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  3. this is a heat and mass transfer problem consider the...

Question: this is a heat and mass transfer problem consider the...

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This is a heat and mass transfer problem. Consider the window to be a 'slab'. This is about the heat flux through the slab.
3. (42 points) You are working with a team of engineers designing the windows of a plane and tasked with assessing the economic considerations of heat loss for different window materials: soda lime

glass, polycarbonate, and an aerogel. The plane has rectangular windows each 0.38 m tall by 0.25 m wide and L 11 mm in thickness. Flying at an altitude of 36,000 feet, the outside temperature is 7, =- 7°C, and the cabin temperature inside is T,-25℃ The thermal conductivity of the glass materaris kgl = 1.2 W/m. K. The thermal conductivities for the polycarbonate and aerogel are pc -0.18 W/m-K and kag 0.010 W/m-K, respectively. Evaluate the system at steady state. There is no generation in the window panel, and the material properties can be assumed to be constant The temperature in the window pane is isothermal along the y- and -directions. Outside (a) Starting from the governing heat diffusion equation, determine the simplified HDE and find the general solution of the temperature profile Tox) in the window panel. (b) What are the boundary conditions needed to solve for temperature profile Tar) in part a? (c) Solve for the temperature profile in the window panel, T(x) expression. (d) Calculate the heat transfer rate q, through a window made of either soda lime glass, polycarbonate, or acrogel, respectively (e) If the aircraft has 65 windows and the cost to heat the cabin air is SI/kWh, compare the costs associated with the heat loss through the windows for a 12-hour intercontinental flight.

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