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

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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