Heat Transfer

Conduction heat rate is proportional to area and the temperature gradient and flows opposite to it: q = -kA(dT/dx). The negative sign means heat flows from hot to cold.

Thermal conductivity k has units of W/(m·K). It is a material property measuring how readily a substance conducts heat.

Metals (e.g., copper, aluminum) have high k (hundreds of W/m·K) due to free electrons; insulators, gases, and foams have very low k (often <0.1 W/m·K).

R_cond = L/(kA), where L is wall thickness, k conductivity, and A cross-sectional area. Heat rate is then q = ΔT/R.

Heat transfer is modeled like Ohm's law: q = ΔT/R_total, where temperature difference is the 'voltage' and heat rate the 'current'. Resistances combine in series and parallel.