Using the finite difference method, the temperature distribution in the wall can be determined as:
where α is the thermal diffusivity, which is given by: incropera principles of heat and mass transfer solution pdf
Substituting the given values, the temperature distribution in the wall at t = 10 s can be determined as: Using the finite difference method
T(x,t) = 100 - 80 * erf(x / 0.2) + 4 * (1 - (x/0.02)^2) incropera principles of heat and mass transfer solution pdf
T(x,t) = T∞ + (T_i - T∞) * erf(x / (2 * √(α * t))) + (q * L^2 / k) * (1 - (x/L)^2)