This paper proposes an analytical method for the dynamic thermal simulation of energy piles with a short time resolution (e.g., tens of minutes) as an alternative to numerical approaches, which require relevant computational resources. The discussion is tailored to the implementation of analytical models in dynamic energy simulation software for buildings and HVAC systems. The main modeling challenges consist of accounting for the pile thermal capacity, configuration of pipes, and time-varying inlet temperature and flow rate values. The heat transfer process occurs in three characteristic periods, each of them characterized by a 2D or 3D geometry. The first period concerns the evolution of the fluid temperature and heat transfer over the length of the pipes, the second period concerns the thermal diffusion within the heat capacity of the foundation, and the third period is driven by pile geometry and ground source characteristics. For short time resolution analyses, we proposed a general linear set of equations based on the ε-NTU theory for heat exchangers, the infinite composite-medium line source solution, and the finite line source for the ground source. The proposed method is compared with a full transient 3D numerical simulation. The maximum deviation in terms of return temperature to the heat pump is 0.2 K. The general dimensionless form, the short time resolution, and the limited computational time makes the method suitable for building simulation software and optimization codes for thermal analysis and energy pile design.

Internal cooling of the gas turbine blade is critical for the durability of the blade material. One of the ways to accomplish this is by passing coolant through serpentine passages roughened with surface elements to enhance the heat transfer. In the present study, the traditional square rib (SQ-rib) placed normal to the flow direction is modified to a backward-facing step rib (BS-rib) and a forward-facing step rib (FS-rib). Large-eddy simulation (LES) is carried out for a square duct at Re b = 20000. Results show that the modified rib shapes result in substantial increase in heat transfer over the square rib with only a marginal increase in flow losses. The BS-rib shape produces the highest heat transfer augmentation followed by the FS-rib. The overall heat transfer augmentation for the BS-rib and FS-rib is 18% and 10% larger than the SQ-rib, respectively. Thermal-hydraulic performance is enhanced by 15%.

Matrix cooling has opened new possibilities for enhancing the convective heat transfer coefficients without compromising upon the structural rigidity and the life of the gas turbine blade at elevated temperatures. However, the dense structure of the matrix significantly increases the flow resistance and imposes the limitation to its usage. Recently, a matrix with a gap on the sidewalls called open matrix has been proposed by few researchers to reduce the associated pressure penalties. This detailed experimental investigation aims to study the open matrix channel flow and presents the effects of varying sidewall gaps on heat transfer characteristics and friction factor in the open matrixes having rib angle 45 deg for three different subchannel aspect ratios 1.2, 0.8, and 0.4. Liquid crystal thermography has been utilized to discern the detailed heat transfer characteristics. The results have been evaluated in terms of augmentation Nusselt number, friction factor ratio, and overall thermal performance factor over the Reynolds numbers 5800–14,000. The closed matrixes provided the highest augmentation in Nusselt number, and the gaps on the sidewall have shown an overall reduction in augmentation Nusselt number in most cases. However, the suitable sidewall gaps show the effective reduction in pressure penalties for the smaller subchannel aspect ratios. The highest augmentation Nusselt number among the open matrixes has been found as 3.83 with a reduced friction factor ratio for the matrix with a 4-mm gap in subchannel aspect ratio = 0.8 (i.e., 4 subchannels) at Re = 8100.

The asymptotic limit for perimeter averaged convection is generalized for short ducts of arbitrary cross section. A correction factor to Lévêque's original analysis is derived in terms of the state of wall shear stress under conditions of fully developed flows for walls of constant temperature (T) and constant heat flux (H 1 and H 2 ). This analysis is performed for four duct geometries: elliptic, rhombic, rectangular, and regular polygons. The magnitude of this correction is greatest for the H 2 wall condition and for ducts having walls with acute corners. The results of this analysis can be incorporated into a generalized correlation for the full Graetz problem in ducts of arbitrary cross section.

The heat transfer problem in a circular duct with an internal longitudinal fin is investigated under constant wall temperature. Different fin heights are considered. The problem is solved in two stages. In the first stage, the distribution of axial velocity corresponding to the fully developed laminar viscous flow is obtained using comsol multiphysics . In the second stage, the variable-separation method is implemented to reduce the solution of the energy transfer equation under constant wall temperature to an eigenvalue problem. Finally, the temperature distribution is obtained in the analytical form as a series expansion. The influence of fin height on the Nusselt number and the friction factor is discussed.

