Subject:Heat Transfer

Name:Hafiz Luqman Khalil

Roll No:11053123-032

Topic:DIMENSIONLESS

NUMBERS

These are defined as those numbers which have

no dimensions.

These are pure numbers.

For Example:

Grashof Number (Gr)

Biot Number (Bi)

Nusselt Number (Nu)

Prandtl Number (Pr) etc.

1. GRASHOF NUMBER:

The Grashof number Gr is a measure of the

relative magnitudes of the buoyancy force and the

opposing viscous force acting on the fluid.

Gr = gβ ( Ts-T∞ )Lc3 / υ2

Flow regime of heat in forced convection is

governed by Renold Number (Re) but in natural

convection it is governed by Grashof Number (Gr).

• The Grashof number provides the maincriteria in determining whether the fluid flow islaminar or turbulent in natural convection.

• For vertical plates, for example, the criticalGrashof number is observed to be about 109.Therefore, the flow regime on a vertical platebecomes turbulent at Grashof numbers greaterthan 109. When a surface is subjected toexternal flow, the problem involves bothnatural and forced convection. The relativeimportance of each mode of heat transfer is

determined by the value of the coefficient

GrL /ReL2.

• Natural convection effects are negligible if

GrL /ReL2 << 1, forced convection dominates.

Forced convection effects are negligible if

GrL /ReL2 >> 1, free convection dominates.

• Both effects are equally significant and must

be considered if GrL /ReL2 ≈ 1.

• It is used to calculate heat transfer in

natural convection, where fluid velocity

depends on buoyancy.

2. BIOT NUMBER:

“Biot number (Bi) is the index of the ratio of heattransfer resistances inside and at the surface of abody.”

It is a dimensionless number used in heat transfercalculations. It is named after the French PhysicistJean-Baptiste Biot (1774–1862).

• The Biot number is defined as:

Where,

• h = film coefficient or heat transfer coefficient or convective heat transfer coefficient

• LC = characteristic length, which is commonly defined as the volume of the body divided

by the surface area of the body, such that

• kb = Thermal conductivity of the body.

• The metal sphere may be large, causing the characteristic length to increase to the point that the Bi > 1 Now, thermal gradients within the sphere become important, even though the sphere material is a good conductor.

• Equivalently, if the sphere is made of a thermally insulating (poorly conductive) material, such as wood or styrofoam, the interior resistance to heat flow will exceed that of the fluid/sphere boundary, even with a much smaller sphere. In this case, again, the Bi > 1

• Values of the Bi < 1 imply that the heatconduction inside the body is much fasterthan the heat convection away from itssurface, and temperature gradients arenegligible inside of it.

• The Biot number has a variety of applications,including transient heat transfer and use inextended surface heat transfer calculations.

3. NUSSELT NUMBER

“Nusselt Number (Nu) the ratio between total heattransfer in a convection dominated system and theestimated conductive heat transfer.”

In convection studies, it is common practice to nondimensionalize the governing equations andcombine the variables, which group together intodimensionless numbers in order to reduce thenumber of total variables. It is also commonpractice to non dimensionalize the heat transfercoefficient h with the Nusselt number, defined as,

Nu = h×L c / k

q conv = h ∆T

and

q cond = k ∆T / L

Taking their ratios give

q conv / q cond = h ∆T/ (k ∆T / L)

= hL / k

which is the Nusselt number (Nu).

• The Nusselt Number (Nu)represents the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer. The larger the Nusselt Number, the more effective the convection.

• A Nusselt Number of Nu = 1 for a fluid layer represents heat transfer across the layer by pure conduction.

Thank You All!