Laminar flow

Boundary (topology)

Similarity (geometry)

Materials science

Convective heat transfer

Layer (electronics)

Planetary boundary layer

Boundary layer thickness

Computer science

Surface (topology)

Thermodynamics

Boundary layer

Physics

Similarity solution

Boundary layer control

Mathematics

Image (mathematics)

Thermal

Convective Boundary Layer

Mathematical analysis

Artificial intelligence

Geometry

Composite material

Blasius boundary layer

Mechanics

Convection

Communications in Nonlinear Science and Numerical Simulation

This paper considers the classical problem of hydrodynamic and thermal boundary layers over a flat plate in a uniform stream of fluid. It is well known that similarity solutions of the energy equation are possible for the boundary conditions of constant surface temperature and constant heat flux. However, no such solution has been attempted for the convective surface boundary condition. The paper demonstrates that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is proportional to x−1/2. Numerical solutions of the resulting similarity energy equation are provided for representative Prandtl numbers of 0.1, 0.72, and 10 and a range of values of the parameter characterizing the hot fluid convection process. For the case of constant heat transfer coefficient, the same data provide local similarity solutions.

A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition