A two-dimensional transient heat conduction describing the temperature distribution T(x, y, t) is given as a parabolic partial differential equation ∂T/∂t = α(∂²T/∂x² + ∂²T/∂y²) where α = Thermal Diffusivity.
with initial condition and the boundary conditions
Ti=10 °C, T1=25 °C, T2=0 °C, T3=25 °C and T4=50 °C
x (m)=0.01, y (m)=0.01, ∂t=0.01, convergence criteria = 10⁻⁴
a. If the surface is filled with the water, how long will it take over the temperature to go from 10 °C to 50 °C?
b. How will the temperature change over time?
c. What is the effect of boundary conditions on the temperature profile?
d. How do we know if we reached steady-state?
e. What happen if you change the boundary condition to adiabatic and inert case. You can assume the value for the boundary conditions in order to comply with the purpose of adiabatic and inert condition.
f. Repeat the procedure above for different material. This particular case you need to fill the surface with copper. Answer the above question(s) for copper properties.
g. For each case, plot the contour over each 5s and the graph for indicated when the problem reached steady-state.