A flat-plate solar collector is used to heat water by having water flow through tubes attached at the back of the thin solar absorber plate. The absorber plate has an emissivity and an absorptivity of 0.9. The top surface (x = 0) temperature of the absorber is T₀ = 35°C, and solar radiation is incident on the absorber at 500 W/m² with a surrounding temperature of 0°C. Convection heat transfer coefficient at the absorber surface is 5 W/m²∙K, while the ambient temperature is 25°C. Show that the variation of temperature in the absorber plate can be expressed as T(x) = - (q̇₀ /k)x + T₀, and determine net heat flux q̇_H0 absorbed by the solar collector.

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