Thermally Developing Laminar Liquid Flow and Heat Transfer in Microtubes at Slip Regime

Heat transfer enhancement is usually accompanied by an increase in pressure drop. With the implementation of the various drag reduction methods, the researches and applications of DR methods in heat transfer enhancement have attracted more and more attention. The research on drag reduction by introducing superhydrophobic surface shows that the slip regime plays an important role in drag reduction. This study numerically investigated thermally developing laminar liquid flow and heat transfer in microtubes at slip regime, with a hydraulic diameter of 200 μm, a constant heat flux of 105 W/m2, a Re of 100 and a slip length ls ranging from 2 μm to 20 μm. The dimensionless thermal entrance length increases with the increased slip length. The results show that microtube with slip boundary has the larger local Nusselt number and a longer thermal entrance length compared with available experimental data of non-slip boundary. Local and average Nusselt numbers are obtained, and start high and rapidly decrease with the increased dimensionless axial distance. Meanwhile, Nusselt number increases with the increased slip length. The correlations of the dimensionless thermal entrance length and local Nusselt number have mean absolute relative deviation of no more than 0.12% and 1.53% respectively, which can be used to optimize microchannel heat sinks.

Analytical solution and numerical simulation of the thermal entrance region problem for laminar flow through a circular pipe

In this paper, the assumptions implicited in Leveque’s approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge–Kutta fourth order (RK4) method. Finally, other important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail. A comparison with the previous study available in literature has been done and found an excellent agreement with the published data.

Exact Solutions to the Thermal Entry Problem for Laminar Flow Through Annular Ducts

The thermal entrance region for laminar-forced convection of a Newtonian fluid in an annular tube is solved by separation of variables using as many eigenvalues and eigenfunctions as needed to report exact results for a specified range of Graetz numbers. Results for the local and average Nusselt numbers are calculated for a wide range of inner to outer wall radius ratios and for convection to either the inner or outer wall, when the opposing wall is adiabatic. The present benchmark results are utilized to critically examine the accuracy of previous extended Lévêque series solutions that are convergent for short axial distances, and Graetz series solutions that are convergent for long axial distances, and to examine the performance of a new correlation for convection in annular tubes.

Numerical Investigation of Air-Side Heat Transfer and Pressure Drop Characteristics of a New Triangular Finned Microchannel Evaporator with Water Drainage Slits

The present study investigated a new microchannel profile design encompassing condensate drainage slits for improved moisture removal with use of triangular shaped plain fins. Heat transfer and pressure drop correlations were developed using computational fluid dynamics (CFD) and defined in terms of Colburn j-factor and Fanning f-factor. The microchannels were square 2.00 × 2.00 mm and placed with 4.50 mm longitudinal tube pitch. The transverse tube pitch and the triangular fin pitch were varied from 9.00 to 21.00 mm and 2.50 to 10.00 mm, respectively. Frontal velocity ranged from 1.47 to 4.40 m·s−1. The chosen evaporator geometry corresponds to evaporators for industrial refrigeration systems with long frosting periods. Furthermore, the CFD simulations covered the complete thermal entrance and developed regions, and made it possible to extract virtually infinite longitudinal heat transfer and pressure drop characteristics. The developed Colburn j-factor and Fanning f-factor correlations are able to predict the numerical results with 3.41% and 3.95% deviation, respectively.