4. A self-supported steel plate of 8 cm thickness and an initial temperature of 20°C passes through a convective oven at a temperature of 1980°C. What is the core temperature of the plate after 2 minutes? Given: h= 500 w/mk, Ksteel = 63.9W/m k, Csteel = 434 J/m k, Psteel = 7832 kg/m³, Osteel = 18.8 x 10-6 m²/s, Neglect Radiation (State all assumptions and Show All Work)
4. A self-supported steel plate of 8 cm thickness and an initial temperature of 20°C passes through a convective oven at a temperature of 1980°C. What is the core temperature of the plate after 2 minutes? Given: h= 500 w/mk, Ksteel = 63.9W/m k, Csteel = 434 J/m k, Psteel = 7832 kg/m³, Osteel = 18.8 x 10-6 m²/s, Neglect Radiation (State all assumptions and Show All Work)
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Please share assumptions and work I'm not sure where I keep going wrong
Transcribed Image Text:**Problem Statement:**
A self-supported steel plate with a thickness of 8 cm and an initial temperature of 20°C passes through a convective oven at a temperature of 1980°C. What is the core temperature of the plate after 2 minutes?
**Given Data:**
- Convective heat transfer coefficient, \( h = 500 \text{ W/m}^2\text{K} \)
- Thermal conductivity of steel, \( k_{\text{steel}} = 63.9 \text{ W/mK} \)
- Specific heat of steel, \( C_{\text{steel}} = 434 \text{ J/kgK} \)
- Density of steel, \( \rho_{\text{steel}} = 7832 \text{ kg/m}^3 \)
- Thermal diffusivity of steel, \( \alpha_{\text{steel}} = 18.8 \times 10^{-6} \text{ m}^2/\text{s} \)
**Assumptions and Notes:**
- Neglect radiation.
- State all assumptions and show all work.
**Instructions:**
In solving this problem, ensure to apply principles of heat transfer, particularly considering the conduction within the plate and convection from the surface to the surrounding environment. Utilize the appropriate heat transfer equations, possibly involving transient heat conduction analysis.
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