| Summary: | We start with the prototype problem of flow of a Newtonian fluid in the annular region between two infinitely long circular cylinders, with the given
velocity and temperature on the boundaries of the domain.
Then we will try to find out how does geometry affect the behavior of the flow inside of the domain. We will explore two invariant mappings
K_T and K_psi , such that under appropriate conditions on the boundary, the mapping K_T would preserve solution of temperature field from one domain to another and the mapping k_psi would preserve solution of velocity field.
We will prove that if a mapping is conformal, it would preserve the convection-diffusion equation in both domains. After that, we will find which subsets of the conformals would also preserve the velocity field as well. In order to answer that question, we will obtain the required condition for the mapping , such that it would preserve both velocity and temperature fields, from one domain to another.
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