Chapter 3, Problem 3.123P

Consider two plates, A and B, that are each initially isothermal and each of thickness $L=5mm$. The faces of the plates are suddenly brought into contact in a joining process. Material A is acrylic, initially at $T_{i,A}=20°C$ with ${\rho }_A=1900kg/m^3,c_A=1470J/kg\cdot K,\text{and}{k}_A=0.21W/m\cdot K$. Material B is steel initially at $T_{i,B}=300°C$ with ${\rho }_B=7800kg/m^3,c_B=500J/kg\cdot K,\text{and}{k}_B=45W/m\cdot K$. The external (back) surfaces of the acrylic and steel arc insulated. Neglecting the thermal contact resistance between the plates, determine how long it will take for the external surface of the acrylic to reach its softening temperature, $T_{soft}=90°C$. Plot the acrylic’s external surface temperature as well as the average temperatures of both materials over the time span $0\le t\le 300s$. Use 20 equally spaced nodal points.