Modulo di Elementi di Trasmissione del Calore Convezione Università degli studi di Cassino Facoltà di Ingegneria Corso di Laurea in Ingegneria Civile Modulo di Elementi di Trasmissione del Calore Convezione Titolare del corso Prof. Giorgio Buonanno Assistenti al corso Ing. Gaspare Giovinco Anno Accademico 2005-2006

Problema fisico-matematico Moto laminare e turbolento Definizione di h Convezione Problema fisico-matematico Moto laminare e turbolento Definizione di h Equazione di Newton Condizioni al contorno Variabilità di h

Conservazione della massa Conservazione della quantità di moto Conservazione dell’energia

1 Solido Fluido X-axis Y-axis 2

Definizione di moto laminare e turbolento

Laminair naar turbulent Op de tip van plaat (“leading edge”) altijd eerst laminaire (voor kleine x) en verder (grotere x) kan turbulente stroming Voor Rex < 5*105 is de stroming laminair ReL is het Reynolds-getal voor de volledige lengte van de plaat, L.

Definition of h Heat transfer in the fluid considering a h From surface T y=0 to fluid at T Heat transfer in the fluid at the surface only conduction (no-slip surface: V=0 m/s) Steady state: fluxes are in series and must be equal

Equations Governing Convection Energy (steady state) Velocity h depends on: - geometry - distance along flowpath - Re - Pr

Boundary layers ( 99% of the change) Velocity Velocity in this layer 2 separate regions inside layer (large grad.) outside layer (small grad.) Thermal Temperature in this layer 2 separate regions inside layer (large grad.) outside layer (small grad.) therm=y where Ts-T = 0.99 Ts-T y vel=yu=0.99u= 5x Rex1/2 Laminair: therm= vel/Pr1/3 Similarity Pr =  /  (visk. /therm. diff.)

h for various situations Variation with position Laminar vs. Turbulent flow Variation with geometry Variation with surface orientation Orders of magnitude for various situations

Compare Nusselt no. and Biot no. compares diffusive vs. convective resistance in the fluid k Characteristic length L is also different !!!! conductive resist. in the solid vs. convective resist. in the fluid k

Non-Dimensional Parameters (Significance). Reynolds # Nusselt # Prandtl # Biot # Grashof # Rayleigh #

h for various situations: semi-empirical via correlations Equations for: Flat plate - forced convection Flat plate - natural convection (vertical and horiz.) Cylinder - natural convection Cylinder - forced convection Cylinder - flow through center Sphere - natural convection Sphere - forced convection

Flat Plate, Forced Convection

Horizontal plate/ natural convection Hot up; cold down: always relative !!! Hot down; cold up: always relative !!! Horizontal plate/ natural convection

Vertical plate; natural convection

Ts T∞ Free Convection Forced Convection Flow Over Cylinder

T∞ Flow Over Sphere Ts Free Convection Forced Convection

Flow through Cylinder, Forced Convection Ts