CONVECTION HEAT TRANSFER

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Introduction• Convection involves the transfer of heat

by the motion and mixing of "macroscopic" portions of a fluid

• This macroscopic motion is same as flow of a fluid past a solid boundary.

• The term natural convection is used if this motion and mixing is caused by density variations resulting from temperature differences within the fluid.

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• The term forced convection is used if this motion and mixing is caused by an outside force, such as a pump. • Heat transfer by convection is more difficult to analyze than heat transfer by conduction

• No single property of the heat transfer medium, such as thermal conductivity, can be defined to describe the mechanism.

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• Heat transfer by convection varies from situation to situation (upon the fluid flow conditions), and it is frequently coupled with the mode of fluid flow.

• In practice, analysis of heat transfer by

convection is treated empirically (by direct observation).

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Convection heat transfer is treated empirically, because of the factors that affect the stagnant film thickness:

Fluid velocity Fluid viscosity Heat flux Surface roughness Type of flow (single-phase/two-phase)

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bs TThAQ

Newton’s law of cooling suggests a basic relationship for heat transfer by convection:

h is called as Convection Heat Transfer Coefficient, W/m2K

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• Convection involves the transfer of heat between a surface at a given temperature (Ts) and fluid at a bulk temperature (Tb).

• The exact definition of the bulk temperature (Tb) varies depending on the details of the situation.

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• For flow adjacent to a hot or cold surface, Tb is the temperature of the fluid "far" from the surface.

• For boiling or condensation, Tb is the saturation temperature of the fluid.

• For flow in a pipe, Tb is the average temperature measured at a particular cross-section of the pipe.

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Local Convection Heat Transfer

Consider convection heat transfer as a fluid passes over a surface of arbitrary shape:

Apply Newton’s law cooling to a local differential element with length dx.

TTTThq ss ''

h is called as Local Convection Heat Transfer Coefficient, W/m2K9

Types of convection

• Free convection If the motion is mainly due to the density

variations associated with temperature gradientswith in the fluid called as free Convection.

• Forced convection In this the fluid motion is principally Produced by some superimposed velocity field(like a fan, a blower or a pump). 10

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This fluid layer then acts to retard the motion of particles of next fluid layer and so on, until a distance y = from the surface reaches, where these effects become negligible and the fluid velocity u reaches the free stream velocity u∞. as a result of frictional effects between the fluid layers, the local fluid velocity u will vary from x =0, y = 0 to y = .

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The total heat transfer rate q is

avgSavg

A

s TAhdAqqs

''

Where, havg is the average convection heat transfer coefficient for the entire surface.

avg

A

ss

avg T

dAqA

h s

''1

sA

sss

avg dATTA

T1

where

s

s

A

ss

A

s

avgdATT

dAq

h

''Therefore How to Evaluate q’’?

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• The fluid packets close to a solid wall come to thermal equilibrium with the wall.

• The fluid particles will exchange maximum possible energy flux with the solid wall.

• A Zero temperature difference exists between wall and fluid packets at the wall.

• A small layer of fluid particles close the the wall come to Mechanical, Thermal and Chemical Equilibrium With solid wall.

• Fundamentally this fluid layer is in Thermodynamic Equilibrium with the solid wall.

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Example: A heavy lubricating oil (µ = 0.8 N.s/m2 , k = 0.15 W/m. K) flows in the clearance between a shaft and its bearing. If the bearing and the shaft are kept at 10°C and 30°C respectively and the clearance between them is 2mm,determine the maximum temperature rise and the heat flux to the plates for a velocity U = 6 m/s.

Example:

For the flow system in ex.7.1 calculate the local heat transfer coefficient at x= 0.4m and the heat transferred from the first 40 cm of the plate.

Fundamental Aspects of Convection

• How to evaluate q’’ ?

• How the heat is transferred from solid to the first layer of the fluid?

• Is this a part of convection?

• What is the temperature of the fluid particle, just adjacent to the wall?

• What part of the fluid domain is under pure convection transfer?

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Concept of Solid Fluid Interaction : Maxwell’s Theory

Diffuse reflection

U2

U U

Φ

U2

Φ

U1

U1

Φ

U2

Specular reflection

• Perfectly smooth surface (ideal surface) Real surface

• The convective heat transfer is defined for a combined solid and fluid system.

• The fluid packets close to a solid wall attain a zero relative velocity close to the solid wall : Momentum Boundary Layer.

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