Heat Transfer of Turbulent Gaseous Flow in Microtubes with Constant Wall Temperature

Experiments were conducted with nitrogen gas flow in two microtubes with constant wall temperature, made of stainless-steel and copper with diameters of 524 and 537 micrometers, to measure the total temperature at the inlet and outlet and quantitively determine the heat transfer rates. The temperature differences between the inlet and the wall were maintained at 3, 5 and 10 K by circulating water around the inlet and the wall. The stagnation pressures were controlled such that the flow with atmospheric back pressure reached Reynolds numbers as high as 26000. To measure the total temperature, a polystyrene tube with thermally insulated exterior wall containing six plastic baffles, was attached to the outlet. Heat transfer rates were obtained from the gas enthalpy difference by using the pressures and the total temperatures measured at the inlet and outlet. Heat transfer rates were also compared with those obtained from the ideal gas enthalpy using the measured total temperatures and from the Nusselt number for incompressible flow. It was found that the measured total temperature at the microtube outlet was higher than the wall temperature. Also, the heat transfer rates calculated from the total temperature difference were higher than the values obtained from the incompressible flow theory.

Non-isothermal rarefied gas flow in microtube with constant wall temperature

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.

Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

Numerical study of heat transfer of laminar air flow in perforated trapezoidal corrugated plate-fin ducts

A novel trapezoidal corrugated perforated fin core is proposed in this study. The porosity of the fin surface, or perforations, is indicated to promote the unusual behavior of increasing the heat transfer coefficient, while reducing the friction factor with respect to its non-perforated counterpart, primarily due to surface transpiration, which leads to better flow mixing and successive boundary layer disturbances. This allows the heat exchanger to be built much more compact with a smaller volume and a front area. To highlight this, the results of the computational simulations for velocity and temperature fields in typical trapezoidal corrugated perforated plate-fin ducts are presented. Constant property, fully or periodically developed laminar airflow [Formula: see text] with Reynolds number [Formula: see text] passing through inter-fin passages, with fins at constant wall temperature T, in which the fin walls have perforations equally spaced along the length of the duct, is considered and a parametric study of the effects of the duct geometry, including the variation of the inclination angle [Formula: see text] of the diverging plane, the aspect ratio of the channel or period length and fin density effects [Formula: see text] and the converging-diverging ratio of the plate [Formula: see text], is performed. The results of the Fanning friction factor and the Nusselt number over the wide range of the Reynolds number, which was treated in this study, show the improved performance. The improvement is assessed quantitatively by the area goodness factor ( j/ f) relative to Re, comparison with simple flat channels. It is seen that increasing ϕ to [Formula: see text] improves the core performance; As ϕ increases beyond [Formula: see text], performance starts to decrease. j/ f increases with increasing λ; and λ = 3.6 acts as an inflection point. It is better to have a large λ value for lower Re range and vice versa. As ε increases, the performance increases; so, the highest area goodness factor value occurs at [Formula: see text]. In case 11, with [Formula: see text], [Formula: see text], and [Formula: see text] at Re = 200, compared to the non-perforated channel, the friction factor decreases about 11%, and the area goodness factor increases about 72%. Thus, the area goodness factor of the perforated case reaches 0.37.

CFD study of Convective Heat Transfer of Water Flow Through Micro-Pipe with Mixed Constant Wall Temperature and Heat Flux Wall Boundary Conditions

