Consider two plates, A and B, that are each initially isothermal and each of thickness L = 5 mm. The faces of the plates are suddenly brought into contact in a joining process. Material A is acrylic, initially at Ti, A = 20°C with p A = 1990 kg/m3, c A = 1470 J/kg - K, and kA = 0.21 W/m - K. Material B is steel initially at Tia = 300°C with p B = 7800 kg/m3, c B = 500 J/kg -K, and 1(13 = 45 W/m-K. The external (back) surfaces of the acrylic and steel are insulated. Neglecting the thermal contact resistance between the plates, use the explicit method to 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 ( t ( 300 s. Use 20 equally spaced nodal points.
Propose an equation to find the surface temperature at steady state. What is this temperature? Hint: For nodes 10 and 11, for heat going from node 10 to 11 or vice-versa, use the thermal resistance equation we used in early chapters.