Optimal discrete distribution of heat flux elements for in-tube laminar forced convection

A new technique is proposed to enhance the heat transfer from a discretely heated pipe to a developing laminar fluid flow. Unlike the common heating situation where the fluid is continuously heated along the pipe wall with uniform heat flux, the proposed technique consists in heating the fluid with stepwise distributed heat flux, namely by placing insulated segments between the heated segments. Applying this technique, the effective length of the thermal entrance region is enlarged and as a result, the average heat transfer is invigorated. In order to maximize the heating performance, an optimal placement of the insulated segments between the heated segments is calculated according to constructal design. This serves to describe the optimal stepwise distribution of the heat flux. Owing that the total heat load is considered fixed, the maximization of the heating performance translates into the minimization of the peak temperature (‘hot spot’) of the pipe wall. The analytical results demonstrate that the optimal location of the insulated segments along with the reduction of the peak temperature strongly depend on the Graetz number. It is also shown that for intermediate values of the Graetz number, the peak temperatures are remarkably reduced in response to the optimal placement of the insulated/heated segments.