### Projects (1999 - Spring 2008)

Engineering >> Industrial & Management Systems

## by Katrina Stine

Submitted : Spring 2012

The goal of this project was to find the optimum cycle time T, number of cycles per year N, and the heating element area A that would minimize the total annual cost and corresponding total hours of operation of an industrial concentrator. The three unknown variables can be determined by manipulating the given equation for Q, the instantaneous rate of evaporation in kg/hr, through integration by including various constraints and isolating one variable, A. Using a formulated equation for the total annual cost one can substitute the expression for A into the total annual cost equation. Through partial derivatives of the total annual cost equation and setting them equal to 0, the values for N and T are N = 2.4845 cycles/yr and T = 400 hrs and by substitution A = 55.9 m2. Therefore the industrial concentrator will have a minimum total annual cost of \$48,720.50 per year and will operate for 993.8 hours per year to meet production goals of evaporating 1x106 kg of water per year.