This document presents a detailed solution to a heat transfer assignment, focusing on the analysis of a composite wall system. The solution begins by calculating the thermal resistances of various layers, including a flexible plastic vapor barrier, R20 insulation, and a concrete layer, along with the thermal contact resistance between the concrete-soil interface. The calculations utilize thermal conductivity values and layer thicknesses to determine the thermal resistance of each component. The solution then proceeds to calculate the total heat loss through the composite wall, considering the combined effect of all thermal resistances. Furthermore, the document analyzes the percentage contribution of each layer to the overall thermal resistance. Finally, the solution explores the impact of adding an additional layer of foam insulation to the exterior of the wall, recalculating the heat loss and determining the reduction in heat loss achieved by this modification. The document includes references to relevant engineering resources and provides a comprehensive understanding of heat transfer principles in composite wall systems.