# Why does the convection coefficient decay in the

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Why does the convection coefficient decay in the laminar region? Why does it increase significantly with transition to turbulence, despite the increase in the boundary layer thickness? Why does the convection coefficient decay in the turbulent region?
Boundary Layer Equations The Boundary Layer Equations Consider concurrent velocity and thermal boundary layer development for steady, two-dimensional, incompressible flow with constant fluid properties and negligible body forces . ( 29 , , p c k μ Apply conservation of mass , Newton’s 2 nd Law of Motion and conservation of energy to a differential control volume and invoke the boundary layer approximations . Velocity Boundary Layer: Thermal Boundary Layer:
Boundary Layer Equations (cont.) Conservation of Mass: In the context of flow through a differential control volume, what is the physical significance of the foregoing terms, if each is multiplied by the mass density of the fluid? Newton’s Second Law of Motion: What is the physical significance of each term in the foregoing equation?
Boundary Layer Equations (cont.) What is the physical significance of each term in the foregoing equation? What is the second term on the right-hand side called and under what conditions may it be neglected? Conservation of Energy:
Similarity Considerations Boundary Layer Similarity As applied to the boundary layers, the principle of similarity is based on determining similarity parameters that facilitate application of results obtained for a surface experiencing one set of conditions to geometrically similar surfaces experiencing different conditions. (Recall how introduction of the similarity parameters Bi and Fo permitted generalization of results for transient, one- dimensional condition). Dependent boundary layer variables of interest are: For a prescribed geometry, the corresponding independent variables are: Geometrical : Size ( L ), Location ( x,y ) Hydrodynamic : Velocity ( V ) Fluid Properties:
Similarity Considerations (cont.) Key similarity parameters may be inferred by non-dimensionalizing the momentum and energy equations. Recast the boundary layer equations by introducing dimensionless forms of the independent and dependent variables.