Q$3$: A constant$-$property inviscous liquid having the far upstream temperature $T_o$

and velocity $V$ flows steadily through an infinitely long tube of cross$-$sectional area

A and periphery $P.$ The wall thickness of the tube is negligible. The downstream

half of the tube is subjected to the constant heat flux $q^{\text{'}\text{'}}$; the upstream half is

insulated $($see Figure $2\mathrm{.}5).$ We wish to know the axial temperature distribution of

the liquid, based on a radially lumped analysis.

One$-$dimensional, Steady$-$State Condition

Chapter: Two

Solution

Figure $2\mathrm{.}5$: A constant$-$property liquid flows steadily through an infinitely long tube.

Consider the radially lumped, axially differential control volume shown in Figure

$2\mathrm{.}5.$ Let us apply the general laws to this control volume as follows.