New generalized correlations for predicting the average fanning friction factor f and average Nusselt number Nu for laminar flow in plain plate-fin compact cores of rectangular cross section are presented. These are based on extended experimental data, as well as three-dimensional computational simulations, obtained for a broad range of fin density and geometrical attributes. The results indicate that while the fully developed forced convection scales only with the interfin channel cross-sectional ratio α (fin spacing by fin height), the entrance region hydrodynamic and thermal performance is additionally a function of the fin-core length L, flow Reynolds number Re, and fluid Prandtl number Pr. The developing flow and convection is further shown to scale as: ( f Re ) ∼ ( L / d h Re ) 1 / 2 , and Nu ∼ ( L / d h Re ) 1 / 2 Pr 1 / 3 ϕ ( α ) , where f, Re, and Nu are all based on the hydraulic diameter d h of the interfin flow channel. Generalized correlations for both ( f Re ) and Nu are developed by the corresponding scaling of the forced convection behavior and asymptotic matching of the entrance or developing flow (short fin-core flow length) and the fully developed flow (large fin-core flow length) region performance. Finally, the predictions from these correlations are found to be within ±15% of all available experimental data for air, water, and glycol (0.71 ≤ Pr ≤ 10), and fin cores with 0 < α ≤ 1.

The objective of this work is to investigate the aerodynamics and thermal interactions between a spreading flame and the surrounding walls as well as their effects on fire behaviors. A three-dimensional transient computational fluid dynamics (CFD) combustion model is used to simulate concurrent-flow flame spread over a thin solid sample in a narrow flow duct. The height of the flow duct is the main parameter. The numerical results predict a quenching height for the flow duct below which the flame fails to spread. For duct heights sufficiently larger than the quenching height, the flame reaches a steady spreading state before the sample is fully consumed. The flame spread rate and the pyrolysis length at steady-state first increase and then decrease when the flow duct height decreases. The detailed gas and solid profiles show that flow confinement has multiple effects on the flame spread process. On one hand, it accelerates flow during thermal expansion from combustion, intensifying the flame. On the other hand, increasing flow confinement reduces the oxygen supply to the flame and increases conductive heat loss to the walls, both of which weaken the flame. These competing effects result in the aforementioned nonmonotonic trend of flame spread rate as duct height varies. Near the quenching duct height, the transient model reveals that the flame exhibits oscillation in length, flame temperature, and flame structure. This phenomenon is suspected to be due to thermodiffusive instability.

Heat transfer characteristics of a circular cylinder in the branch of a T-junction duct are experimentally investigated in a low-speed wind tunnel with Reynolds number of Re b = 9163. Local and average heat transfer distributions around the circular cylinder are obtained for the cylinder positions ranging from 0.5 to 13 and the velocity ratios ranging from 0.117 to 0.614. It is found that the overall heat transfer characteristics in a T-junction duct at high velocity ratio are lower than those at low velocity ratio, and both are higher than those in the straight duct. The local Nusselt number in the T-junction duct is an asymmetrical distribution and weakens with increasing velocity ratios and/or positions of the cylinder. The angles of the front and rear stagnation points in the T-junction duct are the same as those in the straight duct at certain velocity ratio and/or position of the cylinder. However, the angles of the front and rear separation points in the T-junction duct do not match those in the straight duct. Both the heat transfer correlation coefficients and the amplitude ratios increase with increasing positions of the circular cylinder and/or velocity ratios.

High-porosity metal foam (MF) is a popular option for high-performance heat exchangers as it offers significantly higher heat transfer participation area per unit volume compared to other convection enhancement cooling methods. Further, metal foams provide highly tortuous flow paths resulting in thermal dispersion assisted by enhanced mixing. This paper presents experimental and numerical studies and the detailed underlying physics of jet array impingement onto high-porosity ( ε ∼ 0.95 ) thin aluminum foams. The jet and foam configurations were designed for the maximum utilization of the foam area for heat transfer and reduced penalty on the pumping power requirement. Three different pore density foams were tested with three different array-jet impingement configurations. The minimum possible thickness for each pore density was tested, viz., 5 pores-per-inch (PPI): 19 mm, 10 PPI: 12.7 mm, and 20 PPI: 6.35 mm. The baseline case for these foam-based jet impingement configurations was the corresponding configuration of orthogonal jet impingement onto a smooth heated surface, where the distance between the jet-issuing plane and the heated surface was maintained at the foam thickness level. In general, thinner foams facilitated greater jet penetration and increased foam volume usage, resulting in higher heat transfer rates for a given pore density, especially when combined with jet configurations with larger open areas. Finally, we evaluated the thermal hydraulic performance for different foam configurations and the optimum value of a given PPI was found to be at an intermediate rather than the lowest foam thickness.

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.

