Let us revisit of homework assignment 2 wherein we analyzed and determined the steady state temperature of an electric heater. If the heater is made out of pure solid Aluminium (its density is 2702kg/m3 and its specific heat is 903J/kg/K) and if it was initially at room temperature (300K) determine how long it takes for the heater to reach 95% of its steady temperature value which we calculated it to be 72.4oC. (Hints: The process is not steady state; the system (i.e. the heater) is a solid, hence incompressible. Start with the rate form of the 1st Law of thermodynamics to produce a differential equation with temperature and time being the variables.)
Problem: A cylindrical electric resistance heater has a diameter of 1cm and length of 0.25m. When water at 30oC flows across the heater a heat-transfer coefficient of 15W/(m2oC) exists at the surface. If the electrical input to the heater is 5W, what is the steady state surface temperature? of the heater?