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1. The water of lake Michigan freezes over the water surface and snow falling on the ice starts accumulating. On a typical winter day the air temperature is 12C and the temperature of the ice-water interface is 0C. (a) Find the thickness of ice and snow layer if the surface temperature of snow is 6C. [20pts] Snow is very reflective of sunlight with absorptivity of 0.25. Convective heat transfer coefficient of the air is 20W/m2.K. (b) Find the thickness of only ice layer (when all snow transforms to ice) is the absorptivity of ice is 0.7. [15 pts] 2. Hot water at 80C is carried through a long insulation pipe (average thermal conductivity, k=0.15W/mK ) with an inner diameter 2cm and outer diameter 4cm. Convection heat transfer coefficient of hot water and outside air ( at 20C) is 150W/m2K and 12W/m2K, respectively). (a) Write down the energy balance equation and initial and boundary conditions during initial transient period. [10 pts] (b) solve the equation during steady state operation and find the temperature 1.5cm from the center of the pipe (halfway between inner and outer surface). [20 pts] 1. The water of lake Michigan freezes over the water surface and snow falling on the ice starts accumulating. On a typical winter day the air temperature is 12C and the temperature of the ice-water interface is 0C. (a) Find the thickness of ice and snow layer if the surface temperature of snow is 6C. [20pts] Snow is very reflective of sunlight with absorptivity of 0.25. Convective heat transfer coefficient of the air is 20W/m2.K. (b) Find the thickness of only ice layer (when all snow transforms to ice) is the absorptivity of ice is 0.7. [15 pts] 2. Hot water at 80C is carried through a long insulation pipe (average thermal conductivity, k=0.15W/mK ) with an inner diameter 2cm and outer diameter 4cm. Convection heat transfer coefficient of hot water and outside air ( at 20C) is 150W/m2K and 12W/m2K, respectively). (a) Write down the energy balance equation and initial and boundary conditions during initial transient period. [10 pts] (b) solve the equation during steady state operation and find the temperature 1.5cm from the center of the pipe (halfway between inner and outer surface). [20 pts]