Natural convectionConvection divided into two basic processesa) forced convectionb) natural convection* the flow arises naturally from the effect of a density difference,resulting from a temperature or concentration difference in a body force field such as gravity.* The density difference gives rise to buoyancy forces due to which the flow is generated.

The main difference between natural and forced convection lies in the mechanism by which flow is generated.

In forced convection, externally imposed flow is generally known. In natural convection it results from an interaction of the density difference with the gravitational (or some other body force) field and is therefore inevitably linked with and dependent on the temperature and/or concentration fields.

Determination of motion.The motion determined from a consideration of the - heat and mass transfer process coupled with fluid flow mechanisms. velocities and the pressure differences

Natural convection flow over a vertical surfaceNatural convection flow over a vertical surface

Boundary layer development on a heated vertical plate. (a) Velocity and temperature profiles in the boundary layer at the location x. (b) Boundary layer transitional flow conditions.

Some empirical relationsThe Nusselt number, Nu:The Prandtl number, Pr :The Grashof number, Gr:The Rayleigh number, Gr: = (Gr.Pr)

(Gr.Pr) is also called as Rayleigh Number 2. If {GrL/Re2L} >> 1, it is Free convection.1. If {GrL/Re2L} 1, it is Forced convection.3. If {GrL/Re2L} = 1, it is Mixed convection

Select the appropriate correlation.Correlation Selection Rules. Identify the flow surface geometry. Does the problem involve flow over a flat plate, a cylinder, or a sphere? Or flow through a tube of circular or non-circular cross-sectional area? Specify the appropriate reference temperature and evaluate the pertinent fluid properties at that temperature. For moderate boundary layer temperature differences, the film temperature, Tf, defined as the average of the surface and free stream temperatures. Calculate the Reynolds number. Using the appropriate characteristic length, calculate the Reynolds number to determine the boundary layer flow conditions. If the geometry is the flat plate in parallel flow, determine whether the flow is laminar, turbulent, or mixed. Decide whether a local or surface average coefficient is required. The local coefficient is used to determine the heat flux at a point on the surface; the average coefficient is used to determine the heat transfer rate for the entire surface.

The Churchill-Chu correlation may be applied over the entire range of RaLFor laminar flow

Summary of Free Convection Correlations for Immersed Geometries

Analytical solutionFlow over a Heated Vertical Plate in AirHeated PlateTemp ProfilexLaminar FlowTurbulent FlowVelocity ProfileHBuoyant ForceViscous ForcedxgEdge of thermal & momentum boundary layeredControl volume for heated vertical plateTWACDB

Assumptions:1. The flow is steady, Laminar and two dimensional.2. The temperature difference between the plate and the fluid is small to moderate. Hence the fluid may be treated as having constant properties.3. The fluid is incompressible. (exception variable density in buoyancy force)4. Boundary layer approximation.Inertia force = buoyancy force + friction forceIn case of,Low Prandtl Number (liquid metals): Viscous effects are small.High Prandtl Number (heavy oils): inertia effects are small.With increase in Prandtl Number: Maximum vertical velocity decreases.: t decreases.: Thus there is higher heat transfer.

Governing EquationsThe reduced x-momentum equation is written as

The reduced x-momentum equation is written as

Let be the volumetric Thermal Expansion Coefficient

The reduced x-momentum equation is written asThe presence of temperature in the buoyancy term of the momentum equation couples the flow to the temperature.But the overall Mass and Energy Conservation equation remain unchanged.

Let us choose a control volume ABCD having height H, length dx and unit thickness normal to the plane of paper.Conservation of Mass:

Conservation of Momentum

The functional relationship for velocity and temperature profiles that satisfy the boundary conditions is :

The heat transfer coefficient can be evaluated from

The non-dimensional equation for heat transfer coefficient is given as

Limitation of Analytical SolutionExcept for the analytical solution for flow over a flat plate, experimental measurements are required to evaluate the heat transfer coefficient.Since in free convection systems, the velocity at the surface of wall and the edge of the boundary layer is zero and its magnitude within the boundary layer is so small , it is very difficult to measure them.

Expression for h for a heated Vertical Cylinder in AirThe characteristic length used for Gr and Pr is Height of the surface.If is not too large compared with the diameter of the cylinder, h can be evaluated by using expressions for vertical Plate.That is, when D/L 35/(GrL)0.25

These results are irrespective of whether TW>T or TW 1, t = Local Nusselt Number, NuX = {GrX/4}0.25.g(Pr)

Problem:A 0.5 m high flat plate of glass at 93 0C is removed from an annealing furnace and hung vertically in the air at 28 0C, 1 atm. Calculate the initial rate of heat transfer to the air. The plate is 1 m wide.Solution:1. Q = hL A (Tw - T) .. h 2. hL => (avg)NuL, 3. (avg)NuL = 4/3 NuL, ..> NuL4. Local Nusselt Number, NuX = {GrX/4}0.25.g(Pr)5. Calculate Gr and Pr.6. Decide if flow is laminar or turbulent, calculate (avg)Nu, (avg)h and then Q

Solution: Gr =7.44 x 108, Pr = 0.701, NuL = 58.27, (avg)NuL= 77.69, (avg) h = 4.465 w/m^2 K and Q = 145.1 W

Free Convection from Other Geometriesa) Inclined PlateIf is the angle of inclination from the vertical. + : upward-facing heated surface- : downward-facing heated surfaceCorrelations for vertical surface can be used by replacing g with g cos in the range of +200 to -600b) For SpheresNu = 2+0.43(Gr.Pr)0.25For 3 x 105

c) For Short Cylinders (D=H)Nu = 0.775 (Gr.Pr)0.208d) For Other SolidsNu = 0.52 (Gr.Pr)0.25