ME-66 CONVECTIVE HEAT AND MASS TRANSFER A. W. Date Mechanical Engineering Department Indian Institute of Technology, Bombay Mumbai - 400076 India LECTURE- INTRODUCTION () March 7, 00 / 7
LECTURE- INTRODUCTION Modes of Heat and Mass Transfer Important Definitions Examples of Convective Heat and Mass Transfer 4 Syllabus and References () March 7, 00 / 7
MODES OF HEAT TRANSFER - L( 5 ) Whenever Temperature Difference exists, Heat Transfer Q ( J / s = W ) takes place Spontaneously by CONDUCTION ( Solid, Liquid, Gas ) Molecular Phenomenon RADIATION ( Transparent Medium including Vaccuum ) Electromagnetic Phenomenon CONVECTION ( Liquid, Gas ) Transfer of Energy by Bulk Motion and Conduction () March 7, 00 / 7
MODES OF MASS TRANSFER - L( 5 ) Whenever Concentration Difference exists, Mass Transfer ṁ ( kg / s ) takes place Spontaneously by DIFFUSION ( Solid, Liquid, Gas ) Molecular Phenomenon CONVECTION ( Liquid, Gas ) Transfer of Mass by Bulk Motion and Diffusion There is no RADIATION-LIKE counterpart in Mass Transfer () March 7, 00 4 / 7
SCOPE OF THIS COURSE - L( 5 ) The Course Content is designed for MTech and PhD students - careers in Research and Development. Our concern is with CONVECTIVE phenomena Familiarity with Introductory PG courses in Fluid Mechanics, Heat Transfer and Thermodynamics is assumed. You have already determined Heat and mass Transfer Coefficients from Experimental Correlations ( eg. Nu = C Re m Pr n ) The aim of this course is to determine coefficients from Theory of Mass, Momentum and Energy transfer in moving fluids () March 7, 00 5 / 7
Definition of Heat Flux - L( 4 5 ) VELOCITY PROFILE TEMPERATURE PROFILE T T ref ref T > T w ref y x T q ZERO SLIP w w T w CONDITION ( q > 0 ) ( q < 0 ) w w q w Due to No-slip condition, Heat Transfer Flux q w across interface area A is defined as q w = Q w A = k f T y y=0 [ W m ] () () March 7, 00 6 / 7
Definition of H T Coef h - L( 5 5 ) h q w (T w T ref ) (Experiment) k f T / y y=0 (T w T ref ) (Theory) VELOCITY PROFILE TEMPERATURE PROFILE T T ref ref In general, h ( W / m -K ) can be both positive or negative T ref must be known or knowable k f is fluid conductivity y x ZERO SLIP CONDITION T w q w T w ( h > 0 ) ( h < 0 ) T > T w ref T < T w ref q w, T w and T ref need be defined. q w () March 7, 00 7 / 7
Definition of M T Coef g - L( 6 5 ) Unlike heat transfer, in mass transfer states must be considered: Reference state ( ref ) far into the Considered Phase Interface state ( w ) Trans Subs state ( T ) deep into Transferred Substance Phase M T Flux ( N w ) kg / m -s is defined as N w g B () y VELOCITY PROFILE x REFERENCE STATE φ w TRANSFERRED SUBSTANCE PHASE CONSIDERED PHASE N w φ ref N w INTERFACE φ T B = Φ ref Φ w Φ w Φ T () M T Coef ( g ) kg / m - s, B is dimensionless, Φ is a Conserved Property. () March 7, 00 8 / 7
Mass Transfer Considerations - L( 7 5 ) In general, there are types of mass transfer Mass Transfer without heat transfer and chemical reaction Mass Transfer with heat transfer but without chemical reaction Mass Transfer with heat transfer and chemical reaction In each case, Conserved Property Φ must be appropriately defined - details will be considered later () March 7, 00 9 / 7
Engineer s Tasks - L( 8 5 ) Engineer is concerned with Design and Performance Evaluation Design implies Sizing ( For a given Q w, A must be determined ) Safety ( For a given q w, T w < T safe ) Economy ( Capital cost and compactness are related to A and Running cost is related to pressure drop ) 4 Hence, A must be so structured that p is small Fluid Mechanics determines p and velocity profile. The latter determines the T and/or Φ profiles and hence, their gradients at the wall/interface 4 Thermodynamics cannot help Design. Knowledge of h and/or g is required. Thermodynamics can help performance evaluation. Examples follow. () March 7, 00 0 / 7