The plate fin heat exchangers usually have either rectangular or triangular shaped flow passage. In comparison to triangular flow passage, rectangular flow passage gives comparatively higher heat transfer at the cost of higher pumping power. In the present investigation, flow passage is modified by rounding the corner of triangular passage to investigate the heat and flow characteristics of air flowing through it. Comparison of performance between modified and rectangular flow passage has also been presented and discussed. The radius of curvature of the rounded corner has been kept constant with value of 0.49 times duct height (H). The dimple was also fabricated at the inner side of the flow passage and arranged in rectangular array. Distance between them was defined by two different dimensionless parameters, relative transverse width (x/h), and relative streamwise length (z/h), whereas, dimensionless height of the protrusion is defined by relative dimple height (h/D). Noticeable increment in both heat transfer and friction factor has been observed by modifying the duct corners and 2.98 times increment in Nusselt number resulted due to dimples in modified duct for h/D, x/h, and y/h value of 0.44, 10, and 10, respectively, in comparison to smooth duct at Reynolds number of 19,500. For similar combination of roughness parameters, highest frictional penalty was estimated with value of 4.46 times that of the smooth duct at Reynolds number of 4400. Additionally, the comparative assessment of heat transfer enhancement (Nu enh ), frictional penalty (f penalty ), and thermohydraulic performance index (THPi) has also been carried out to understand the suitability of round cornered duct. In comparison to protruded rectangular duct, 28% higher THPi is obtained in modified duct under similar conditions.

Heat transfer characteristics in a latticework duct with various sidewalls are numerically investigated. The crossing angle is 90 deg and the number of subchannels is eleven on both the pressure side and suction side for each latticework duct. The thickness of the ribs is 8 mm and the distance between adjacent ribs is 24 mm. The investigation is conducted for various Reynolds numbers (11,000 to 55,000) and six different sidewalls. Flow structure, pressure drop, and heat transfer characteristics are analyzed. Results revealed that the sidewall has significant effects on heat transfer and flow structure. The triangle-shaped sidewall provides the highest Nusselt number accompanied by the highest friction factor. The sidewall with a slot shows the lowest friction factor and Nusselt number. An increased slot width decreased the Nusselt number and friction factor simultaneously.

A generalized correlation for combined entry convection in ducts of arbitrary cross section has been developed. The correlation is constructed for the average Nusselt number using knowledge of fully developed transport constants. The general correlation reproduces the first principle solutions for the well-established round and parallel plate duct geometries to within ±5% for both constant temperature and constant heat flux wall conditions when Pr ≥ 0.7. A survey of the literature demonstrates that the new generalized correlation performs as well or better than existing correlations, which are expressed for specific geometries and wall conditions. The new correlation is generally in good agreement with the first principle solutions of less common duct geometries so long as the duct has a convective surface equal to the wetted perimeter. The new correlation is not recommended for ducts having small aspect ratios that pinch the flow when convection is prescribed by the H 2 constant heat flux wall condition.

The experimental and numerical investigations of the heat transfer of supercritical pressure n-decane flowing through a pipe at various rotational speeds, mass flow rates, heat fluxes, and pressures, are presented. This pipe is 2 mm in diameter, 200 mm in length, with a radius of 0.328 m, and is parallel to the rotating axis. The wall temperature was measured at four positions around the periphery of the pipe at each of the five selected cross section along the pipe's length. Maximum convective heat transfer was observed at the outer edge of the horizontal section, while its corresponding minimum was observed at the inner edge. The heat transfers at the two sides of the channel were observed to be similar. The density and pressure differences between the outer and inner edges increased at increasing rotating speeds. However, the temperature difference between the outer and inner edges decreased with increased rotational speed mainly because of the increase of secondary flows in the section. The section's average convective heat transfer coefficient increased with an increase in the rotational speed, and its value at 1000 rpm was approximately twice than that at static conditions. The phenomenon of oscillation was observed near the exit of the horizontal section, and was caused by the flow and considerable property changes near the pseudo critical temperature. A computational fluid dynamics (CFD) model was developed using the real gas thermal properties and was coupled with the heat transferred owing to fuel flow. The predicted fuel and wall temperatures were in good agreement with the experimental data. A new local Nusselt number correlation of the heat transfer of n-decane in a rotating horizontal section was proposed.

A numerical method was used to study the effect of the broken rib locations on the heat transfer and flow structure in the latticework duct with various rotational numbers. The latticework duct had eleven subchannels on both the pressure side and the suction side. The crossing angle for each subchannel was 45 deg. The numerical studies were conducted with five different broken rib locations and six rotational numbers (0–0.5). The Reynolds number was fixed as 44,000. The flow structure, wall shear stress, and Nusselt number distributions were analyzed. It was found that the upward spiral flow and helical flow dominated the flow structure in the latticework duct. In addition, the impingement region (at the beginning of the subchannel) induced by the upward spiral flow was responsible for the high Nusselt number and wall shear stress. After adoption of the broken rib in the latticework duct, the Nusselt number was increased by 6.12% on the pressure endwall surface and increased by 6.02% on the rib surface compared to the traditional latticework duct. As the rotational number was increased, the Nusselt number on the pressure endwall surface was decreased by up to 5.4%. However, the high rotational number enhanced the heat transfer on the suction side. The high rotational number also decreased the friction factor in the latticework duct. Furthermore, the overall thermal performance was increased by 12.12% after adoption of the broken ribs on both the turn region and the impingement region.

