Diffusion term, convective term and time double derivative

In summary, the conversation discusses the use of a Green Naghdi heat transport equation for heat transfer, which includes terms for density, heat capacity, and temperature. The questioner is confused about the concept of diffusivity and convection, as well as the representation of these terms in the equation. The provided link may contain more information on this topic.
  • #1
adnan jahan
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[itex]_{}[/itex]Dear Fellows,
I am just using a Green Naghdi heat transport equation which is represented as,

ρ[itex]\times[/itex]C[itex]\times[/itex]T''+aT_0[itex]\times[/itex]U'_i,i=K[itex]\times[/itex]T'_i,i+K*[itex]\times[/itex]T_i,i

where (')=derivative with respect to time
(,i)= derivative with respect to space.

I am being informed that
U_i,i= is a convetive term
U_i,ii= diffusive term


I am very confused in this concept of diffusivity and convetion and specially T'' what it is representing??


Why diffusive term is represented by double derivative and single referred to convetion of heat ??
 
Mathematics news on Phys.org

1. What is the diffusion term and how does it affect a system?

The diffusion term is a mathematical term used in the study of fluid dynamics and heat transfer. It represents the rate of transfer of a property (such as mass, heat, or momentum) through a medium due to random molecular motion. Diffusion can cause mixing and homogenization of properties in a system, and can also decrease concentration gradients over time.

2. How does the convective term differ from the diffusion term?

The convective term refers to the transport of a property through a medium by bulk motion of the medium itself. This is different from diffusion, which occurs due to random molecular motion. Convective transport can be caused by factors such as fluid flow or thermal currents, and can be either enhanced or hindered by diffusion.

3. What is the significance of the time double derivative in these terms?

The time double derivative, also known as the acceleration term, represents the rate of change of a property over time. In the context of diffusion and convection, it accounts for the effect of time on the transport of a property. It is important to consider this term in order to accurately model and predict the behavior of a system over time.

4. How are these terms used in real-world applications?

Diffusion and convection are fundamental processes in many natural and man-made systems, such as in the atmosphere, oceans, and industrial processes. These terms are used in mathematical models and simulations to understand and predict the behavior of these systems. For example, they are essential in predicting weather patterns and in optimizing heat transfer in engineering designs.

5. Can diffusion and convection be controlled or manipulated?

Yes, diffusion and convection can be controlled and manipulated in certain scenarios. For instance, in industrial processes, diffusion can be enhanced by increasing temperature or by using mechanical stirring. In fluid dynamics, convection can be manipulated by controlling the flow rate or by introducing barriers to alter the direction of flow. Understanding these terms and their effects is crucial in designing systems with desired outcomes.

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