## Related questions with answers

Heat is generated uniformly in a stainless steel plate having $k=20 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$. The thickness of the plate is $1.0 \mathrm{~cm}$ and the heat-generation rate is $500 \mathrm{MW} / \mathrm{m}^3$. If the two sides of the plate are maintained at 100 and $200^{\circ} \mathrm{C}$, respectively, calculate the temperature at the center of the plate.

Solution

Verified$\rule{430pt}{1pt}$

$\text{\textcolor{#4257b2}{\textbf{Given}}}$

-The thermal conductivity of stainless steel plate $K=20\ \mathrm{W/m.\text{\textdegree} \ \mathrm{C}}$

-The thickness of the plate $L=1\times 10^{-2}\ \mathrm{m}$

-The heat generation rate $\dot{q}=500\times 10^{6}\ \mathrm{W/m^{3}}$

-The first temperature $T_1=100\text{\textdegree} \ \mathrm{C}$

-The second temperature $T_2=200\text{\textdegree} \ \mathrm{C}$

$\text{\textcolor{#4257b2}{\textbf{Required}}}$

-The temperature at the center of the plate

$\text{\textcolor{#4257b2}{\textbf{Assumption}}}$

-Steady state condition

-One dimensional conduction

-Constant properties

-Negligible constant resistance

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