# Consider a fuel pellet of volume V, surface area A, density ?, and specific heat c. The pellet is…

Consider a fuel pellet of volume V, surface area A, density

_, and specific heat c. The pellet is initially at temperature Ti. At time

zero, heat is produced in the pellet at a constant rate of Q. At the same time,

the pellet is exposed to the surroundings being at the constant free stream

temperature of Tf. The heat transfer coefficient between the pellet

and the free stream is h. Assuming a lumped heat capacity method applies a) set

up the governing differential equation, b) show that the pellet temperature

versus time (t) is given as:

where _ = _cV/hA and c) find the pellet

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Consider a fuel pellet of volume V, surface area A, density

_, and specific heat c. The pellet is initially at temperature Ti. At time

zero, heat is produced in the pellet at a constant rate of Q. At the same time,

the pellet is exposed to the surroundings being at the constant free stream

temperature of Tf. The heat transfer coefficient between the pellet

and the free stream is h. Assuming a lumped heat capacity method applies a) set

up the governing differential equation, b) show that the pellet temperature

versus time (t) is given as:

where _ = _cV/hA and c) find the pellet

equilibrium temperature (i.e., when t >> _). [Hint: Use Equation

IIa.6.4 to obtain the governing differential equation. Then use Equation

VIIb.2.5 to solve the equation].

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