Answer:
Temperature distribution = ( T( λ , T ) - Ta ) / (T₉ - Ta) = erf ( λ / 2 √∝T )
Explanation:
Determine the temperature distribution in the Rod T( x,t )
Given data :
Length: L
Thermal conductivity ; K
t > 0
Taking a 2nd order derivative
d^2 T / dx^2 = 1 /∝ * dT/dS
considering boundary conditions
T( λ , 0 ) = Ti
T ( 0,T ) = Ta given that t>0
T ( ∝ , 1 ) = T₉ for ₉ >0
Finally the General equation for the temperature distribution in the Rod
= ( T( λ , T ) - Ta ) / (T₉ - Ta) = erf ( λ / 2 √∝T )
