Part 2 the accuracy of these equations as a simple chilling time prediction method is tested experimentally for model food systems. In Part 3 their application to real foods is considered.