Heat Transfer of Conductive

Conduction will take place if there exist a temperature gradient in a solid (or stationary fluid) medium.
Energy is transferred from more energetic to less energetic molecules when neighboring molecules collide. Conductive heat flow occur in direction of the decreasing temperature since higher temperature are associated with higher molecular energy.

Fourier's Law express conductive heat transfer as

q = k A dT / s         (1)
where
q = heat transferred per unit time (W, Btu/hr)
A = heat transfer area (m², ft²)
k = thermal conductivity of the material (W/m.K or W/m ^oC, Btu/(hr ^oF ft²/ft))
dT = temperature difference across the material (K or ^oC, ^oF)
s = material thickness (m, ft)

Efficiency of Carnot

A ideal reversible cycle where heat is taken in at a constant upper temperature and rejected at a constant lower temperature was suggested by Sadi Carnot. The theoretically most efficient heat engine cycle, the Carnot cycle, consists of

• two isothermal processes and
• two adiabatic processes

Since the second law of thermodynamics states that not all supplied heat in a heat engine can be used to do work, the Carnot efficiency limits the fraction of heat that can be used.

The Carnot efficiency can be expressed as

μ_C = (T_i - T_o) / T_i         (1)
where
μ_C = efficiency of the Carnot cycle
T_i = temperature at the engine inlet (K)
T_o = temperature at engine exhaust (K)

The wider the range of temperature, the more efficient becomes the cycle. The lowest temperature is limited by the temperature of the sink of heat - if it is the atmosphere or the ocean, river or whatever available. Normally the lowest temperature available is in the range 10 - 20 ^oC. The maximum temperature is limited by the metallurgical strength of available materials.  

Solar radiation absorbed by various materials

Absorbed Solar Radiation by Surface Color

In general the solar energy absorbed can be approximated by the surface color

Surface Color	Absorb Factor - Fraction of Incident Radiation Absorbed (approximated)
White smooth surfaces	0.25 - 0.40
Grey to dark grey	0.40 - 0.50
Green, red and brown	0.50 - 0.70
Dark brown to blue	0.70 - 0.80
Dark blue to black	0.80 - 0.90