We consider conjugate forced-convection heat transfer in a rectangular duct. Heat is exchanged through the isothermal base of the duct, i.e., the area comprised of the wetted portion of its base and the roots of its two side walls, which are extended surfaces within which conduction is three-dimensional. The opposite side of the duct is covered by an adiabatic shroud, and the external faces of the side walls are adiabatic. The flow is steady, laminar, and simultaneously developing, and the fluid and extended surfaces have constant thermophysical properties. Prescribed are the width of the wetted portion of the base, the length of the duct, and the thickness of the extended surfaces, all three of them nondimensionalized by the hydraulic diameter of the duct, and, additionally, the Reynolds number of the flow, the Prandtl number of the fluid, and the fluid-to-extended surface thermal conductivity ratio. Our conjugate Nusselt number results provide the local one along the extended surfaces, the local transversely averaged one over the isothermal base of the duct, the average of the latter in the streamwise direction as a function of distance from the inlet of the domain, and the average one over the whole area of the isothermal base. The results show that for prescribed thermal conductivity ratio and Reynolds and Prandtl numbers, there exists an optimal combination of the dimensionless width of the wetted portion of the base, duct length, and extended surface thickness that maximize the heat transfer per unit area from the isothermal base.

The H2-forced convection in a rectangular duct of large aspect ratio (>10) is studied. It is found that the short ends have non-negligible effects on the Nusselt number and the temperature distribution. Even at infinite aspect ratios, the Nusselt number depends on the net heat addition from the ends, but not how they are distributed.

The analytical solutions for condensation (and evaporation) rates of laminar humid air flow in the channels of a battery pack at both entrance and downstream regions are obtained/modeled. The effects of the entrance fluid velocity profile and the aspect ratio of the flow channel are taken into consideration. Initially, an analytical solution for laminar humid air flows' condensation at the flow channel with infinite aspect ratio and fully developed flow profile at the entrance is obtained. The solution is in good agreement with the simulation result obtained from a correlated fluent condensation model. After performing simulations of water vapor condensation and evaporation in the flow channel for different aspect ratios and entrance velocity profiles, the analytical solutions of condensation and evaporation rate of water vapor are presented in analytic forms by adding appropriate coefficients/correction factors to the solution for the flow in the channel with infinite aspect ratio. The resulting model accurately captures the effects of the entrance velocity profile and aspect ratio.

In a recent contribution, the authors show that the uncertainty in heat transfer results obtained using the Monte Carlo ray-trace (MCRT) method is related to the median of the radiation distribution factor probability density function (PDF). The value of this discovery would be significantly enhanced if the median could be known a priori without first computing the distribution factors. This would allow the user to determine the number of rays required to achieve the desired accuracy of a subsequent heat transfer analysis. The current contribution presents a correlation for the median of the distribution factor PDF as a function of emissivity and the number of surface elements defining an enclosure. The correlation involves a single parameter whose value is unique for a given enclosure geometry. We find that the radiation behavior of a given enclosure can be classified on a scale ranging from reflection-dominated to geometry-dominated. The correlation is shown to work well for reflection-dominated enclosures but less well for geometry-dominated enclosures.

A detailed understanding of the flow of a liquid metal in a rectangular duct subject to a strong transverse magnetic field is vital in a number of engineering applications, notably for proposed blanket technologies for fusion reactors. Fusion reactors offer the potential for clean base-load energy and their development is now entering an engineering phase where the practical means by which the energy released can be converted into useful heat must be addressed. To such ends, this article considers the convective heat transfer processes for fully developed laminar magnetohydrodynamic (MHD) flows in rectangular ducts of the kind proposed in some blanket designs. Analytical solutions which incorporate the nonuniformity of peripheral temperature and heat flux and the effect of volumetric heating, are developed as functions of magnetic field strength and duct aspect ratio. A distinct feature of these MHD problems, not yet addressed in the literature, is that unlike the conventional characterization of heat transfer by a Nusselt number, it is necessary to generalize the concept to vectors and matrices of Nusselt coefficients, due to the extreme anisotropy of both the flow and heating. The new analytical results presented here capture more complex heat transfer behavior than non-MHD flows and in particular characterize the importance of aspect ratio. The importance of these new results lie not only in the improved understanding of this complex process but also in the provision of characterizations of convective heat transfer which underpin progress toward systems scale simulations of fusion blanket technology which will be vital for the realization of practical fusion reactors.