Heat Transfer by Convection
What is Convection?
Convection is a mode of heat transfer between a solid (or liquid)
surface and its adjacent liquid or gas that is in bulk motion. It
involves combined effect of conduction and fluid motion.
Newtonโs Law of Cooling
๐๐๐๐๐ฃ = โ๐ด๐ ๐๐ โ ๐โ
โ is the Convection Heat Transfer Coefficient
Types of Convection
1. Forced Convection:- when the fluid is forced to flow over the surface by external means
such as a fan, pump or wind.1. Natural (or Free) Convection:
- when fluid flow is caused by buoyancy forces that are induced by density differences due to variation of temperature of the fluid.
The Nusselt Number
โข It is a dimensionless number.
โข It is also known as Dimensionless Convective heat Transfer
Coefficient.
โข It represents the enhancement of heat transfer due to bulk fluid
motion over a surface with respect to the heat transfer by
conduction.
๐๐ข =โ๐ฟ๐ฮป
The Flow Regimes
The Reynold Number
โข It is a dimensionless number.
โข It is the ratio of Inertia Forces to the Viscous Forces in a flowing
fluid.
โข The value of the Reynoldโs Number indicates whether the flow is
laminar or turbulent.
โข The value of Reynoldโs Number above which the flow corresponds to
turbulent flow is called Critical Reynoldโs Number.
โข The value of Critical Reynoldโs Number depends on the geometry and
flow conditions.
โข Typical value of Critical Reynoldโs Number over a flat plate = 5 ร 105
๐ ๐ =๐๐ฟ๐ฮฝ
ฮฝ is the Kinematic Viscosity of the fluid ฮฝ =๐
๐,
Where ๐ is the dynamic (or shear) viscosity.
The Boundary Layer
The Prandtle Number
โข It is a dimensionless number.
โข It is the ratio of Momentum Diffusivity (Kinematic Viscosity) to
Thermal Diffusivity.
โข It is the relative thickness of velocity and thermal boundary layers.
๐๐ =ฮฝ
๐ผ=๐๐ถ๐ฮป
Relationship between Dimensionless Numbers
๐๐ข = ๐ถ๐ ๐๐๐๐๐
For Forced Convection over a flat plate due to flow parallel to
the plate:
๐๐ข = 0.664๐ ๐ 1 2๐๐ 1 3a) Laminar Flow:
๐๐ข = 0.037๐ ๐ 4 5๐๐ 1 3a) Turbulent Flow:
Numerical Exercise
1. A flat plate is supplied with a constant heat flux of 100 [W/m2]
from bottom. The plate has 0.5m2 area and is kept in a room with
ambient temperature 20ยฐC. If it has a steady state temperature of
32ยฐC what is the heat transfer coefficient?
๐ = 100 [ ๐ ๐2]
๐ = โ ๐๐ โ ๐๐
๐๐ = 305[๐พ]
๐๐ = 293[๐พ]
Numerical Exercise
2. The air has the following properties at 27C: Density = 1.18
[kg.m-3], Dynamic Viscosity = 1.85X10-5 [kg.m-1.s-1], Specific
Heat capacity, ๐ถ๐ = 1.005 [kJ.kg-1.K-1]. If the thermal conductivity
of air at that temperature is ฮป = 0.026 [W.m-1.K-1], what is the
average Nusselt Number over a flat plate of dimension 10 cm X
10 cm when air is flowing parallel to its surface with a speed 1
[ms-1]?
๐ฟ๐ = 0.1 [๐]
๐ = 1 [ ๐ ๐ ]๐ ๐ =
๐๐๐ฟ๐๐
๐๐ =๐๐ถ๐ฮป
๐๐ข = 0.664๐ ๐12๐๐
13
Numerical Exercise
1. Find out the thermal resistance per unit length of a plastic
insulating tube having internal radius ๐1 = 0.001 [๐] and external
radius ๐2 = 0.0015 [๐]. The thermal conductivity of the plastic is
ฮป = 0.25 [๐.๐โ1. ๐พโ1].
๐1
๐2
๐ = ฮป 2๐๐๐ฟ๐๐
๐๐
1
2๐๐ฟฮป
๐1
๐2 ๐
๐๐๐ =
๐1
๐2
๐๐
๐ =2๐๐ฟฮปโ๐
ln๐2๐1
๐ ๐๐ฆ๐ =โ๐
๐=ln
๐2๐1
2๐๐ฟฮป