Convection Heat Transfer

Abstract

There are only two fundamental physical modes of energy transfer, conduction and radiation. In conduction, energy slowly diffuses through a medium from a point of higher temperature to a point of lower temperature, whereas in radiation, energy is transmitted with the speed of light by electromagnetic waves (or photons), and a transmitting medium is not required. Thus from a conceptual viewpoint, convection is not a basic mode of heat transfer. Instead, it occurs by a combined effect of conduction (and/or radiation) and the motion of the transmitting medium.

Nomenclature, Greek Letters and Subscripts

A

Area (m²)

A _s

Surface area (m²)

Bi

Biot number

C

Molar concentration (kmol/m³)

C _f

Friction coefficient

c _p

Specific heat at constant pressure (J/kg⋅K)

c _v

Specific heat at constant volume (J/kg⋅K)

D

Diameter (m)

D _AB

Binary mass diffusion coefficient (m²/s)

D _h

Hydraulic diameter (m)

E

Specific internal or thermal (sensible) energy (J/kg)

F _BX , F _BY , F _BZ

Components of the body force per unit volume (N/m³)

F _SX , F _SY , F _SZ

Components of the surface force

F

Friction factor

Gr

Grashof number

G

Gravitational acceleration (m/s²)

H

Convection heat transfer coefficient (W/m² ⋅K)

$\overline{h}$

Average convection heat transfer coefficient (W/m² ⋅K)

h _m

Convection mass transfer coefficient (m/s)

h _rad

Radiation heat transfer coefficient (W/m² ⋅K)

K

Thermal conductivity (W/m⋅K)

L

Characteristic length (m)

Le

Lewis number

M

Mass (kg)

Ṁ

Mass flow rate (kg/s)

ṁ″

Mass flux (kg/m² ⋅ s)

ṁ ^″ _i

Mass flux of species i (kg/m² ⋅ s)

Nu

Nusselt number

P

Perimeter (m)

Pe

Peclet number (RePr)

Pr

Prandtl number

P

Pressure (N/m²)

Q

Energy generation rate per unit volume (W/m³)

${\dot{q}}^{\prime }$

Heat transfer rate per unit length (W/m)

${\dot{q}}^{{\prime\prime} }$

Heat flux (W/m²)

R

Universal gas constant

Ra

Rayleigh number

Re

Reynolds number

r, ϕ, z

Cylindrical coordinates

r, θ, ϕ

Spherical coordinates

Sc

Schmidt number

Sh

Sherwood number

St

Stanton number

T

Temperature (K)

T

Time (s)

U

Overall heat transfer coefficient (W/m² ⋅K)

u, v, w

Mass average fluid velocity components (m/s)

x, y, z

Rectangular coordinates (m)

x _fd,h

Hydrodynamic entry length (m)

x _rd,t

Thermal entry length (m)

α

Thermal diffusivity (m²/s)

β

Volumetric thermal expansion coefficient (K^–1)

δ

Hydrodynamic boundary layer thickness (m)

δ _t

Thermal boundary layer thickness (m)

δ _d

Mass transfer boundary layer thickness (m)

η

Similarity variable

θ

Zenith angle (rad)

ϕ

Azimuthal angle (rad)

μ

Viscosity (kg/s⋅m)

ν

Kinematic viscosity (m²/s)

ρ

Mass density (kg/m³)

σ _ij

Components of the stress tensor (N/m²)

ψ

Stream function (m²/s)

τ

Shear stress (N/m²)

A,B

Species in a binary mixture

Conv

Convection

D

Diameter; drag

F

Fluid properties

Fd

Fully developed conditions

H

Heat transfer conditions

H

Hydrodynamic; hot fluid

L

Based on characteristic length

Max

Maximum fluid velocity

S

Surface conditions

Sur

Surroundings

T

Thermal

X

Local conditions on a surface

∞

Free stream conditions