Exact solution for heat transfer problem in the entrance region of annuli considering constant heat flux on one wall and constant temperature on other wall with radially constant velocity

The work deals with heat transfer in the entrance region of annuli. It is assumed that the flow is thermally developing in the entrance region. It is also assumed that the axial fluid velocity in radial direction is constant. Since velocity in radial direction is constant, there is no need to solve momentum equation. To solve the heat transfer problem, only the energy equation in cylindrical coordinate system is solved. The inner and outer cylinder surfaces are kept at constant temperature and constant heat flux respectively. It is assumed that heat transfer appears in the direction of the outer and inner cylinder surfaces to flow. Such boundary conditions dictate existence of an adiabatic surface in the flow between the outer and inner cylinder surfaces. Separation of variable method, eigenvalue problem, Sturm-Liouville system, Bessel differential equation and properties of Ortogonal functions are utilized in the solution. Analytical solution for governing equation, namely for the energy equations is found. This naturally leads to temperature distribution, and as a result, to local mean fluid temperature. The local Nusselt number and the local convection heat transfer coefficient on both the outer and inner cylinder surfaces are found. The local temperature or local heat flux of a wall is calculated if heat flux or temperature on that wall is known, respectively. The local location and the local temperature of the adiabatic surface are found as well.