Newtons Law of Cooling

Newton s law of cooling states that the temperature difference between a refrigerant T and (for example) an ice cream mix (T jx) determines the rate at which it cools down (equation 2.9). 

Thus colder refrigerants cool faster. The coldest refrigerant available to the Victorians was ice and salt at about — 20°C. Today ice cream factories typically use liquid ammonia at — 30 °C, and ice cream making is much faster. In fact, Newton s law of cooling explains why the world record for the fastest ice cream ever made used liquid nitrogen at —196 °C2 This is demonstrated in Experiment 12 in Chapter 8. 

We consider a macroscopic, homogeneous system with cylindrical shape of length I and cross-sectional area A the temperature of the cylinder is T, which is generally time-dependent. Heat is transported across the boundary of the cylinder at each end in contact with two thermal baths, one with temperature Ti at one end, and the other with T2 at the other end without restrictions we assume Ti T2. We take the conduction of heat to be given by Newton s equations  

The rate of entropy production is the product of the heat flux times the conjugated force 

At equilibrium, at Ti = T2, the entropy production rate has an extremum which is a minimum. 

---

The definition of the heat-transfer coefficient is arbitrary, depending on whether bulk-fluid temperature, centerline temperature, or some other reference temperature is used for ti or t-. Equation (5-24) is an expression of Newtons law of cooling and incorporates all the complexities involved in the solution of Eq. (5-23). The temperature gradients in both the fluid and the adjacent solid at the fluid-solid interface may also be related to the heat-transfer coefficient ... 

For both the forced and the free convection situations, the overall heat transfer rate between the fluid and the surface is governed by Newtons law of cooling, wdiich is gjven by... 

Heat balance equation of a simple body. Tbe Newton law of cooling... 

---