Final answer:
The rate of heat flow through a wall is determined by the temperature difference, the combined R-values of the materials, and the wall's surface area. Wooden studs within the wall affect its overall R-value, necessitating a calculation that considers the different heat flows through insulation and studs.
Step-by-step explanation:
To determine the rate of heat flow through an exterior wall consisting of multiple layers with different R-values in scenario (a), we use the formula Q = ΔT / (R_total × Area), where ΔT is the temperature difference across the wall, R_total is the sum of the R-values of the materials, and Area is the surface area of the wall.
The heat flow rate is thus found by taking the temperature difference across the wall (22 °C - (-2 °C) = 24 °C) and dividing it by the total R-value (0.56 + 2.6) multiplied by the area of the wall (3m × 10m).
In scenario (b), the presence of 2-by-4 wooden studs alters the R-value over the parts of the wall they cover.
To calculate the heat current realistically, one would need to account for the reduced R-value of the wall sections with studs and perform a weighted average of the heat flow through the insulation and the studs to find the overall heat flow through the wall.