A large flat heating element is attached at its bottom surface to a perfectly insulating material (see diagram below). The heating element is 15mm thick and has a thermal conductivity of 50W/mK. The heating element dissipates electrical energy at a rate of q=7107W/m3. (a) In certain conditions, the bottom of the heating element is found to have a constant temperature of TB=250C, and the top surface has a constant temperature TS. (i) Derive an equation for the temperature distribution in the heating element. Show work. (ii) Calculate the surface temperature Ts. (b) For the conditions in (a), what is the maximum temperature reached in the heating element? (c) Now the heating element is exposed on the top surface to oil at 25C, and that exposure is associated with convection heat transfer coefficient of 100W/m2K. At the exact moment of exposure to the oil, the heating element is suddenly turned off. From the moment the heating element is turned off, how long will it take for the bottom surface of the heater to cool to 150C from its initial temperature of 250C ? The heat capacity and density of the heater material are 275J/kgK and 8570kg/m3, respectively. As always, show your work and justify your approach to the solution. A large flat heating element is attached at its bottom surface to a perfectly insulating material (see diagram below). The heating element is 15mm thick and has a thermal conductivity of 50W/mK. The heating element dissipates electrical energy at a rate of q=7107W/m3. (a) In certain conditions, the bottom of the heating element is found to have a constant temperature of TB=250C, and the top surface has a constant temperature TS. (i) Derive an equation for the temperature distribution in the heating element. Show work. (ii) Calculate the surface temperature Ts. (b) For the conditions in (a), what is the maximum temperature reached in the heating element? (c) Now the heating element is exposed on the top surface to oil at 25C, and that exposure is associated with convection heat transfer coefficient of 100W/m2K. At the exact moment of exposure to the oil, the heating element is suddenly turned off. From the moment the heating element is turned off, how long will it take for the bottom surface of the heater to cool to 150C from its initial temperature of 250C ? The heat capacity and density of the heater material are 275J/kgK and 8570kg/m3, respectively. As always, show your work and justify your approach to the solution