4. A thin (2 cm) “mild" steel plate of area 16 m? is heated by steady solar radiation of 900kW. The temperature measured on the other shady side of the plate is measured as85°C and the convective heat transfer coefficient is 20 W/m°C. What is the temperature of the plate surface with the incident solar radiation? Ignore heat loss from the edges.Solve this two ways: a) Using the principle of thermal resistance networks. (15 pts) b) Using differential equations and boundary conditions. Express the differential equation governing this heat transfer (5 pts) Express the applicable boundary conditions (8 pts) Solve for the constants in the general solution to the governingdifferential equation. This should result in an equation for temperature inthe base plate based on thickness. (12 pts) Solve the equation to determine the temperature on the plate surface (5pts) c) Also, if it was partly cloudy, and this system could not be approximated as steady state, demonstrate (do the calculation) how you would determine if the lumped system approximation would be valid.(8 pts)

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