Only for phd in vicoelastic fluid flow in boundary layer?
1 what is non similarsolution
2 what are boundary conditions
Answer:
It is difficult to answer these questions concisely and without the use of diagrams, but the previous post is not entirely correct.
1. A similarity solution is used to simplify the governing differential equations (continuity and momentum) from partial differential equations to ordinary differential equations so they are easier to solve. This is done by re-expressing the equations using a "similarity" variable that essentially does not change with position in the boundary layer. A non-similar solution would solve the equations by different methods.
2. Boundary conditions are known values of some property of the fluid (probably velocity for your case) at certain locations within your problem. These are normally at the "boundaries" of the region of interest such as at the solid object surface or the top of the boundary layer. Boundary conditions are required in order to solve the differential equations since unknown constants arise from integration.
Viscoelastic fluids are fluids that behave elastically (think "stretchy"). Some examples are oils or polymers. I don't know why you would be studying viscoelastic flow as it is a more advanced topic.
This is a complex problem and I hope some of my explanation made sense to you. You should consult an undergraduate textbook to get more thorough explanations. I've listed a couple of excellent books below.
1. non similar solution:
If you are referring to self-similar versus non self-similar, then they can be described as follows:
self-similar refers to an object that is exactly or approximately similar to a part of itself. e.g., Koch snowflake (source wikipedia)
non-self-similar refers to an object that does not exhibit any similarities at all within itself. e.g., fatigue crack growth (source: Journal of Engineering Materials and Technology)
2. Boundary Conditions:
They are a set of restraints in a boundary value problem. The differential equations solution must also satisfy the boundary conditions. An examples of such problems are commonly seen in heat transfer, fluid mechanics, among others. There are 3 types of boundary conditions:
Neumann, Dirichlet , and Cauchy
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2 what are boundary conditions
Answer:
It is difficult to answer these questions concisely and without the use of diagrams, but the previous post is not entirely correct.
1. A similarity solution is used to simplify the governing differential equations (continuity and momentum) from partial differential equations to ordinary differential equations so they are easier to solve. This is done by re-expressing the equations using a "similarity" variable that essentially does not change with position in the boundary layer. A non-similar solution would solve the equations by different methods.
2. Boundary conditions are known values of some property of the fluid (probably velocity for your case) at certain locations within your problem. These are normally at the "boundaries" of the region of interest such as at the solid object surface or the top of the boundary layer. Boundary conditions are required in order to solve the differential equations since unknown constants arise from integration.
Viscoelastic fluids are fluids that behave elastically (think "stretchy"). Some examples are oils or polymers. I don't know why you would be studying viscoelastic flow as it is a more advanced topic.
This is a complex problem and I hope some of my explanation made sense to you. You should consult an undergraduate textbook to get more thorough explanations. I've listed a couple of excellent books below.
1. non similar solution:
If you are referring to self-similar versus non self-similar, then they can be described as follows:
self-similar refers to an object that is exactly or approximately similar to a part of itself. e.g., Koch snowflake (source wikipedia)
non-self-similar refers to an object that does not exhibit any similarities at all within itself. e.g., fatigue crack growth (source: Journal of Engineering Materials and Technology)
2. Boundary Conditions:
They are a set of restraints in a boundary value problem. The differential equations solution must also satisfy the boundary conditions. An examples of such problems are commonly seen in heat transfer, fluid mechanics, among others. There are 3 types of boundary conditions:
Neumann, Dirichlet , and Cauchy
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