14.1.3. Heat Transfer Considerations

The conservation of momentum which is required for you to know it, how the fluid particles are moving it, what could be the force exerting on that, what could be the velocity. Similar way, we can understand the energy conservation which plays a major role for us when the fluid comes from one location to other locations, how much of work is done by the fluid or into the fluid.

This chunk discusses the principles of conservation of momentum and energy in fluid flow. Conservation of momentum explains how forces affect the motion of fluid particles, while energy conservation helps us understand the work done by or on the fluid as it moves from one place to another. This means that the energy available in one location can influence what happens in another location, ensuring a balance according to the conservation laws.

Imagine pushing a swing. The swing represents a fluid particle. When you push it (forcibly applying momentum), it moves forward at a certain speed (velocity). If there’s a playground where kids are swinging, the energy from your push translates into work done on the swing, showing how energy conservation plays out in a real-life scenario.

Whether there is heat transfers happening which you can feel it, if there is a temperature gradient there will be heat transfer either to the surrendering of the systems or into the systems or out of the system, that is what we can do.

In this chunk, the focus is on heat transfer related to temperature gradients. A temperature gradient indicates that there is a difference in temperature between two areas, causing heat to transfer from the warmer area to the cooler area. For instance, if you touch a hot stove, heat from the stove transfers to your hand, illustrating this concept of heat transfer from one system to another based on temperature differences.

Think of a warm cup of coffee sitting on a table. The coffee is hot (high temperature), while the surrounding air is cooler (low temperature). Over time, heat from the coffee will flow into the air until the cup and the air reach the same temperature. This natural tendency for heat to flow from hotter to cooler places is what we mean by a temperature gradient.

Now, let me define two types of properties that we have; one is called extensive property and the other is the intensive property. The extensive property which is considered as proportional to the amount of mass. When you apply extensive properties, that means you are the properties which are proportional to the amount of mass. That means, as mass increases you will have extensive properties going to increase.

This section introduces extensive and intensive properties of materials. Extensive properties depend on the amount of matter or mass present in a system. For example, mass itself, volume, and total energy are extensive properties because if you have more fluid, you have more mass, volume, and total energy. Conversely, intensive properties are independent of mass, like temperature and pressure, meaning no matter how much fluid you have, the temperature remains the same for a given condition.

Consider an ice cube and a glass of water. The temperature of the water (intensive property) remains constant regardless of how much ice or water you have. However, if you add more ice, you increase the total mass (extensive property) and therefore the amount of total energy in the system, although the temperature remains unchanged.

Now, we will go to derive Reynolds transport theorem. The derivation of the Reynolds transport theorem are available in almost all the fluid mechanics books. The idea for me is to introduce the Reynolds transport theorem so that you can easily understand it.

The Reynolds transport theorem describes how a quantity (such as mass, momentum, or energy) changes in a control volume (the defined space through which fluid flows) over time. It establishes a connection between how changes occur within a system and how they manifest across the control volume, emphasizing the interactions between the contained system and its surroundings.

Imagine a water tank being filled from a pipe while also having water drain from the bottom. The Reynolds transport theorem helps you calculate how the volume of water changes inside the tank, considering both the inflow and outflow. Just like tracking how much water is added and how much spills out helps you understand the overall amount of water in the tank at any moment.

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