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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.
Newton’s Law of Cooling
𝑄𝑐𝑜𝑛𝑣 = ℎ𝐴𝑠 𝑇𝑠 − 𝑇∝
ℎ 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
• It is a dimensionless number.
• It is also known as Dimensionless Convective heat Transfer
Coefficient.
• It represents the enhancement of heat transfer due to bulk fluid
motion over a surface with respect to the heat transfer by
conduction.
𝑁𝑢 =ℎ𝐿𝑐λ
The Flow Regimes
The Reynold Number
• It is a dimensionless number.
• It is the ratio of Inertia Forces to the Viscous Forces in a flowing
fluid.
• The value of the Reynold’s Number indicates whether the flow is
laminar or turbulent.
• The value of Reynold’s Number above which the flow corresponds to
turbulent flow is called Critical Reynold’s Number.
• The value of Critical Reynold’s Number depends on the geometry and
flow conditions.
• Typical value of Critical Reynold’s Number over a flat plate = 5 × 105
𝑅𝑒 =𝑉𝐿𝑐ν
ν is the Kinematic Viscosity of the fluid ν =𝜇
𝜌,
Where 𝜇 is the dynamic (or shear) viscosity.
The Boundary Layer
The Prandtle Number
• It is a dimensionless number.
• It is the ratio of Momentum Diffusivity (Kinematic Viscosity) to
Thermal Diffusivity.
• It is the relative thickness of velocity and thermal boundary layers.
𝑃𝑟 =ν
𝛼=𝜇𝐶𝑝λ
Relationship between Dimensionless Numbers
𝑁𝑢 = 𝐶𝑅𝑒𝑚𝑃𝑟𝑛
For Forced Convection over a flat plate due to flow parallel to
the plate:
𝑁𝑢 = 0.664𝑅𝑒 1 2𝑃𝑟 1 3a) Laminar Flow:
𝑁𝑢 = 0.037𝑅𝑒 4 5𝑃𝑟 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 20°C. If it has a steady state temperature of
32°C what is the heat transfer coefficient?
𝑞 = 100 [ 𝑊 𝑚2]
𝑞 = ℎ 𝑇𝑝 − 𝑇𝑎
𝑇𝑝 = 305[𝐾]
𝑇𝑎 = 293[𝐾]
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, 𝐶𝑝 = 1.005 [kJ.kg-1.K-1]. If the thermal conductivity
of air at that temperature is λ = 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]?
𝐿𝑐 = 0.1 [𝑚]
𝑉 = 1 [ 𝑚 𝑠]𝑅𝑒 =
𝜌𝑉𝐿𝑐𝜇
𝑃𝑟 =𝜌𝐶𝑝λ
𝑁𝑢 = 0.664𝑅𝑒12𝑃𝑟
13
Numerical Exercise
1. Find out the thermal resistance per unit length of a plastic
insulating tube having internal radius 𝑟1 = 0.001 [𝑚] and external
radius 𝑟2 = 0.0015 [𝑚]. The thermal conductivity of the plastic is
λ = 0.25 [𝑊.𝑚−1. 𝐾−1].
𝑟1
𝑟2
𝑄 = λ 2𝜋𝑟𝐿𝑑𝑇
𝑑𝑟
1
2𝜋𝐿λ
𝑟1
𝑟2 𝑄
𝑟𝑑𝑟 =
𝑇1
𝑇2
𝑑𝑇
𝑄 =2𝜋𝐿λ∆𝑇
ln𝑟2𝑟1
𝑅𝑐𝑦𝑙 =∆𝑇
𝑄=ln
𝑟2𝑟1
2𝜋𝐿λ