Heat Transfer Convection Heat Exchangers

What does the Nusselt number (Nu) represent in convection heat transfer?

The Nusselt number represents the enhancement of heat transfer through a fluid layer due to convection compared to pure conduction. A larger Nu indicates more effective convection.

What is the formula for the Nusselt number?

Nu=\frac{q_{conv}}{q_{cond}}=\frac{hL}{k}

where

h is the convective heat transfer coefficient

L is a characteristic length

k is the thermal conductivity of the fluid.

What is the formula for the Mach number?

Ma=\frac{V}{C}

where

V is the flow velocity

C is the speed of sound in the medium C=\sqrt{KRT}

Classification of Mach number

Mach Number	Name
< 0.8	Subsonic
0.8 - 1.2	Transonic
1	Sonic
1.2 - 1.5	Supersonic
5 - 10	Hypersonic
10 - 25	High Hypersonic
> 25	Re-entry Speed

What is the formula for Reynolds Number?

Re=\frac{\rho VL}{\mu_{d}}=\frac{\rho VD}{\mu_{d}}=\frac{VD}{\mu_{k}}

where

\rho is the fluid density

V is the flow velocity

L is a characteristic length

\mu_{d} is the dynamic viscosity of the fluid (Pa-s, PSI-s with force)

\mu_{k} is the kinematic viscosity of the fluid (m²/s, in²/s without force)

Characteristics of Flow by Reynolds Number

Re	Characteristics of Flow
< 2000	Laminar, Critical at 2000
2000 - 4000	Transitional
> 4000	Turbulent

Dynamic Viscoscity

Determines the amount of resistance to shear stress, with force

Unit: Pa-s, Dyne-s/cm² (poise), psi-s

\mu_{d}=\frac{\tau}{\frac{dv}{dy}}

Where

\tau is shear stress

\frac{dv}{dy} is velocity gradient V/L

Kinematic Viscoscity

Ratio of the dynamic viscosity of the fluid to the mass density, without force

Unit: m²/s, cm²/s (stoke), in²/s

\mu_{k}=\frac{\mu_{d}}{\rho}

Where

\mu_{d} is dynamic viscosity

\rho is density

AMTD Formula

AMTD=\frac{\Delta T_{A}+\Delta T_{B}}{2}

Where

\Delta T_{A}=T_1-T_4

\Delta T_{B}=T_2-T_3

LMTD Formula

LMTD=\frac{\Delta T_{A}-\Delta T_{B}}{\ln\left(\frac{\Delta T_{A}}{\Delta T_{B}}\right)}

Where

\Delta T_{A}=T_1-T_4

\Delta T_{B}=T_2-T_3

Heat Formulas

Q=mc_{p}\Delta T=U\cdot A\cdot LMTD

c_{p,water}

c_{p,water}=4.187\frac{kJ}{\operatorname{kg}\cdot K}=1\frac{BTU}{\operatorname{lb}\cdot R}

c_{p,air}

c_{p,water}=1.0062\frac{kJ}{\operatorname{kg}\cdot K}