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Question

A stainless-steel sphere $\left[k=16 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right]$ having a diameter of $4 \mathrm{~cm}$ is exposed to a convection environment at $20^{\circ} \mathrm{C}, h=15 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$. Heat is generated uniformly in the sphere at the rate of $1.0 \mathrm{MW} / \mathrm{m}^3$. Calculate the steady-state temperature for the center of the sphere.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 11**Data given:**

- Thermal conductivity: $k=16~\frac{\text{ W}}{\text{ m}\text{ \degree C}}$;
- Diameter of sphere: $d=4\text{ cm}$;
- Temerature of enviroment: $T_{\infty}=20\text{ \degree C}$;
- Heat transfer coefficient for convection: $h=15~\frac{\text{ W}}{\text{ m}^\text{ 2}\text{ \degree C}}$;
- Heat generated per unit volume: $\dot{q}=1~\frac{\text{ MW}}{\text{ m}^\text{ 3}}$.

**Required:**

- At the center of a sphere temperature needs to be calculated.

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