2. CONVECTION : An Activity at Solid Boundary P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Identify and Compute Gradients at Boundary …..

3. Heat Transfer in Equilibrium Layer The thickness of stagnant layer decides the magnitude of normal temperature gradient at the wall. And hence, the thickness of wall fluid layer decides the magnitude of convective heat transfer coefficient. Typically, the convective heat transfer coefficient for laminar flow is relatively low compared to the convective heat transfer coefficient for turbulent flow. This is due to turbulent flow having a thinner stagnant fluid film layer on the heat transfer surface. At the wall for fluid layer : At Thermodynamic equilibrium

4. Estimation of Heat Transfer Coefficient Estimation of heat transfer coefficient is basically computation of temperature profile. A general theoretical and experimental study to understand how the stagnant layer is developed. The global geometry of the solid wall and flow conditions will decide the structure of stagnant layer. Basic Geometry : Internal Flow or External Flow.

5. Internal Flows Internal flow can be described as a flow whose boundary layer is eventually constrained as it develops along an adjacent surface. The objectives are to determine if: the flow is fully developed (no variation in the direction of the flow laminar or turbulent conditions the heat transfer

6. Entrance and developed flows

7. q’’ TiTi T s (x) TiTi q’’ Hot Wall & Cold Fluid Cold Wall & Hot Fluid Temperature Profile in Internal Flow

8. External Flows Any property of flow can have a maximum difference of Solid and free stream properties. There will be continuous growth of Solid surface affected region in Main stream direction. The extent of this region is very very small when compared to the entire flow domain. Free stream flow and thermal properties exit during the entire flow.

9. A continuously Growing Solid affected Region. The Boundary Layer

10. CONVECTION BOUNDARY LAYER P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi A tiny but very effective part of A Fluid Flow……

11. De Alembert to Prandtl 1752 1904 Ideal to Real 1822 1860

12. Introduction A boundary layer is a thin region in the fluid adjacent to a surface where velocity, temperature and/or concentration gradients normal to the surface are significant. Typically, the flow is predominantly in one direction. As the fluid moves over a surface, a velocity gradient is present in a region known as the velocity boundary layer, δ(x). Likewise, a temperature gradient forms (T ∞ ≠ T s ) in the thermal boundary layer, δ t (x), Therefore, examine the boundary layer at the surface (y = 0). Flat Plate Boundary Layer is an hypothetical standard for initiation of basic analysis.

13. Velocity Boundary Layer Fluid particles in contact with the surface have zero velocity u(y=0) = 0; no-slip boundary condition Fluid particles in adjoining layers are retarded δ(x): velocity boundary layer thickness

14. At the surface there is no relative motion between fluid and solid. The local momentum flux (gain or loss) is defied by Newton’s Law of Viscosity : Momentum flux of far field stream: The effect of solid boundary : ratio of shear stress at wall/free stream Momentum flux

15. Coefficient of friction:

16. Thermal Boundary Layer Fluid particles in contact with the surface attain thermal equilibrium T(y=0) = Ts Fluid particles transfer energy to adjoining layers δ t (x): thermal boundary layer thickness

17. Hot Surface Thermal Boundary Layer Plate surface is warmer than the fluid (T s > T ∞ )

18. Cold Surface Thermal Boundary Layer Plate surface is cooler than the fluid (T s < T ∞ )

19. At the surface, there is no fluid motion, heat transfer is only possible due to heat conduction. Thus, from the local heat flux: This is the basic mechanism for heat transfer from solid to liquid or Vice versa. The heat conducted into the fluid will further propagate into free stream fluid by convection alone. Use of Newton’s Law of Cooling:

20. Temperature distribution in a boundary layer of a fluid depends on: Scale of temperature:

21. Prandtl Number: The ratio of momentum diffusion to heat diffusion. Other scales of reference: Length of plate: L Free stream velocity : u oo n Potential for diffusion of momentum change (Deficit or excess) created by a solid boundary. a Potential for Diffusion of thermal changes created by a solid boundary.

23. This dimensionless temperature gradient at the wall is named as Nusselt Number: Local Nusselt Number

24. Average Nusselt Number

25. Computation of Dimensionless Temperature Profile First Law of Thermodynamics for A CV Energy Equation for a CV How to select A CV for External Flows ? Relative sizes of Momentum & Thermal Boundary Layers …