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Calculus in Heat Transfer
Transcript of Calculus in Heat Transfer
Heat conduction is when heat is transferred through molecular motion. An entire object doesn't move, rather it's particles will cause a change in heat.
Heat convection refers to the movement of heat through a gas or a liquid that causes heat to move into cooler areas.
Heat radiation is the transfer of heat through electromagnetic waves that move heat away from the object that emits the wave.
What is average rate of change?
Average rate of change refers to the change in the value of a quantity over a certain amount of time. Graphically, this is the change in a y value divided by the x-value for two points.
How does rate of change connect to heat transfer?
The formula for average rate of change can be used to calculate the change in temperature of a system, such as a nuclear reactor.
Heat transfer refers to how systems change internal energy. Heat is normally transferred from high to low temperature and this can be done in 3 ways:
A nuclear rod that is 0.04m long is 172 degrees Celsius and a rod that is 0.05m wide is 156 degrees Celsius. What is the average rate of change from 0.04 to 0.05m?
While average rate of change deals with change over time, instantaneous rate of change looks at change at a certain instant or point.
Instantaneous Rate of Change
Newtons Law of Cooling
Newtons Law of Cooling deals with heat transfer busing instanteanous rate of change because it states that the rate of change of temperature in a system is directly proportional to the difference between the system's own temperature and the temperature of the systems surroundings.
Newtons Law of Cooling Equation
Newtons Law of cooling can be expressed as a mathematical differential equation:
dT/dt = rate of change
-k= the constant of proportionality
T= temperature of the object
Tout= temperature of the surrounding environment
The topic of Newtons Law of Cooling allows us to calculate how long it will take for an object to cool down or reach a certain temperature.
Heat transfer applies to our every day life because without heat transfer we wouldnt be able to cook or heat up our food. Additionally, the transfer of heat, such as the heat that comes from our sun is what allows plants to grow, which in turn allows us to eat. Heat is energy and without energy, we would not be able to function.