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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, C'steel = 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)

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, C'steel = 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)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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I got to=601°C

**Problem Statement:** 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:** - 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 capacity 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:** - Neglect radiation effects - One-dimensional heat conduction - Constant properties (density, specific heat capacity, thermal conductivity) - Uniform initial temperature **Solution Approach:** Use heat transfer equations and analysis to compute the core temperature of the steel plate after 2 minutes, clearly stating any steps or equations used in the process. Be detailed in the derivation and include any necessary diagrams or graphs for clear understanding, if applicable.
Transcribed Image Text:**Problem Statement:** 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:** - 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 capacity 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:** - Neglect radiation effects - One-dimensional heat conduction - Constant properties (density, specific heat capacity, thermal conductivity) - Uniform initial temperature **Solution Approach:** Use heat transfer equations and analysis to compute the core temperature of the steel plate after 2 minutes, clearly stating any steps or equations used in the process. Be detailed in the derivation and include any necessary diagrams or graphs for clear understanding, if applicable.
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