NATURAL (Aka: FREE) CONVECTION NATURAL CONVECTION

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NATURAL (aka: FREE) CONVECTION

NATURAL CONVECTION Many familiar heat transfer applications involve natural convection as the primary mechanism of heat transfer. Examples?

cooling of hot food warming of cold drinks

1 Buoyancy force: upward force exerted by a fluid on a body completely or partially immersed in it in a gravitational field

The “chimney effect” induces upward flow of hot combustion gases through a chimney due to the buoyancy differences.

at rest except in the Free Convection vicinity of the hot surface Heat transfer that occurs in a quiescent fluid due to convection currents induced by buoyancy forces n Heat transfer equation is the same as for forced convection. n Volume expansivity, β, is a property that indicates the variation in density with temperature:

for an ideal gas

2 In natural convection, the flow rate is established by the dynamic balance of buoyancy and friction.

An interferometer produces a map of interference fringes (lines of constant temperature). Smooth and parallel lines in (a) indicate laminar flow. Eddies and irregularities in (b) indicate turbulent flow. Lines are closest near the surface indicating a higher temperature gradient. Isotherms in natural convection over a hot plate in air

FLUID MOTION The thickness of the boundary layer increases in the flow direction. Fluid velocity is zero at the outer edge of the velocity boundary layer AND at the surface of the plate. At the surface, the fluid temperature is equal to the plate temperature. In the case of cold surfaces, the shape of the velocity and temperature profiles remains the same but their direction is reversed.

Typical velocity and temperature profiles for natural convection over a hot vertical plate at

temperature Ts inserted in a fluid at temperature T∞.

3 The Grashof Number The Grashof number Gr is a measure of the relative magnitudes of the buoyancy force and viscous force acting on the fluid: g βρ2(T −T )L3 g β(T −T )L3 Gr = s f char = s f char L µ2 υ2 g = gravitational acceleration (m/s2) β = volume expansivity (1/K) (β=1/T for ideal gases) o Ts = surface temperature ( C) o Tf = fluid temperature ( C) Lchar = characteristic length (m) ρ = density (kg/m3) µ = dynamic viscosity (N-s/m2) ν = kinematic viscosity (m2/s) The Grashof number is the main criterion in determining whether fluid flow is laminar or turbulent in natural convection. For vertical plates, the critical Grashof number is about 109.

External flow involves both natural and forced convection. The relative importance of each mode is determined by Gr/Re2: • Gr/Re2 >> 1 (Natural convection dominates; forced convection is negligible) • Gr/Re2 << 1 (Forced convection dominates; natural convection is negligible) • Gr/Re2 ≈ 1 BOTH effects are significant (mixed convection)

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Natural Convection over Surfaces Depends on: surface geometry & orientation variation of surface temperature thermophysical properties of the fluid Most natural convection relations are based on experimental studies: Nu = f (Gr Pr) Rayleigh number = Ra =Gr Pr% Nu =C(Gr Pr)n C and n depend on surface geometry and flow regime n = 1/4 for laminar flow n = 1/3 for turbulent flow

Fluid properties evaluated at the film temperature: Tfilm = (Ts + Tf)/2

5 Dimensionless parameters

ρvL vL Re = = µ υ

Horizontal Plates For a hot surface in a cool environment: If the hot surface is facing up, the heated Natural convection on the fluid rises freely, inducing strong natural upper and lower surfaces of convection currents. Effective heat a horizontal hot plate: transfer. If the hot surface is facing down, the plate blocks the heated fluid from rising. Heat transfer is impeded.

Characteristic length:

Lc = a/4 for a horizontal square surface of length a

Lc = D/4 for a horizontal circular surface of diameter D

6 Inclined Plates A hot plate in a cooler environment:

lower surface has weak Natural convection occurs on the upper and lower surfaces of convection currents à rate of an inclined hot plate. heat transfer is lower than that for a vertical plate upper surface has a thicker boundary layer à rate of heat transfer is higher than that for a vertical plate (opposite occurs for a cold plate in a warmer environment)

Horizontal Cylinders and Spheres

The boundary layer over a hot horizontal Natural convection cylinder starts to develop at the bottom, over a horizontal hot increasing in thickness along the cylinder: circumference, and forming a rising plume at the top. Local Nusselt number is highest at the bottom and lowest at the top when the boundary layer flow remains laminar. (The opposite is true in the case of a cold horizontal cylinder in a warmer fluid)

7 Example 1… (to do in class) A square plate (50 cm on a side) is in a 30oC room. One surface of the plate is maintained at 90oC and the other surface is insulated. Determine the rate of heat transfer from the plate by natural convection if the plate is:

(a) Vertical

(b) Horizontal with the hot surface facing down