HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1
CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the presence of bulk fluid motion Natural (free) Convection Forced Convection (depending on how the fluid motion is initiated) Dr. Şaziye Balku 2
CLASSIFICATION OF FLUID FLOWS Viscous-inviscid Internal flow- External flow Open-closed channel Compressible- Incompressible Laminar- Turbulent Natural- Forced Steady- Unsteady One-,two-,threedimensional Dr. Şaziye Balku 3
VISCOSITY When two fluid layers move relative to each other, a friction force develops between them and the slower layer tries to slow down the faster layer. internal resistance to flow cohesive forces between the molecules in liquid molecular collisions in gases. Viscous flows: viscous effects are significant Inviscid flow regions: viscous forces are negligibly small compared to inertial or pressure forces. measure of stickness or resistance to deformation 1. Kinematic viscosity 2. Dynamic viscosity Dr. Şaziye Balku 4
VISCOSITY DEPENDS ON TEMPERATURE PRESSURE For liquids dependence of pressure is negligible For gases kinematic viscosity depends on pressure since its relation to density µ Dynamic viscosity (kg/m.s or poise) ν µ ρ ν Kinematic viscosity, m 2 /s or stroke Dr. Şaziye Balku 5
Convection heat transfer - Dynamic viscosity - Thermal conductivity - Density - Specific heat - Fluid velocity - Geometry - Roughness - Type of fluid flow Dr. Şaziye Balku 6
NEWTON S LAW OF COOLING Qconv h ha ( T T ) S S (W) Convection heat transfer coefficient (W/m 2. 0 C) The rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature difference Dr. Şaziye Balku 7
GENERAL THERMAL ANALYSIS Qconv ha ( T T ) S S Q mc p( Te Ti ) Dr. Şaziye Balku 8
FORCED CONVECTION Dr. Şaziye Balku 9
LAMINAR FLOW Smooth streamlines Highly- ordered motion (highly viscous fluids in small pipes) TURBULENT FLOW Velocity fluctuations Highly-disordered motion TRANSITIONAL FLOW Dr. Şaziye Balku 10
REYNOLDS NUMBER Flow Regime: Geometry Surface roughness Flow velocity Surface temperature type of fluid v Ratio of the inertial forces to viscous forces in the fluid υ m D µ / Re ρ υmd ρυmd v µ Mean flow velocity Characteristic length of the geometry Kinematic viscosity Dr. Şaziye Balku 11
Definition of Reynolds number Critical Reynolds number (Re cr ) for flow in a round pipe Re < 2300 laminar 2300 Re 4000 transitional Re > 4000 turbulent Note that these values are approximate. For a given application, Re cr depends upon Pipe roughness Vibrations Upstream fluctuations, disturbances (valves, elbows, etc. that may disturb the flow) Dr. Şaziye Balku 12
HYDRAULIC DIAMETER For non-round pipes, the hydraulic diameter D h 4A c /P A c cross-section area P wetted perimeter Dr. Şaziye Balku 13
Velocity No-slip condition Dr. Şaziye Balku 14
THERMAL BOUNDARY LAYER Flow region over the surface in which the temperature variation in the direction normal to the surface Velocity profile influences temperature profile Dr. Şaziye Balku 15
VELOCITY A flow field is best characterized by the velocity distribution, and velocity may vary in three dimension r υ ( x, y, z) in rectangular ( r, θ, z) υ r in cylinderical coordinates One dimensional flow in a circular pipe In which direction does the velocity change in this figure??? Dr. Şaziye Balku 16
NUSSELT NUMBER (Dimensionless number) hlc Nu k q cond T k L q conv h T qconv q cond h T k T / L hl k Nu Dr. Şaziye Balku 17
PRANDTL NUMBER Boundary layer theory Pr µc p k Pr molecular diffusivity of molecular diffusivity of momentum heat ν α µ C k p Pr<<1 heat diffuses very quickly in liquid metals, tbl thicker Pr>>1 heat diffuses very slowly in oils relative to momentum, tbl thinner than vbl Dr. Şaziye Balku 18
PARALLEL FLOW OVER FLAT PLATES ρυ x cr Re cr 5 10 µ 5 Nu hl k 0.5 1/ 3 0.664 ReL Pr ReL < 5 10 5 laminar Nu hl k 0.037 Re 0.8 L Pr 1/ 3 0.6 Pr 60 turbulent 5 10 5 Re L 10 7 Dr. Şaziye Balku 19
NATURAL CONVECTION Dr. Şaziye Balku 20
CONVECTIVE HEAT TRANSFER COEFFICIENT Coefficient of volume expansion Grashof number Rayleigh number Prandtl number Gr L gβ ( T Ra L Gr L s T 2 υ Pr ) L 3 C viscosity Nusselt number hl C Nu k CRa Dr. Şaziye Balku 21 n L Table 20-1