Cooling Rate - L( 9 5 ) A hot metal sphere is dropped in cold water in an insulated vessel Thermodynamics can determine the final temperature T f of water and sphere Thermodynamics cannot answer: What is the cooling rate of the sphere? COLD WATER INSULATED VESSEL HOT METAL SPHERE Knowledge of h between sphere and water is required () March 7, 00 / 7
Sizing a Condenser - L( 0 5 ) In a Steam Condenser, knowing ṁ st and condenser pressure, Thermodynamics can determine ṁ water when allowable temperature rise T cooling is specified. Thermodynamics cannot determine tube-surface area A ( dia, length, number of tubes ) for allowable pressure drops on shell and tube side Cooling Water T in T out Tubes Low pressure steam Condensate Knowledge of h on steam and water side is required. Pressure drops must be determined from fluid mechanics () March 7, 00 / 7
Gas Turbine Blade Cooling - L( 5 ) Thermodynamics dictates that T gas leaving the Comb Chamber must be high Designer must ensure that T blade < T safe to prevent blade twisting Cooling air from Compressor must be as small to prevent reduction in engine thrust HOT GASES LEADING EDGE RIBS COOLANT AIR PIN FIN TRAILING EDGE SERPENTINE PASSAGE How should the internal passages be shaped? Rib Roughness, Bends, Jet impingement increase h () March 7, 00 / 7
Cooling Water Pond - L( 5 ) Thermal Power Plants often use cold water from Ponds as Condenser Cooling water It is of interest to determine evaporation loss under the action of wind and solar radiation Daily Topping-up water can be estimated from knowledge of g between water surface and air POWER PLANT COOLING WATER CONDENSER HOT WATER DISCHARGE PIPE SOLAR RADIATION WIND TOP UP WATER LARGE BODY OF WATER Driving force B depends on water vapour mass fractions Φ = ω v and temperatures Φ = T in air, water surface and deep inside the pond Simultaneous Heat and Mass transfer must be considered () March 7, 00 4 / 7
Pulverised Fuel Furnace - L( 5 ) In a PF boiler, coal particles ( < 50 µm ) are injected with air in the form of a jet It is of interest to determine Particle Burning Rate to size the furnace Secondary air is added to reduce NO x emissions WATER TUBES SECONADRY AIR A PRIMARY AIR + PF SUPERHEATER TUBES RADIATION SECTION ASH TO TURBINE UPPER STEM DRUM CONVECTION SECTION A SCRUBBER LOWER STEAM DRUM AND ECONOMISER TO FORCEDAIR PREHEATER PRECIPITATOR PRIMARYAIR+ PF SECTION A A Simultaneous Heat and Mass transfer with Chemical Reaction must be considered () March 7, 00 5 / 7
Syllabus - L( 4 5 ) Definitions and Flow Classifications ( ) Derivation of Transport Equations s ( 4 ) D Laminar Velocity and Temperature Boundary Layers Solutions ( 6 ) 4 Developing and Fully Developed Laminar Duct Flow and Heat Transfer Solutions ( 8 ) 5 Nature of Turbulent flows & Wall Laws ( 4 ) D Turbulent Velocity and Temperature Boundary Layer Solutions ( 4 ) Energy Budgets and Modeling ( ) Formulation of the Mass Transfer Problem using different Models ( 6 ) 4 Application of Reynolds Flow Model to different problems ( 4 ) () March 7, 00 6 / 7
References - L( 5 5 ) Kays W M and Crawford M E, Convective Heat and Mass Transfer, McGraw-Hill, rd Edition, ( 99 ) Spalding D B, Introduction to Convective Mass Transfer McGraw-Hill, ( 96 ) Bird R B, Stewart W E and Lightfoot E N, Transport Phenomena, John Wile& Sons, ( 960 ) 4 Schlichting H, Boundary Layer Theory, 6th Edition, McGraw-Hill, ( 968 ) 5 Incropera F P and DeWitt D P, Fundamentals of Heat and Mass Transfer, 4th Edition, John-Wiley & Sons, ( 996 ) 6 Cebeci T and Cousteix J, Modeling and Computation of Boundary Layer Flows, nd Edition, Springer, ( 005 ) Additional references will be given during the lectures () March 7, 00 7 / 7