This document discusses several dimensionless numbers used in heat transfer calculations, including the Grashof number, Biot number, and Nusselt number. The Grashof number provides criteria for determining laminar or turbulent fluid flow in natural convection. The Biot number is a ratio of heat transfer resistances inside and at a body's surface used to determine if temperature gradients are important inside the body. The Nusselt number represents the enhancement of heat transfer through convection relative to conduction across a fluid layer.

1. Subject:
Heat Transfer
Name:
Hafiz Luqman Khalil
Roll No:
11053123-032

2. Topic:
DIMENSIONLESS
NUMBERS

3.  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.

4. 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∞ )Lc
3 / 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).

5. • The Grashof number provides the main
criteria in determining whether the fluid flow is
laminar or turbulent in natural convection.
• For vertical plates, for example, the critical
Grashof number is observed to be about 109.
Therefore, the flow regime on a vertical plate
becomes turbulent at Grashof numbers greater
than 109. When a surface is subjected to
external flow, the problem involves both
natural and forced convection. The relative
importance of each mode of heat transfer is

6. determined by the value of the coefficient
GrL /ReL
2.
• Natural convection effects are negligible if
GrL /ReL
2 << 1, forced convection dominates.
Forced convection effects are negligible if
GrL /ReL
2 >> 1, free convection dominates.
• Both effects are equally significant and must
be considered if GrL /ReL
2 ≈ 1.
• It is used to calculate heat transfer in
natural convection, where fluid velocity
depends on buoyancy.

7. 2. BIOT NUMBER:
“Biot number (Bi) is the index of the ratio of heat
transfer resistances inside and at the surface of a
body.”
It is a dimensionless number used in heat transfer
calculations. It is named after the French Physicist
Jean-Baptiste Biot (1774–1862).

8. • 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.

9. • 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

10. • Values of the Bi < 1 imply that the heat
conduction inside the body is much faster
than the heat convection away from its
surface, and temperature gradients are
negligible inside of it.
• The Biot number has a variety of applications,
including transient heat transfer and use in
extended surface heat transfer calculations.

11. 3. NUSSELT NUMBER
“Nusselt Number (Nu) the ratio between total heat
transfer in a convection dominated system and the
estimated conductive heat transfer.”
In convection studies, it is common practice to non
dimensionalize the governing equations and
combine the variables, which group together into
dimensionless numbers in order to reduce the
number of total variables. It is also common
practice to non dimensionalize the heat transfer
coefficient h with the Nusselt number, defined as,
Nu = h×L c / k

12. q conv = h ΔT
and
q cond = k ΔT / L
Taking their ratios give
q conv / q cond = h ΔT/ (k ΔT / L)
= hL / k
which is the Nusselt number (Nu).

13. • 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.

14. Thank You All!