## Related questions with answers

A spherical interplanetary probe, with a diameter of 2 m, is sent out into the solar system. The probe surface is made of material having an emissivity of 0.9 and an absorptivity of 0.1. Signals from the sensors monitoring the probe surface temperatures are indicating an average value of $−40^\circ C$ for a space temperature of 0 K. If the electronics inside the probe is generating heat at a rate of $100 W/m^3,$ determine the incident radiation rate on the probe surface.

Solution

VerifiedThe probe surface area is

$A=\pi D^2=\pi*2^2=12.57\ \text{m}^2$

```
The probe volume is
```

$\textbf{V}=\dfrac{\pi}{6}D^3=\dfrac{\pi}{6}*2^3=4.19\ \text{m}^3$

```
Making a heat balance for the probe at steady state
```

$\begin{align*} \dot{E}_\text{in}+\dot{E}_\text{gen}&=\dot{E}_\text{out}\\ \alpha \dot{E}_\text{incident}+\textbf{V}\dot{q}_\text{gen}&=\varepsilon \sigma A\left(T_\text{s}^4-T_\text{surr}^4\right)\\ 0.1*\dot{E}_\text{incident}+4.19*100&=0.9*5.67*10^{-8}*12.57*\left(233^4-0^4\right) \end{align*}$

```
Hence, the incident radiation rate is
```

$\color{#c34632}{\dot{E}_\text{incident}=14.71\ \text{kW}}$

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