Problem $2\mathrm{.}6$ Consider axi$-$symmetric, laminar flow of an incompressible, constant$-$property

fluid in a heated tube $($see Figure P $2\mathrm{.}6).$ Write the steady$-$state mass, momen$-$

tum, and energy conservation equations, and nondimensionalize them, using the

following definitions:

$u^{**}=\frac{u}{U_m},v^{**}=\frac{v}{U_m}R{e}_{D}Pr,r^{**}=\frac{r}{R_0},$

$x^{**}=\frac{\frac{x}{R_0}}{R_{0}Pr},P^{**}=\frac{P-P_1}{U_m^{2}Pr},=\frac{T-T_s}{T_{in}-T_s},$

where $R{e}_D=U_m\frac{2R_0}{}$ and $U_m$ represents the mean velocity.