Topic: Heat Transfer
A packed bed of solid spheres acts as a thermal energy storage system. In a charging process, heat transfer from the hot gas increases thermal energy stored within the spheres. Consider two beds, one with aluminium spheres $(\rho=2700~kg/m^{3},$ $C=950~J/kg-K$, $k=240~W/m-K)$ and other with copper spheres ($\rho=8900~kg/m^{3},$ $C=400~J/kg-K,$ $k=380~W/m-K)$. Select the correct graph for the temperature rise of a sphere at the inlet of the bed
- A. Graph (a)
- B. Graph (b)
- C. Graph (c)
- D. Graph (d)
Answer: A. Graph (a)
Explanation: Thermal diffusivity $\alpha = \frac{k}{\rho C_{p}}$. For Aluminium, $\alpha_{Al} = \frac{240}{2700 \times 950} = 9.35 \times 10^{-5}$. For Copper, $\alpha_{Cu} = \frac{380}{8900 \times 400} = 10.67 \times 10^{-5}$. Since Copper has a higher thermal diffusivity, its temperature responds and rises faster to steady state initially compared to Aluminium, meaning the curve for Copper will be above Aluminium during the transient phase.