# Forced Convection for Internal Laminar Flow

Forced Convection for Internal Laminar Flow

The first analytical solution for laminar flow forced convection inside tubes was derived by Graetz in 1885. Here, the Mathematica built-in function NDSolve is used to plot the temperature profile versus radial position at different axial positions. Average fluid velocity and diffusivity can be selected by the user. The governing equation and boundary conditions are as follows:

21-=αr

v

avg

2

r

R

∂T

∂x

1

r

∂

∂r

∂T

∂r

T=0,x=0

0≤r≤R

T=1,x>0

r=R

∂T

∂r

r=0