Final answer:
To find the rate of heat flow through the wall, one must calculate the total R-value of the wall using the sum of the R-values for each layer. For a wall with studs, the effective R-value is adjusted to account for the thermal bridging effect of the studs. The heat current is then calculated using the wall area, temperature difference, and total thermal resistance.
Step-by-step explanation:
To calculate the rate of heat flow through a wall, we use the formula ΔQ/Δt = A(T inside - T outside) / R total, where ΔQ/Δt is the rate of heat flow, A is the area of the wall, T inside and T outside are the inside and outside temperatures, and R total is the total thermal resistance of the wall. First, add the R-values of each layer to get the total R-value (R total = R drywall + R insulation + R siding). For part (a), with no studs considered, this is straightforward: R total = 0.56 + 3.5 (converted to R-value) + 2.6
However, calculating the effective R-value for part (b) is more complex due to the thermal bridging effect of the studs. We calculate the combined R-value of the insulation and studs by taking their proportional areas into account. This is given by Rtotal = (Rstud × areastud + Rinsulation × areainsulation) / A. With this effective R-value, we can then calculate the heat current.