Thermal energy storage systems commonly involve a packed bed of solid spheres, through which a hot gas flows if the system is being charged, or a cold gas if it is being discharged. In a charging process, heat transfer from the hot gas increases thermal energy stored within the colder spheres; during discharge, the stored energy decreases as heat is transferred from the warmer spheres to the cooler gas.

as the exercise is incomplete, I add the information that is missing:

Consider a packed bed of 75-mm-diameter aluminum spheres ? = 2700 kg/m3, and c = 950 J/kg

The copper can store 34.1% more thermal energy at 272.42ºC

Explanation:

Given:

Diameter packed bed = 75 mm

Density = 2700 kg/m³

specific heat = 950 J/kg K

initial temperature sphere = 25ºC

thermal conductivity = 240 W/m K

temperature of gas = 300ºC

convection coefficient = 75 W/m²K

The characteristic length is

The Biot number is equal to

Bi < 1, we will use the lumped capacitance method

The energy transfer is equal to:

(eq. 1)

Replacing in eq. 1

The temperature at the center of sphere is

We obtain the percentage increase

Cpcu = 385 J/kg K

(pCp)cu = 8933 * 385 = 3439205 J/m³K

from water:

(pCp)wa = 2700 * 950 = 2565000 J/m³K

the percentage increase is

%P = (3439205 - 2565000)/2565000 = 34.1%

The copper can store 34.1% more thermal energy.

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explanation:

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