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# Numerical investigations on the difference between aiding and opposing flows in the developing regime of laminar mixed convection in vertical tubes

Date Issued

01-01-2023

Author(s)

Gorai, Somenath

Das, Sarit K.

Samanta, Devranjan

Abstract

The present article discusses the numerical simulation results of laminar mixed convection flow in vertical tubes. A comparative analysis of the thermal and hydrodynamic features of both buoyancy-assisted and opposed flows was performed for Reynolds number ((Formula presented.)), Grashof number ((Formula presented.)) and Richardson number ((Formula presented.)) with uniform heat flux boundary condition. 2-D axisymmetric steady state simulations were carried out for a length-to-diameter ((Formula presented.)) ratio of (Formula presented.) with water as the working fluid. Numerical simulations were performed by employing SIMPLE scheme for pressure–velocity coupling in momentum equations and second order UPWIND scheme for solving energy equations. In case of assisting flow ((Formula presented.)), at fully developed state the centerline velocity decreases, and velocity is increased near the tube wall due to heat flux induced free convection. With increasing heat flux, the decrement in centerline velocity compared to the no-heat flux condition increases. Further, with increasing heat flux, the increase in friction factor and Nusselt number was observed. Therefore, at the same (Formula presented.) the variation of heat flux led to unique velocity profiles and temperature gradients. The variation of centerline velocity and temperature in developing region was also studied. While centerline temperature was monotonically increasing with length, the centerline velocity increased up to a maximum in the developing region and then attained the steady state at a lower value in the fully developed state. Subsequently we studied the dependence of (Formula presented.) on the hydrodynamic and thermal features. For constant (Formula presented.) friction factor and Nusselt number was observed to increase with increase in (Formula presented.) from 0.1 to 1.5 range. At fixed (Formula presented.) variation of heat flux leads to variation of (Formula presented.) or (Formula presented.) Hence, the buoyancy effect has a significant role in the entrance length development. The hydrodynamic entry length after an initial increase, attained an almost constant value with increasing (Formula presented.) On the other hand, the thermal entry length exhibited a decreasing trend with increasing (Formula presented.) Similarly, at constant (Formula presented.) Nusselt number increased with increasing (Formula presented.) for a range of 100–1000. It was evident that for a given (Formula presented.) and (Formula presented.) the heat transfer in the developing flow is always higher as that of the fully developed flow. Contrasting observations were observed for buoyancy-opposed flow. Velocity is accelerated at the center as compared to the tube wall in case of opposing flow for same (Formula presented.) and (Formula presented.) For a fixed (Formula presented.) the friction factor and Nusselt number decreased with increasing the (Formula presented.) Both the hydrodynamic and thermal entry length increases for opposing flows. Finally, we have developed correlations for fully developed friction factor ((Formula presented.)) with (Formula presented.) as well as (Formula presented.) and Nusselt number ((Formula presented.)) with (Formula presented.) for buoyancy-assisting and buoyancy-opposing flows. Two independent correlations are also produced for (Formula presented.) with Graetz number ((Formula presented.)) for developing and fully developed regimes in both assisting as well as opposing flows.

Volume

84