Question

Sol – air temperature for a wall of absorptivity 0.9, exposed to an ambient temperature of 35°C, solar radiation of 260 W/m², outside heat transfer coefficient 23 W/m²K is 
1. 45.2°C
2. 48°C
3. 41.2°C
4. 47.2°C

Answer 1

Correct Answer - Option 1 : 45.2°C

Concept:

Sol-air temperature (T_sol-air) is a variable used to calculate the cooling load of a building and determine the total heat gain through exterior surfaces. it is calculated by,

 \({{\rm{T}}_{{\rm{sol}} - {\rm{air}}}} = {{\rm{T}}_0} + \frac{{\left( {{\rm{α I}} - {{∇\rm{Q}}_{{\rm{ir}}}}} \right)}}{{{{\rm{h}}_{\rm{o}}}}}\)

Where T₀ = Ambient temperature, α = Absorptivity, I = Solar irradiation, ∇ Q_ir = Extra infra red radiation, h_o = Heat transfer coefficient.

Calculation:

Given:

α = 0.9, T₀ = 35°C, h_o = 23 W/m2K, I = 260 W/m2

\({{\rm{T}}_{{\rm{sol}} - {\rm{air}}}} = {{\rm{T}}_0} + \frac{{\left( {{\rm{α I}} - {{∇\rm{Q}}_{{\rm{ir}}}}} \right)}}{{{{\rm{h}}_{\rm{o}}}}}\)

\({{\rm{T}}_{{\rm{sol}} - {\rm{air}}}} = {35} + \frac{{\left( {{\rm{0.9\;\times \;260}} - {0}} \right)}}{{{{\rm{23}}}}}\)

T_sol-air = 45.2°C