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Governing equations vs Transport equations

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Old   July 15, 2019, 08:25
Default Governing equations vs Transport equations
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Mandeep Shetty
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This is a basic question. But I did not find any explanations for this. How are governing equations, like mass, momentum, energy conservations equations, different from 'Transport equation'?. Is a conservation equation, like energy equation (heat equation), a transport equation for the temperature?
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Old   July 15, 2019, 09:49
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Originally Posted by granzer View Post
This is a basic question. But I did not find any explanations for this. How are governing equations, like mass, momentum, energy conservations equations, different from 'Transport equation'?. Is a conservation equation, like energy equation (heat equation), a transport equation for the temperature?



Transport equation is a general denomination for the advection-diffusion PDE, see https://en.wikipedia.org/wiki/Convec...usion_equation
The equation is not necessarily related to a flow problem, for example they are often referred as to the transport of chemical species (advecion velocity prescribed).



On the other hand, when we use the conservative form of mass, momentum and total energy we could see those as a more complex expression of the simple advection-diffusion equation.



Do not worry if you read in literature some discrepancy
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Old   July 15, 2019, 10:19
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The mass, momentum, and energy equations (and many others) in CFD are indeed transport equations. The heat equation is a transport equation for the internal energy (or enthalpy depending on formulation) and an equation of state is usually invoked to write in with temperature as the primitive variable.


In general (widespread in non-fluids fields), a governing equation need not be a transport equation and a transport equation need not be a governing equation. A governing equation need not be a conservation either (economics, the stock market, etc...). In fluids, the main governing equations that you play with just happen to be transport equations based on the principles of mass, momentum, and energy conservation laws and they all are referring to the same thing.
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