Free Convection Film Flows and Heat Transfer

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1 Deyi Shang Free Convection Film Flows and Heat Transfer With 109 Figures and 69 Tables < J Springer

2 Contents 1 Introduction Scope Application Backgrounds Previous Developments For Accelerating Boundary Layers and Film Flow of Newtonian Fluids For Gravity-Driven Film Flow of Non-Newtonian Power-Law Fluids Recent Development A Novel System of Analysis Models A New Approach for the Treatment of Variable Thermophysical Properties Hydrodynamics and Heat and Mass Transfer Recent Experimental Measurements of Velocity Field in Boundary Layer 12 References 13 Part I Laminar Free Convection 2 Basic Conservation Equations for Laminar Free Convection Continuity Equation Momentum Equation (Navier-Stokes Equations) Energy Equation Basic Equations of Free Convection Boundary Layer Continuity Equation Momentum Equations (Navier-Stokes Equations) Energy Equations 34

3 X Contents 3 Brief Review of Previous Method for Analysis of Laminar Free Convection Falkner-Skan Transformation for Fluid Laminar Forced Convection Falkner-Skan Transformation for Fluid Laminar Free Convection For Boussinesq Approximation Consideration of Variable Thermophysical Properties Some Previous Methods for Treatment of Variable Thermophysical Properties 45 References 47 4 Laminar Free Convection of Monatomic and Diatomic Gases, Air, and Water Vapor Introduction Governing Partial Differential Equations Similarity Transformation of the Governing Equations Assumed Dimensionless Variables with Velocity Component Method The Similarity Transformation Treatment of Variable Thermophysical Properties Temperature Parameters Temperature Parameter Method Heat Transfer Analysis Numerical Results Effect of Variable Thermophysical Properties on Heat Transfer Summary Remarks Calculation Example 73 References 74 5 Laminar Free Convection of Polyatomic Gas Introduction Variable Thermophysical Properties Governing Partial Differential Equations and their Similarity Transformations Heat Transfer Analysis Numerical Solutions Curve-Fit Formulas for Heat Transfer Summary Remarks Calculation Example 94 References 95

4 Contents 6 Laminar Free Convection of Liquid Introduction Governing Partial Deferential Equations and their Similarity Transformation Governing Partial Differential Equations Dimensionless Transformation Variables Similarity Transformation Identical Buoyancy Factor Treatment of Variable Thermophysical Properties Heat Transfer Analysis Numerical Solutions A Curve-Fit Formula for Heat Transfer Summary Ill 6.8 Remarks Ill 6.9 Calculation Examples 113 References Heat Transfer Deviation of Laminar Free Convection Caused by Boussinesq Approximation Introduction Governing Equations of Fluid Laminar Free Convection under Boussinesq Approximation For Fluid Laminar Free Convection For Gas Laminar Free Convection Heat Transfer Deviation of Liquid Laminar Free Convection Caused by Boussinesq Approximation Boussinesq Solutions for Laminar Free Convection Models for Predicted Deviation on Heat Transfer Caused by Boussinesq Approximation Prediction of Heat Transfer Deviation E^x for Water Laminar Free Convection Heat Transfer Deviation of Gas Laminar Free Convection Caused by Boussinesq Approximation Boussinesq Solutions for Gas Laminar Free Convection Models on Predicted Deviation of Heat Transfer of Gas Laminar Free Convection Caused by Boussinesq Approximation Prediction Results of Deviation E^x for Gas Laminar Free Convection Summary Remarks Calculation example 136 References 138 XI

5 XII Contents 8 Experimental Measurements of Free Convection with Large Temperature Difference Introduction Experimental Measurements of Velocity Field for Air Laminar Free Convection Experimental Devices and Instruments Measurement Results Governing Equations The Numerical Solutions Experimental Measurements of Velocity Field for Water Laminar Free Convection Main Experimental Apparatus The Results of Experiment Governing Equations Numerical Solutions Remarks 153 References Relationship on Laminar Free Convection and Heat Transfer Between Inclined and Vertical Cases Introduction Fluid Free Convection on inclined plate Physical Model and Basic Equations Similarity Transformation of the Basic Equations Relationships of Momentum, Heat, and Mass Transfer between Inclined and Vertical Cases Gas Free Convection on Inclined Plate Summary Remarks Calculation Example 175 Appendix A. Derivation of Equations (9.1)-(9.3) Derivation of equation (9.1) Derivation of equation (9.2) Derivation of equation (9.3) 181 References 182 Part II Film Boiling and Condensation 10 Laminar Film Boiling of Saturated Liquid Introduction Governing Partial Differential Equations Similarity Transformation Similarity Transformation Variables Similarity Transformation 192

