Determine the temperatures along a 1-m horizontal rod described by the heat conduction equation (Eq. 30.1). Assume that the right boundary is insulated and that the left boundary (x = 0) is represented by

where k’ = coefficient of thermal conductivity (W/m · °C), h = convective heat transfer coefficient (W/m² · °C), T_o = ambient temperature (°C), and T₀ = temperature of the rod at x = 0 (°C). Solve for temperature as a function of time using a spatial step of Δx = 1 cm and the following parameter values: k = 2 x 10^-5 m²/s, k’ = 10 W/m · °C, h = 25 W/m² · °C, and T_α = 50 °C. Assume that the initial temperature of the rod is zero.

= li (T aT - To) ax