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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 layerthickness?Why does the convection coefficient decay in the turbulent region?
Boundary Layer EquationsThe 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,,pckμ•Apply conservation of mass, Newton’s 2ndLaw of Motion and conservation of energyto 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 physicalsignificance 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 conditionsmay it be neglected?•Conservation of Energy:
Similarity ConsiderationsBoundary Layer Similarity•As applied to the boundary layers, the principle of similarity is based ondetermining similarity parameters that facilitate application of results obtainedfor a surface experiencing one set of conditions to geometrically similar surfacesexperiencing different conditions. (Recall how introduction of the similarityparameters Biand Fopermitted 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:
SimilarityConsiderations (cont.)•Key similarity parameters may be inferred by non-dimensionalizing the momentumand energy equations.•Recast the boundary layer equations by introducing dimensionless forms of theindependent and dependent variables.