The dissipation of heat in tiny engineering systems can be achieved with fluid flow through micro pipes. They have the advantage of less volume to large surface ratio convective heat transfer. There are deep-rooted analytical relations for convective heat transfer available for fluid flow through macro size pipes. But differences exist between the convective heat transfer for fluid flow through macro and micro pipes. Therefore, there is a good scope of work in micro convection heat transfer to study the mechanism of fundamental flow physics. There have been studies with either constant heat flux wall boundary conditions or constant wall temperature boundary conditions with constant and variable property flows. In this article, first, the numerical simulations are validated with the experimental data for 2D axisymmetric conventional pipe with pipe diameter of 8 mm is taken with laminar, steady, and single-phase water flows with constant wall heat flux boundary condition of 1 W/cm2. The computed Nusselt number is compared to the experimental results at different Reynolds numbers of 1350, 1600 and 1700. In the next study, three-dimensional micropipe laminar flow is studied numerically using water with an inlet velocity of 3 m/s and pipe diameter of 100 µm. The mixed wall boundary conditions with upper half pipe surface subjecting to constant wall temperature of 313 K and lower half surface subjecting to 100 W/cm2 are used in the simulations. The focus of research would be to consider the effect of temperature-dependent properties like thermal conductivity, viscosity, specific heat, and density (a combined effect we call it as variable properties) on micro-pipe flow characteristics like Nusselt number at mixed wall boundary conditions and compare it with the constant property flows. The conventional pipe showed no significant difference with variable and constant property flows with different Reynolds numbers. On contrary the flow through 3D micropipe shows that the Nusselt number with variable property flows is less as compared to the constant property flows.

Heat Transmission Reinforcers Induced by MHD Hybrid Nanoparticles for Water/Water-EG Flowing over a Cylinder

The assumptions that form our focus in this study are water or water-ethylene glycol flowing around a horizontal cylinder, containing hybrid nanoparticles, affected by a magnetic force, and under a constant wall temperature, in addition to considering free convection. The Tiwari–Das model is employed to highlight the influence of the nanoparticles volume fraction on the flow characteristics. A numerical approximate technique called the Keller box method is implemented to obtain a solution to the physical model. The effects of some critical parameters related to heat transmission are also graphically examined and analyzed. The increase in the nanoparticle volume fraction increases the heat transfer rate and liquid velocity; the strength of the magnetic field has an adverse effect on liquid velocity, heat transfer, and skin friction. We find that cobalt nanoparticles provide more efficient support for the heat transfer rate of aluminum oxide than aluminum nanoparticles.

Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study

The thermal entrance problem (also known as the classical Graetz problem) is studied for the complex rheological Carreau fluid model. The solution of two-dimensional energy equation in the form of an infinite series is obtained by employing the separation of variables method. The ensuing eigenvalue problem (S–L problem) is solved for eigenvalues and corresponding eigenfunctions through MATLAB routine bvp5c. Numerical integration via Simpson’s rule is carried out to compute the coefficient of series solution. Current problem is also tackled by an alternative approach where numerical solution of eigenvalue problem is evaluated via the Runge–Kutta fourth order method. This problem is solved for both flat and circular confinements with two types of boundary conditions: (i) constant wall temperature and (ii) prescribed wall heat flux. The obtained results of both local and mean Nusselt numbers, fully developed temperature profile and average temperature are discussed for different values of Weissenberg number and power-law index through graphs and tables. This study is valid for typical range of Weissenberg number W e ≤ 1 $\left(We\le 1\right)$ and power-law index n < 1 $\left(n{< }1\right)$ for shear-thinning trend while n > 1 $\left(n{ >}1\right)$ for shear-thickening behaviour. The scope of the present study is broad in the context that the solution of the said problem is achieved by using two different approaches namely, the traditional Graetz approach and the solution procedure documented in M. D. Mikhailov and M. N. Ozisik, Unified Analysis and Solutions of Heat and Mass Diffusion, New York, Dover, 1994.

An Experimental-Theoretical Study on Static Batch Sublimation with Laminar Flow and Constant Wall Temperature

The major features of a static batch sublimation process over a hot plate with constant temperature were investigated in an experimental-theoretical study. An experimental apparatus with a real-time display was built to sublimate dry ice blocks of different sizes, in either circular or rectangular geometries. When temperature of the hotplate was changed from -30 to 200 oC, heat transfer coefficient “hsub” decreased from 126 to 70 W/m2K, while thermal flux increased, linearly. Weight and area of the block had a positive/negative effects on heat transfer, respectively. In theoretical part, two “linear- gradient” and “cubic” models were developed by a combined mass-momentum-energy balance. The latter used Von Karman temperature profile, and in cases of circular and rectangular geometries could estimate “hsub” with 17.8 and 13.5 % average error. Linear-gradient was analytic, with similar accuracy in the circular case. The developed model are especially useful for design of sublimation equipment in purificationofthechemicals