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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