6 Contents XIII 10.4 Numerical Calculation Treatment of Variable Thermophysical Properties Numerical Calculation Numerical Results Heat Transfer Heat Transfer Analysis Curve-fit Equation for Heat Transfer Mass Transfer Mass Transfer Analysis Curve-Fit Formulae for Mass Transfer Remarks Calculation Example 209 References Laminar Film Boiling of Subcooled Liquid Introduction Governing Partial Differential Equations Similarity Transformation Transformation Variables Similarity Transformation Numerical Calculation Treatment of Variable Thermophysical Properties Numerical Calculation Heat and Mass transfer Heat Transfer Analysis Curve-Fit Equations for Heat Transfer Mass Transfer Analysis Summary Remarks Calculation Example 243 References Laminar Film Condensation of Saturated Vapor Introduction Governing Partial Differential Equations Similarity Variables Similarity Transformation of Governing Equations Numerical Solutions Treatment of Variable Thermophysical Properties Calculation Procedure Solution Heat and Mass Transfer Analysis for Heat and Mass Transfer Curve-Fit Equations for Heat and Mass Transfer Remarks 265

7 XIV Contents 12.8 Calculation Example 265 Appendix A. Derivation of Similarity Transformation of Governing Equations (12.1)-(12.5) 270 References Effects of Various Physical Conditions on Film Condensations Introduction Review of Governing Equations for Film Condensation of Saturated Vapor Partial Differential Equations Similarity Variables Transformed Dimensionless Differential Equations Different Physical Assumptions Assumption a (with Boussinesq Approximation of Condensate Film) Assumption b (Ignoring Shear Force at Liquid- Vapor Interface) Assumption c (Ignoring Inertia Force of the Condensate Film) Assumption d (Ignoring Thermal Convection of the Condensate Film) Effects of Various Physical Conditions on Velocity and Temperature Fields Effects of Various Physical Conditions on Heat Transfer Effects of Various Physical Conditions on Condensate Film Thickness Effect of Various Physical Conditions on Mass Flow Rate of the Condensation Remarks Effects of Boussinesq Approximation Effects of Shear Force at the Liquid-Vapor Interface Effect of Inertial Force of the Condensate Film Effects of Thermal Convection of the Condensate Film. 299 References Laminar Film Condensation of Superheated Vapor Introduction Governing Partial Differential Equations with Two-Phase Film Similarity Transformation Transformation Variables Ordinary Differential Equations Treatment of Variable Thermophysical Properties Numerical Solutions Calculation Procedure 310

8 Contents Numerical Solution Heat Transfer Heat Transfer Condensate Mass Flow Rate Summary Remarks Calculation Example 326 References 329 XV Part III Falling Film Flow of Non-Newtonian Fluids 15 Hydrodynamics of Falling Film Flow of Non-Newtonian Power-Law Fluids Principal Types of Power-Law Fluids Newtonian Fluids Power-Law Fluids Introduction of Studies on Hydrodynamics of Gravity-Driven Film Flow of Non-Newtonian Power-Law Fluids (FFNF) Physical Model and Governing Partial Differential Equations A New Similarity Transformation Numerical Solutions Local Skin-Friction Coefficient Mass Flow Rate Length of Boundary Layer Region Critical Film Thickness Effect of Wall Inclination Summary Remarks Calculation Example 354 References Pseudosimilarity and Boundary Layer Thickness for Non-Newtonian Falling Film Flow Introduction Physical Model and Governing Partial Differential Equations Similarity Transformation Local Prandtl Number Pseudosimilarity for Energy Equation Critical Local Prandtl Number Analysis of Boundary Layer Thickness Precautions for Pr x > Pr* Precautions for Pr x < Pr* Remarks 375 References 377

9 XVI Contents 17 Heat Transfer of the Falling Film Flow Introduction Governing Equations Heat Transfer Analysis Numerical Solution for Heat Transfer Local Similarity vs. Local Pseudosimilarity Summary Remarks Calculation Example 394 References 397 A Tables with Thermophysical Properties 399 References 405 Index 407

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