Say you have a furnace wall at a temperature at 400 degrees C and you have oven gas at 200 degrees C and you place an copper rod in to the furnace. The copper rod has an initial temperature of 25 degrees C and a length of 1 meter and a diameter of 2cm. You want to find what find the time it takes for the copper rod to reach 150 degrees C. The furnace is a sqaure with a LxWXH of 3x3x3 meters respectively. You can assume 1D transient problem in the radius direction and you only need to take into consideration convection of the gas and the radiation of the walls of the oven. The oven can be treated as a black body and the copper rod as a grey body with an emissitivity of 0.5 to 0.8. Should I be using heat equations to solve this problem or should I use lumped capacitance method? Also is heat equations always related to only conduction or can it be applied to both convection and radiation? Thanks in advance.