Thermal Conduction

Thermal ConductivityConsider a material of uniform cross-sectional area A and length x whose ends are kept at temp. θ and θ’ respectively. Let θ’ > θ.The quantity of heat flowing through the material is found to be proportional to the area of cross-section, temp. difference between the two ends, time of passage of heat and inversely proportional to distance between two ends.Where K is known as thermal conductivity or coefficient of thermal expansion.From the above equation,Where (θ’-θ)/x is temperature gradient.When (θ’-θ)/x is unity, A=1 sq. m & t=1s Then K=QTherefore thermal conductivity can be defined as the quantity of heat flowing per second across a material of uniform cross sectional area when unit temperature gradient is maintained. S.I. unit of thermal conductivity is Watt/metre Kelvin.We know,Comparing the above 2 eqns. we find that x/KA is analogous to resistance and is known as thermal resistance.Thermal resistance is the opposition offered by the material against heat flow. S.I. unit of thermal resistance is Kelvin/Watt.