Thermal Conduction - Finding Temperature of Interface Between 2 Slabs

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To find the temperature at the interface between the steel and copper slabs, the thermal resistances of both materials need to be calculated using their thermal conductivities and dimensions. The heat transfer rate can be determined using the formula Q = kA(ΔT/L), where Q is the heat transfer rate, k is the thermal conductivity, A is the area, ΔT is the temperature difference, and L is the length of the slab. By treating the slabs as resistors in series, the interface temperature can be derived by applying the concept of thermal equilibrium, where the heat transfer rate through both slabs is equal. The calculations will yield both the interface temperature and the rate of heat transfer across the slabs. Understanding these principles is crucial for solving the problem effectively.
MadmanMurray
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Homework Statement


Two well-insulated slabs, one of steel the other of copper, are in close contact as illustrated.

Find the temperature at the interface between the two slabs & also the rate at which heat is transferred across the slabs.

Thermal conductivities of steel and copper are 50WmK and 385WmK

Left side of steel slab has an area of 90cm2 and temperature of 427C. The steel slab has a length of 20cm.

Right side of copper slab has area of 90cm2 and temperature of 77C. Length of slab is 30cm



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The Attempt at a Solution


I'm completely stuck. I know a formula to find the rate of heat transfer through the slabs but I don't have a clue how to find the temperature at the interface of these 2 slabs.
 
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Just think of them as resistors in series = a potential divider.
 

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