Exponential and Logarithmic Models

In diis section, we will discuss exponential and logarithmic models and their basic characteristics. 

The Cooling of Steel Plates In an annealing process—a process wherein materials such as glass and metal are heated to hi temperatures and then cooled slowly to toughen them—thin steel plates k = thermal conductivity = 40 W/m K, p = density = 7800 kg/m and c = specific heat - 400 J/kg IQ are heated to temperatures of900°C and then cooled in an enviroiunent with temperature of 35°C and a heat transfer coefficient of A = 25 W/m K. Eadi plate has a thickness of = 5 cm. We are interested in determining what die temperature of the plate is after one hour. 

Those of you vdio will pursue aerospace, ciiemical, medbaidcal, or materials engineering will learn about the underlying concepts that lead to the solution in your heat-transfer class. For now, in order to determine the tempoature of a plate after one hour, we use the following ponential equation. 

Another interesting form of an exponential foncdon isjf(jf) = e . bu will find diis type of exponential fimcdon in expressing probabilit7 distributions. wiU discuss probabil- 

In this secdon, we will discuss logadthmic fimcdons. In order to show the importance of logadthmic fimcdons, we will revisit the cooling of steel plates example, and ask a dififerent quesdon. 

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