Constant Surface Temperature Boundary Condition Research Articles

Turbulent melting characteristics of hybrid nano-enhanced molten salt phase change material in rectangular enclosure

The turbulent melting characteristics of hybrid nano-enhanced phase change material (HNEPCM) in a three-dimensional rectangular enclosure has been numerically investigated. The lower and upper walls are partially heated and cooled using constant surface temperature boundary condition and the other surfaces are specified with adiabatic boundary condition. The rectangular enclosure is filled with molten salt phase change material (PCM) of potassium nitrate (KNO3) with melting temperature of 334 °C. The transient melting rates of PCM are investigated by dispersing hybrid mono-dispersed spherical nanoparticles of Aluminum oxide (Al2O3) combined with Silicon dioxide (SiO2), Titanium dioxide (TiO2) and Multi-walled carbon nanotubes (MWCNT). The Rayleigh number (Ra) and particle volume fraction (ϕ) are varied in the range of 106≤Ra≤1010 and 2%≤ϕ≤5%. The turbulent phase change process of PCM is modeled using enthalpy–porosity approach with Lam–Bremhorst k−ϵ turbulence model. The three-dimensional governing equations are discretized using Finite difference technique and computations are carried out using Fortran 90 in-house code. The stronger thermal buoyancy force accelerates the melting rate and the melting pattern indicates the accumulation of large quantity of molten metal in the upper regions of the rectangular enclosure. The average melting velocity and turbulent kinetic energy of pure KNO3 PCM is increased by 51.17% and 77.84% by the addition of Al2O3−MWCNT hybrid nanoparticles. The impact of hybrid nanoparticles on the melting rate and thermal performance of PCM is significant in higher Rayleigh number flows than transitional flows. The present results are validated and are in close agreement with the benchmark experimental results.

The Stefan Problem With Internal Heat Generation in Spherical Coordinates

Abstract A weakly time-dependent equation for the evolution of the solid–liquid interface in spherical coordinates, driven by internal heat generation, is derived for constant surface temperature boundary conditions. The derivation comes by making an assumption that the interface moves slowly compared to the changes in the temperature so that the technique of separation of variables may be applied for Stefan numbers less than one. Under this approximation, we can separate the nonhomogeneous heat diffusion equation into transient and steady-state terms, and then integrate to get the temperature relations. With the temperature equations in hand, the derivatives are inserted into the interface equation giving a first-order differential equation for the location of the solid–liquid interface as a function of time. The results are compared to a previously derived quasi-static solution and a numerical simulation generated using the method of catching of the front. This method allows for direct tracking of a moving boundary via the calculation of the time it takes to move from node to node in a discretized grid characteristic of classical finite difference methods. Plots of the interface evolution show excellent agreement between the three methods, especially for lower Stefan numbers. The quality of the approximation decreases as the Stefan number increases, but the model is more accurate than the previously studied quasi-static model. For the Stefan numbers St = 1.0 and 10.0, the weakly time-dependent solutions are in better agreement with the numerical results than the quasi-static solutions.

Impact of Additive Manufacturing on Internal Cooling Channels With Varying Diameters and Build Directions

AbstractThe use of additive manufacturing (AM) processes, such as direct metal laser sintering, provides the design freedom required to incorporate complex cooling schemes in gas turbine components. Additively manufactured turbine components have a range of cooling feature sizes and, because of the inherent three-dimensionality, a wide range of build angles. Previous studies have shown that AM built directions influence internal channel surface roughness that, in turn, augment heat transfer and pressure loss. This study investigates the impact of AM on channel feature size and builds direction relative to tolerance, surface roughness, pressure losses, and convective cooling. Multiple AM coupons were built from Inconel 718 consisting of channels with different diameters and a variety of build directions. An experimental rig was used to measure pressure drop to calculate friction factor and was used to impose a constant surface temperature boundary condition to collect Nusselt number over a range of Reynolds numbers. Significant variations in surface roughness and geometric deviations from the design intent were observed for distinct build directions and channel sizes. These differences led to notable impacts in friction factor and Nusselt number augmentations, which were a strong function of build angle.

Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions

Abstract A laminar electrically-conducting flow inside an electrically-insulated rectangular duct in a uniform transverse magnetic field with both uniform surface temperature and uniform heat flux boundary conditions are considered numerically. The problem with aspect ratios of the range from 1:10 to 10:1 and Hartmann number M up to 1000 is solved using a highly accurate technique which is spectral method. The flow variables are expanded in terms of linear combinations of Chebyshev polynomials chosen to satisfy the boundary conditions implicitly. The resulting equations are collocated using the Gauss points to produce a system of nonlinear algebraic equations which is solved iteratively using Gauss elimination. Convergence properties of the numerical method reveals that for aspect ratio of less than 4 to 1, the flow is well resolved with as small as 29 by 29 Chebyshev polynomials; however, as the aspect ratio increases to more than 4 to 1, the number of polynomials required for an adequate resolution can be as high as 49 by 49 polynomials. It is found when the magnetic field is turned on, the pressure drop, in general, increases with the field for different aspect ratios. However, the pressure drop increase will be slower near the aspect ratio of 10. Also, the heat transfer increases with the field for most of the cases, but for some cases the field will have adverse effect on the heat transfer, particularly, for constant surface temperature boundary condition at aspect ratio > 4 and M 4 and M

Numerical investigation on the heat transfer characteristics of liquid-liquid plug-train in microchannels

Liquid-liquid plug-train is of great importance due to its wide applications in the heat transfer enhancement and the richness of underlying physics. This paper presented a theoretical and numerical study of the liquid-liquid plug-train in a microchannel. Based on the analytical model of flow field, the heat transfer process in liquid-liquid plug-train was investigated. The constant surface temperature boundary condition was considered. Nusselt number (Nu) and heat transfer index (η) were employed to evaluate the heat transfer characteristics of liquid-liquid plug-train in the microchannel. Three stages of the heat transfer process in liquid-liquid plug-train were identified: (i) development of thermal boundary layer (TBL); (ii) advection of heated/fresh fluid in the liquid-liquid plug train; and (iii) thermally fully developed flow. The effects of the thermal conductivity ratio and the plug length ratio were investigated. A low plug length ratio was found to be effective in heat transfer enhancement in the microchannel.

Conjugated Heat Transfer Simulation of a Fin-and-Tube Heat Exchanger

ABSTRACTHeat transfer and pressure drop of a fin-and-tube heat exchanger are studied by taking into account the conjugated heat transfer between the flow and the fin. The temperature distribution of the fin is calculated in respect to the convective heat transfer of the air flowing through the tube bank channel. Contemporary enhancement methods emphasize the importance of local turbulence augmentation which effects the convective heat transfer. In this paper, the importance of conjugated heat transfer, where the temperature of the flow and fin are coupled together is emphasized and compared with a constant surface temperature boundary condition simulation and experiment, which are found in the literature.

Numerical study on the air conditioning characteristics of the human nasal cavity

The air-conditioning characteristics of the human nasal cavity were investigated using computational fluid dynamics. The wall layer was modeled as a heat conducting layer consisting of water with constant thickness placed on top of epithelial cells. By assuming constant tissue temperature, prescribed to be 36 °C, which is close to the alveolar condition, the proposed wall model yielded a spatially varying surface temperature distribution that is in reasonable agreement with the measurement studies in the literature.The results show that the regions of the main airway between the nasal valve, and the anterior of the middle turbinate were shown to have relatively low temperatures, whereas the superior meatus exhibited relatively high temperature. Water vapor flux evaluated at the surface of the mucus layer was found to be quite large in the region between the posterior of the vestibule and the anterior of the middle turbinate. Comparing the results obtained from the present model to those obtained with a constant surface temperature boundary condition of 32.6 °C or 34 °C revealed that temperature, and absolute humidity of the airflow increased faster through the turbinated airway passage. Even in the presence of sizable differences in the distributions of surface temperature and water vapor concentration, distributions of relative humidity of the air were found to be quite similar regardless of temperature boundary conditions.

Optimization of volume to point conduction problem based on a novel thermal conductivity discretization algorithm

A conduction heat transfer process is enhanced by filling prescribed quantity and optimized-shaped high thermal conductivity materials to the substrate. Numerical simulations and analyses are performed on a volume to point conduction problem based on the principle of minimum entropy generation. In the optimization, the arrangement of high thermal conductivity materials is variable, the quantity of high thermal-conductivity material is constrained, and the objective is to obtain the maximum heat conduction rate as the entropy is the minimum. A novel algorithm of thermal conductivity discretization is proposed based on large quantity of calculations. Compared with other algorithms in literature, the average temperature in the substrate by the new algorithm is lower, while the highest temperature in the substrate is in a reasonable range. Thus the new algorithm is feasible. The optimization of volume to point heat conduction is carried out in a rectangular model with radiation boundary condition and constant surface temperature boundary condition. The results demonstrate that the algorithm of thermal conductivity discretization is applicable for volume to point heat conduction problems.

