Principal of convention

1. Principles of
Convection

2. Physical
Mechanism of
Convection
 Convection vs conduction
 Heat in liquids and gases
 Speed of heat transfer because of the motion of molecules
 Convection heat transfer depends on: - fluid properties dynamic
viscosity - thermal conductivity - density - specific heat - fluid
velocity - geometry and the roughness of the solid surface - the
type of fluid flow (such as being streamlined or turbulent).
 𝑄𝑐𝑜𝑛𝑣 = ℎ𝐴𝑠 𝑇𝑠 − 𝑇∞ 𝑊 - Newton’s law of cooling
 Convection heat transfer coefficient, h
 No – slip condition
 Velocity profiles
 No – temperature jump condition
 Pure conduction at solid fluid surface
 Convection heat transfer coefficient (cond. & conv.)

3. Nusselt
Number
 Nusselt number represents the enhancement of heat transfer
through a fluid layer as a result of convection relative to
conduction across the same fluid layer.

𝑞𝑐𝑜𝑛𝑣
𝑞𝑐𝑜𝑛𝑑
=
ℎ∆𝑇
𝑘∆𝑇 𝐿
=
ℎ𝐿
𝑘
= 𝑁𝑢
 < 𝑁𝑢 – effectiveness of convection
 Nu = 1 – pure conduction
 Heat flux, 𝑞 - the rate of heat flow per unit time per unit surface
area

4. Classification
of Fluid Flows
 Viscous versus Inviscid Flow
 Internal versus External Flow – open-channel flow
 Compressible versus Incompressible Flow
 Laminar versusTurbulent Flow
 Natural (or Unforced) versus Forced Flow
 Steady versus Unsteady (Transient) Flow
 One-,Two-, andThree-Dimensional Flows

5. Velocity
Boundary
Layer
 Velocity boundary layer is the region of the flow above the plate
bounded by a layer of thickness in which the effects of the viscous
shearing forces caused by fluid viscosity are felt.
 Upstream velocity
 Free stream velocity 𝑢∞
 Fluid velocity, u
 No – slip condition
 Boundary layer thickness, 𝛿: 𝑢 = 0.99𝑢∞
 Boundary layer region
 Inviscid flow region

6. Surface Shear
Stress
 Shear stress, 𝜏 – friction force per unit area.
 Newtonian fluids e.g. water, gasoline vs non-Newtonian fluids e.g.
blood, plastic fluids
Surface shear stress, 𝜏𝑠 = 𝜇
𝜕𝑢
𝜕𝑦 𝑦=0
(𝑁 𝑚2
) where 𝜇 – dynamic
viscosity of the fluid (𝑘𝑔 𝑚 . 𝑠)
 Kinematic viscosity, 𝜈 =
𝜇
𝜌
(𝑚2 𝑠) where 𝜌 - density
 Viscosity is a measure of a fluid’s resistance to flow, its related to
temperature (liquids and gases)
 Surface shear stress vs velocity profile (friction coefficient,
upstream velocity, friction force, surface area)

7. TheThermal
Boundary
Layer
 Thermal boundary layer develops when a fluid at a specified
temperature flows over a surface that is at a different
temperature
 Thermal boundary layer, 𝛿𝑡 - is the distance from the surface
at which the temperature difference 𝑇 − 𝑇𝑠 = 0.99(𝑇∞ − 𝑇𝑠) .
 𝑇𝑠 = 0; 𝑇 = 0.99𝑇∞vs velocity boundary layer (𝑢 = 0.99𝑢∞)
 Thickness of layer increases with flow direction
 Boundary layer and convection heat transfer
 Velocity boundary layer andThermal boundary layer

8. Prandtl
Number
 Prandt number describes the relative thickness of the velocity and
thermal boundary layers
 𝑃𝑟 =
𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 ℎ𝑒𝑎𝑡
=
𝜐
∝
=
𝜇𝐶𝑝
𝑘
 Pr = 1 – gases
 Pr << 1 – liquid metals
 Pr >> 1 – oils
 Thermal boundary layer vs velocity boundary layer

9. Laminar and
Turbulent
Flows
 Laminar vs turbulent flow
 Characteristics of lamina flow
 Smooth streamlines – no
velocity fluctuations
 Highly ordered motion
 Characteristics of turbulent
flow
 Velocity fluctuations
 Highly disordered motion
 Transition
 Velocity profile (lamina/turbulent)
 Turbulent boundary layer
(laminar sub layer, buffer layer
and turbulent layer)
 Turbulent flow – heat +
momentum – friction –
convection heat transfer
 Design of heat transfer
coefficients - cost say pumps

10. Reynolds
Number
 Reynolds number is the ratio of inertia forces to vicious forces
(upstream velocity, characteristic length, kinematic viscosity
 Factors affecting transition from lamina to turbulent flow: -
surface geometry - surface roughness – free stream velocity -
surface temperature – type of fluid
 Re >
 Re <
 Inertia forces vs viscous – turbulence vs lamina
 Critical Reynolds number, 𝑅𝑒𝑐𝑟

11. Ref:
 Yunus A. Cengel, (2000). HeatTransfer,A PracticalApproach,
Second Edition.