Simplified Case for Systems with Negligible Internal Resistance

2 SIMPLIFIED CASE FOR SYSTEMS WITH NEGLIGIBLE INTERNAL RESISTANCE 

We begin our treatment of transient heat conduction by analyzing a simplified case. In this situation we consider a solid which has a very high thermal conductivity or very low internal conductive resistance compared to the external surface resistance, where convection occurs from the external fluid to the surface of the solid. Since the internal resistance is very small, the temperature within the solid is essentially uniform at any given time. 

An example would be a small, hot cube of steel at 7J, K at time t = 0, suddenly immersed into a large bath of cold water at 7 which is held constant with time. Assume that the heat-transfer coefficient h in W/m K is constant with time. Making a heat balance on the solid object for a small time interval of time dt s, the heat transfer from the bath to the object must equal the change in internal energy of the object. 

This equation describes the time-temperature history of the solid object. The term c pV is often called the lumped thermal capacitance of the system. This type of analysis is often called the lumped capacity method or Newtonian heating or cooling method. 

In using Eq. (5.2-3) the surface/volume ratio of the object must be known. The basic assumption of negligible internal resistance was made in the derivation. This assumption is reasonably accurate when 

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Sec. 5.2 Simplified Case for Systems With Negligible Internal Resistance... 

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