In a system like this, the asymptotic internal resistance to heat at long times is proportional to L/k and the external resistance is proportional to 1/h. The lumped parameter approach is valid if the external resistance dominates, or when $$\frac{1}{h}>>\frac{L}{k}$$or when $$\frac{k}{Lh}>>1$$ or, equivalently, when Bi << 1.Sabra_a said:
The Lumped Capacitance method is a simplified approach to solving heat transfer problems where the temperature of a solid object changes due to a sudden change in its surroundings. It assumes that the object can be treated as a single lumped capacitor with a uniform temperature distribution.
The Lumped Capacitance method is appropriate to use when the Biot number (Bi) is less than 0.1. This means that the heat transfer at the surface of the object is much faster than the heat transfer within the object. It is also suitable for short-duration processes where the temperature change is significant within a short period of time.
The Lumped Capacitance method has several limitations, including the assumption of a uniform temperature distribution in the object, neglecting the internal temperature gradients, and not accounting for convection or radiation effects. It is also not suitable for long-duration processes where the temperature change is gradual.
The accuracy of the Lumped Capacitance method depends on the assumptions made and the conditions of the problem. It can provide reasonable results for short-duration processes with low Biot numbers. However, for more complex and longer processes, it may not accurately capture the temperature distribution within the object.
No, the Lumped Capacitance method is only applicable to certain types of heat transfer problems, specifically those with low Biot numbers and short-duration processes. It is important to carefully consider the conditions and assumptions before deciding to use this method for a particular problem.