---

In the present work, constructal design of annular finned tube has been studied. Geometrical parameters include fin diameter, fin thickness, fin pitch, tube outer diameter, tube length while physical parameters involve pressure drop number, Stanton number, fin-to-air conductivity ratio, and in-tube fluid-to- air conductivity ratio. The aim of this study is to enhance heat transfer by letting the geometrical degrees of freedom to morph. It was observed that at certain flow conditions, there exist optimal geometry and fin number for the finned tube construct in which its thermal resistance is minimum. Fin efficiency and tube-side convective heat transfer coefficient are higher at low pressure drops and Stanton numbers. In these conditions, analytical relationships were proposed to predict optimal heat transfer, optimal fin number and optimal geometry. It was seen that the optimal fin thickness-to-fin pitch ratio is merely dependent on the fin volume fraction; and it rises with the increase in fin volume fraction. Moreover, the optimum fin number is directly proportional to fin spacing – to- fin pitch ratio and inversely proportional to Stanton number. Furthermore, it was seen that in the range of parameters considered in this study, the tube with 3400 fins and aspect ratio of 0.63 has the most heat transfer rate.

---

Pumps consume about 20% of whole electricity power in the world. Centrifugal pump is one of the most common pumps that works by the transfer of angular momentum to the fluid. The behavior of such a fluid flow in the side chamber, may affect the pump performance. The side chamber is defined the free space between the fixed (pump casing) and the rotating (pump impeller) parts. Steady, fully 3D computations of the Reynolds-averaged Navier-Stokes equations using a commercial CFD code are conducted in order to study the flow field in the whole pump including both side chambers. Numerical results are validated by comparison with the existing experiments. The impact of fluid flow in hub and shroud side chambers with the volute is investigated qualitatively by using 2D stream lines. Evaluation of the empirical equations shows that the frictional torque may be decreased more than 10%, by using the proper gap size. Considering this situation, the changes in the flow pattern and the value of power loss resulting from friction in hub and shroud side chamber is studied. It reveals that the variation in friction depends on the initial flow pattern in cavity. Finally, in order to obtain the relationship between the power loss and the flow rate, nondimensional coefficients are derived. These coefficients show that the change in the power loss due to the volumetric flow rate, is the same as its change with the gap changing, but their slopes are not equal.