Dimensionless Parameters and their Significance: The following dimensionless parameters are significent in evaluating the convection heat transfer coefficient:

**FREE AND FORCED CONVECTION DURING
EXTERNAL FLOW OVER PLATES**

**:**

**Dimensionless Parameters and their
Significance**

The following
dimensionless parameters are significent in evaluating the convection heat
transfer coefficient:

(a) *The Nusselt
Number (Nu)-*It is a dimensionless quantity defined as hL/ k, where h =
convective heat transfer coefficient, L is the characteristic length and k is
the thermal conductivity of the fluid The Nusselt number could be interpreted
physically as the ratio of the temperature gradient in the fluid immediately in
contact with the surface to a reference temperature gradient (T_{s} - T
_{inf}) /L. The convective
heat transfer coefficient can easily be obtained if the Nusselt number, the
thermal conductivity of the fluid in that temperature range and the
characteristic dimension of the object is known.

Let
us consider a hot flat plate (temperature T_{w}) placed in a free
stream (temperature T

inf< T_{w}). The temperature distribution is shown ill Fig. 2.4.
Newton's Law of Cooling says that the rate of heat transfer per unit area by
convection is given by

Fig.
2.4 Temperature distribution in a boundary layer: Nusselt modulus

The
heat transfer by convection involves conduction and mixing motion of fluid
particles. At the solid fluid interface (y = 0), the heat flows by conduction
only, and is given by

Since
the magnitude of the temperature gradient in the fluid will remain the same,
irrespective of the reference temperature, we can write dT = d(T - T_{w})
and by introducing a characteristic length dimension L to indicate the geometry
of the object from which the heat flows, we get

(b)
*The Grashof Number (Gr)*-In natural or free convection heat transfer, die
motion of fluid particles is created due to buoyancy effects. The driving force
for fluid motion is the body force arising from the temperature gradient. If a
body with a constant wall temperature T_{w} is exposed to a qui scent
ambient fluid at T _{inf}
, the force per unit volume can be written as

the
acceleration due to gravity.

The
ratio of inertia force × Buoyancy force/(viscous force)^{2} can be
written as

The magnitude of
Grashof number indicates whether the flow is laminar or turbulent. If the
Grashof number is greater than 10^{9}, the flow is turbulent and for
Grashof number less than 10^{8}, the flow is laminar. For 10^{8}
< Gr < 10^{9}, It is the transition range.

(c) *The Prandtl Number (Pr)* - It is a
dimensionless parameter defined as Pr = mC_{p}
/ k =/n a

where mis the dynamic viscosity of the fluid, v = kinematic
viscosity and a = thermal diffusivity.

This number assumes
significance when both momentum and energy are propagated through the system.
It is a physical parameter depending upon the properties of the medium It is a
measure of the relative magnitudes of momentum and thermal diffusion in the
fluid: That is, for Pr = I, the r ate of diffusion of momentum and energy are
equal which means that t he calculated temperature and velocity fields will be
Similar, the thickness of the momentum and thermal boundary layers will be
equal. For Pr <<I (in case of liquid metals), the thickness of the
thermal boundary layer will be much more than the thickness of the momentum
boundary layer and vice versa. The product of Grashof and Prandtl number is
called Rayleigh number. Or, Ra = Gr × Pr.

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Mechanical : Heat and Mass Transfer : Convection : Free and Forced Convection During External Flow Over Plates |

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