Convection Heat TransferInstructor: M.H.Saidi

PhD, Professor

School of Mechanical Engineering

Sharif University of Technology

Fall 2011

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Lecture #4

Convection Heat Transfer

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Convection Heat Transfer

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:Summary of second session

vScale Analysis

vIntroduction to boundary layer flow

vThis session: Laminar Boundary Layer Flow(Velocity and Temperature fields)

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

CONCEPT OF BOUNDARY LAYER

In the d L region, then, the longitudinal momentumequation (8) accounts for the competition between three typesof forces:

From the mass continuity equation, we have:

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

CONCEPT OF BOUNDARY LAYER

If the boundary layer region d L is slender(not Bluff), suchthat:

The last scale in Eq. (14) is the scale most representative of thefriction force. Neglecting the term at the expense of the

term in the x momentum Equation (8) yields:

Similarly the y momentum equation reduces to:

2 2/U x∂ ∂2 2/U y∂ ∂

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

CONCEPT OF BOUNDARY LAYER

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

CONCEPT OF BOUNDARY LAYER

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

CONCEPT OF BOUNDARY LAYER

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

1/ 2Re 1L >>

2/( / 2)fC vτ ρ=

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Tδ δ<<Tδ δ>>

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Tδ δ>>

1<<

>>

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Tδ δ>>

Tδ δ

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Tδ δ>>

Tδ δ>> 1/ 2 1Pr <<

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Tδ δ<<

:

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

VELOCITY AND THERMAL BOUNDARY LAYERS

Tδ δ<<

Tδ δ<< 1/ 3 1Pr >>

Convection Heat Transfer

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LAMINAR BOUNDARY LAYER FLOW

Concept of Reynolds number

Convection Heat Transfer

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:Next session

vLaminar Boundary Layer Flow: Integral Solution