Dikdörtgen Kesitli Kanallarda Laminer Akış ve Isı Transferinin Sayısal Olarak İncelenmesi

In this study, hydrodynamically and thermally developing laminar flow and heat transfer in a rectangular cross-sectional duct have been numerically investigated for steady state and constant surface temperature boundary condition. Numerical solutions have been made for three different aspect ratios (α=0.25, 0.50 and 1.0) and in the Reynolds numbers range of 600 to 2000. Air (Pr0.72) is used as working fluid. A commercial CFD program ANSYS Fluent 13.0 has been employed to carry out the numerical study. Results are given in terms of Nusselt number Nu, Darcy friction factor f, hydrodynamic Lhd and thermal entrance Lth lengths as a function of Reynolds number Re. Also, velocity and temperature contours in the duct are given for different Reynolds numbers. It is seen that the general equation given for circular ducts does not give a true hydrodynamic and thermal entrance length for rectangular ducts. The present results obtained from numerical study are correlated as a function of aspect ratio and Reynolds number involving all aspect ratios and Reynolds numbers used in this study

Effect of bubble coalescence on the wall heat transfer during subcooled pool boiling

This study experimentally investigates the effects of bubble coalescence on the heat fluxes during nucleate pool boiling. A microheater array was used to generate vapor bubbles in FC-72 liquid with constant surface temperature boundary conditions while the heat flux at selected locations was measured for various superheats using a high speed data acquisition system. The heat flux for boiling with coalescence was found to fluctuate much more than when only a single bubble formed on the surface due to the vaporization of the liquid layer trapped between the bubbles and oscillations of the bubbles after coalescence which resulted in relatively long periods of fairly high heat fluxes. The observations also showed that some coalescence events were not accompanied by an increase in the heat transfer rate as the liquid layer between the bubbles was physically pushed away by the rapid bubble growth during the inertial bubble growth stage instead of evaporating. A mechanistic model was developed to predict the conditions for which the heat fluxes do not increase during coalescence. In many other instances, the coalescence dynamics were such that the only bubble remaining on the surface was swept off by the liquid motion from the previous coalescence event with no nucleation of another bubble. This was followed by a long period without bubble nucleation followed by sudden nucleation and explosive coalescence of two bubbles giving rise to a large bubble which departed violently with a large increase in the heat transfer rate.

Small and Large Time Solutions for Surface Temperature, Surface Heat Flux, and Energy Input in Transient, One-Dimensional Conduction

AbstractThis paper addresses one-dimensional transient conduction in simple geometries. It is well known that the transient thermal responses of various objects, or of an infinite medium surrounding such objects, collapse to the same behavior as a semi-infinite solid at small dimensionless time. At large dimensionless time, the temperature reaches a steady state (for a constant surface temperature boundary condition) or increases linearly with time (for a constant heat flux boundary condition). The objectives of this paper are to bring together existing small and large time solutions for transient conduction in simple geometries, put them into forms that will promote their usage, and quantify the errors associated with the approximations. Approximate solutions in the form of simple algebraic expressions are derived (or compiled from existing solutions) for use at both small and large times. In particular, approximate solutions, which are accurate for Fo<0.2 and which bridge the gap between the large Fo (single-term) approximation and the semi-infinite solid solution (valid only at very small Fo), are presented. Solutions are provided for the surface temperature when there is a constant surface heat flux boundary condition, or for the surface heat flux when there is a constant surface temperature boundary condition. These results are provided in terms of a dimensionless heat transfer rate. In addition, the dimensionless energy input is given for the constant surface temperature cases. The approximate expressions may be used with good accuracy over the entire Fourier number range to rapidly estimate important features of the transient thermal response. With the use of the approximations, it is now a trivial matter to calculate the dimensionless heat transfer rate and dimensionless energy input, using simple closed-form expressions.

Entropy Generation in Convective Heat Transfer and Isothermal Convective Mass Transfer

The irreversible generation of entropy for two limiting cases of combined forced-convection heat and mass transfer in a two-dimensional channel are investigated. First, convective heat transfer in a channel with either constant heat flux or constant surface temperature boundary conditions are considered for laminar and turbulent flow. The entropy generation is minimized to yield expressions for optimum plate spacing and optimum Reynolds numbers for both boundary conditions and flow regimes. Second, isothermal convective mass transfer in a channel is considered, assuming the diffusing substance to be an ideal gas with Lewis number equal to unity. The flow is considered to be either laminar or turbulent with boundary conditions at the channel walls of either constant concentration or constant mass flux. The analogy between heat and mass transfer is used to determine the entropy generation and the relations for optimum plate spacing and Reynolds number. The applicable range of the results for both limiting cases are then investigated by non-dimensionalizing the entropy generation equation.