Similarity analysis of axisymmetric free convection on a horizontal infinite plate subjected to a mixed thermal boundary condition

Summary Similarity analysis of the problem of axisymmetric free convection on a horizontal infinite plate is considered assuming that the plate is subjected to a mixed thermal boundary condition. It is shown that the thermal boundary condition is characterized by a nonnegative parameterm and the two cases ofm=0 andm=1 correspond to prescribed plate temperature and prescribed surface heat flux respectively. If one has to compute the heat transfer coefficient for various values ofm, there is no need to solve the boundary value problem everytime; it is enough to solve a certain polynomial equation provided the solution is known for any particular value ofm.Notation a ₀(r),a ₁(r),a ₂(r) coefficients in Eq. (1) - A transition parameter used in Eq. (22) - C function ofr defined in Eq. (8.1) - f dimensionless stream function - F dimensionless pressure - g acceleration due to gravity - G function ofr defined in Eq. (8.2) - m mixed thermal boundary condition parameter - N normalized heat transfer coefficient in Eq. (26) - Nu _r Nusselt number - p fluid pressure - p _e ambient pressure - P normalized pressure drop at the plate - Pr Prandtl number - r radial coordinate - S normalized stress at the plate - T temperature - T _e ambient temperature - u velocity in the radial direction - w velocity in the axial direction - z axial coordinate - coefficient of thermal expansion - dimensionless similarity variable - dimensionless temperature - exponent inC - kinematic viscosity - ambient fluid density - stream function