Table of Contents. Foreword... xiii. Preface... xv

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1 Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers Fundamental equations Local equations Integral conservation equations Boundary conditions Heat-transfer coefficient Dimensionless numbers Flows with variable physical properties: heat transfer in a laminar Couette flow Description of the problem Guidelines Solution Flows with dissipation Description of the problem Guidelines Solution Cooling of a sphere by a gas flow Description of the problem Guidelines Solution... 21

2 vi Convective heat Transfer Chapter 2. Laminar Fully Developed Forced Convection in Ducts Hydrodynamics Characteristic parameters Flow regions Heat transfer Thermal boundary conditions Bulk temperature Heat-transfer coefficient Fully developed thermal region Heat transfer in a parallel-plate channel with uniform wall heat flux Description of the problem Guidelines Solution Flow in a plane channel insulated on one side and heated at uniform temperature on the opposite side Description of the problem Guidelines Solution Chapter 3. Forced Convection in Boundary Layer Flows Hydrodynamics Prandtl equations Classic results Heat transfer Equations of the thermal boundary layer Scale analysis Similarity temperature profiles Integral method Integral equations Principle of resolution using the integral method Heated jet nozzle Description of the problem Solution Asymptotic behavior of thermal boundary layers Description of the problem Guidelines Solution Protection of a wall by a film of insulating material Description of the problem Guidelines Solution... 77

3 Table of Contents vii 3.7. Cooling of a moving sheet Description of the problem Guidelines Solution Heat transfer near a rotating disk Description of the problem Guidelines Solution Thermal loss in a duct Description of the problem Guidelines Solution Temperature profile for heat transfer with blowing Description of the problem Solution Chapter 4. Forced Convection Around Obstacles Description of the flow Local heat-transfer coefficient for a circular cylinder Average heat-transfer coefficient for a circular cylinder Other obstacles Heat transfer for a rectangular plate in cross-flow Description of the problem Solution Heat transfer in a stagnation plane flow. Uniform temperature heating Description of the problem Guidelines Solution Heat transfer in a stagnation plane flow. Step-wise heating at uniform flux Description of the problem Guidelines Solution Temperature measurements by cold-wire Description of the problem Guidelines Solution

4 viii Convective heat Transfer Chapter 5. External Natural Convection Introduction Boussinesq model Dimensionless numbers. Scale analysis Natural convection near a vertical wall Equations Similarity solutions Integral method for natural convection Integral equations Solution Correlations for external natural convection Mixed convection Natural convection around a sphere Description of the problem Solution Heated jet nozzle Description of the problem Solution Shear stress on a vertical wall heated at uniform temperature Description of the problem Solution Unsteady natural convection Description of the problem Guidelines Solution Axisymmetric laminar plume Description of the problem Solution Heat transfer through a glass pane Description of the problem Guidelines Solution Mixed convection near a vertical wall with suction Description of the problem Guidelines Solution Chapter 6. Internal Natural Convection Introduction Scale analysis

5 Table of Contents ix 6.3. Fully developed regime in a vertical duct heated at constant temperature Enclosure with vertical walls heated at constant temperature Fully developed laminar regime Regime of boundary layers Thermal insulation by a double-pane window Description of the problem Solution Natural convection in an enclosure filled with a heat generating fluid Description of the problem Solution One-dimensional mixed convection in a cavity Description of the problem Guidelines Solution Chapter 7. Turbulent Convection in Internal Wall Flows Introduction Hydrodynamic stability and origin of the turbulence Reynolds averaged Navier-Stokes equations Wall turbulence scaling Eddy viscosity-based one point closures Some illustrations through direct numerical simulations Empirical correlations Exact relations for a fully developed turbulent channel flow Reynolds shear stress Heat transfer in a fully developed turbulent channel flow with constant wall temperature Heat transfer in a fully developed turbulent channel flow with uniform wall heat flux Mixing length closures and the temperature distribution in the inner and outer layers Description of the problem Guidelines Solution Temperature distribution in the outer layer Description of the problem Guidelines Solution

6 x Convective heat Transfer Transport equations and reformulation of the logarithmic layer Description of the problem Guidelines Solution Near-wall asymptotic behavior of the temperature and turbulent fluxes Description of the problem Guidelines Solution Asymmetric heating of a turbulent channel flow Description of the problem Guidelines Solution Natural convection in a vertical channel in turbulent regime Description of the problem Guidelines Solution Chapter 8. Turbulent Convection in External Wall Flows Introduction Transition to turbulence in a flat plate boundary layer Equations governing turbulent boundary layers Scales in a turbulent boundary layer Velocity and temperature distributions Integral equations Analogies Temperature measurements in a turbulent boundary layer Description of the problem Solution Integral formulation of boundary layers over an isothermal flat plate with zero pressure gradient Description of the problem Guidelines Solution Prandtl-Taylor analogy Description of the problem Guidelines Solution Turbulent boundary layer with uniform suction at the wall Description of the problem Guidelines Solution

Convective Heat Transfer

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