Physical Properties of Materials

How can we determine the outer surface temperature of the carbon steel?

a) Utilize Fourier's law of heat conduction and assume steady-state conditions.

Answer:

The outer surface temperature of the carbon steel can be calculated by utilizing Fourier's law of heat conduction and assuming steady-state conditions. Using the given parameters and heat transfer rate, two equations representing the stainless steel and carbon steel plate are formed. Solving these equations will give the desired temperature.

Explanation: In this question, we're asked to find the outer surface temperature of a carbon steel plate with thermal conductivity (k) as 43 W/m.K when heat is being transferred from a stainless steel plate at the rate of 100 kW/m². The thickness of the stainless steel and carbon steel are 30 mm and 20 mm respectively.

Utilizing Fourier's law of heat conduction, the rate of conductive heat transfer is given by KA(T₂ – T₁). In this equation, K stands for thermal conductivity, A stands for material cross-section area, and (T₂ – T₁) represents the temperature difference across the material.

To answer this question, let's assume steady state conditions - this means the temperature distribution and heat transfer rate do not change with time. Hence, the heat rate equation for the stainless steel plate can be written as: 100,000 W/m² = 16 W/mK * (T₂ - 300°C) / 0.030 m. The heat equation for the carbon steel plate is: 100,000 W/m² = 43 W/mK * (T₂ - T₃) / 0.020 m.

Here, T₂ is the interface temperature between stainless and carbon steel plates, and T₃ is the outer surface temperature of the carbon steel which we need to find. As the heat transfer rate is the same through both plates, these two equations can be solved simultaneously for T₃.