Analysis of the effect of viscous dissipation for laminar flow in stadium-shaped ducts

The fully-developed laminar forced convection of a Newtonian fluid in a duct with stadium-shaped cross section has been analyzed. The effect of viscous dissipation has been taken into account. Three different thermal boundary conditions have been considered: (T) uniform wall temperature distribution; (H1) axially uniform wall heat flux distribution with peripherally uniform wall temperature distribution; (H2) axially and peripherally uniform wall heat flux distribution. The adiabatic-wall boundary condition has also been analyzed as a special case of the H2 boundary condition. The velocity and temperature distributions in the fluid, as well as the Fanning friction factor and the Nusselt number, have been evaluated numerically, by employing a Galerkin finite element method. As expected, the numerical evaluation of the dimensionless temperature distribution and of the Nusselt number reveals that increasing discrepancies between the H1 and H2 boundary conditions exist if the stadium-shaped duct is gradually flattened.     

Study of heat and mass transfer in MmNi4.6Al0.4 during desorption of hydrogen

In this paper, a numerical investigation of two-dimensional coupled heat and mass transfer during desorption of hydrogen in a cylindrical metal hydride reactor containing MmNi_6.4Al_0.4 is presented. By considering the variation in heat transfer fluid temperature along the axial direction (variable wall temperature boundary condition), the changes in hydride bed temperature at different axial locations are presented. The effect of variable wall temperature boundary condition on hydrogen desorption rate for different hot fluid temperatures and hydride bed thicknesses is investigated. The rate of hydrogen desorption at different hot fluid temperatures showed good agreement with the experimental data reported in the literature. As the desorption progresses, the change in heat transfer fluid temperature along the axial direction is found to decrease with time and becomes unchanged at the end of the process. The effect of variable wall temperature boundary condition on desorption time is found to be significant for the hydride bed thicknesses of about 7.5 mm and more. For a given bed thickness of 17.5 mm, the maximum difference in desorption time between variable wall and constant wall temperature convective boundary conditions is about 375 s at 303 K.     

A numerical study of natural convection in a vertical cylinder bundle

Natural convection in a bundle of vertical cylinders, arranged in equilateral triangular spacing, has been investigated numerically using a boundary‐fitted coordinate system. Numerical calculations for center‐to‐center distance between cylinders S/D = 1.1 to 1.9, 3.0, 4.0, and 7.0 were made of natural convection of air at modified Grashof numbers Gr* from 10 to 10⁸. Local Nusselt number Nu for uniform wall heat flux indicates the same value at the axial locations except for the thermal entrance region. The region for respective cylinder spacing is noted to diminish with decreasing Grashof number. Numerical values of local Nusselt number Nu_i are in relatively good agreement with those obtained from the experiment for air. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 330–341, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10095     

An approach to the design of solar coil collector

A design procedure using the concept of heat exchanger “effectiveness and transfer unit” has been developed and applied to a Solar Coil Collector fabricated and tested earlier. For laminar flow the coil wall temperature T_c is obtained from the modified expression ). Where T_b = bulk liquid temperature; Q = wall heat flux; h_t = heat transfer coefficient in straight tubes; D_t = tube diameter; D_c = coil diameter; and p = a number. The calculated results are checked with the actual dimensions of the collector and are found in agreement.     

Thermal Stresses in a Hollow Cylinder with Convective Boundary Conditions on the Inside and Outside Surfaces

Analytical solutions for thermal stresses (radial, tangential, and axial) in a hollow cylinder with uniform internal heat generation for the thermal boundary condition of convective heating on the inside surface and convective cooling on the outside surface are derived. The analysis assumes the ends of the cylinder to be clamped, the axial strain to be negligible, and the radial stresses on the inside and the outside surfaces to be zero. Results are presented to illustrate the effects of internal heat generation parameter Q, convective environment temperatures ratio θ*, Biot number for convection on the inside surface Bi ₁, Biot number for convection on the outside surface Bi ₂, and the radii ratio ρ on thermal stresses distribution in the cylinder. The analytical solutions should serve as benchmarks for validating the numerical codes for dealing with more complicated cases.     

Ultralightweight Compact Heat Sinks With Metal Foams Under Axial Fan Flow Impingement

Experimental results of ultralightweight compact heat sinks with open-celled copper (Cu) foams under the impingement of axial fan flows are presented. The thermal resistance of the system and the pressure coefficient on heat sink base plate were measured, focusing on the influences of foam height (H_f ) and impinging distance between fan exit and base plate (H). With the impinging distance fixed at H/D = 0.5 (D being the fan diameter), it is demonstrated that an optimum foam height exists at H_f /D = 0.22, providing the lowest thermal resistance. Furthermore, with the foam height fixed at H_f /D = 0.22, reducing the impinging distance to the foam height level reduces the thermal resistance further. In comparison with conventional aluminum (Al) plate-fin heat sinks under identical flow conditions, the Cu foam heat sinks require only 30% of the weight and 50% of the volume to achieve a similar level of heat dissipation performance.     

Thermal performance characteristics of STC system with Phase Change Storage

Storing solar energy heat using Phase Change Materials (PCM) is an effective method. The combination of solar collector and PCM in one unit is being currently studied. The performance characteristics of the proposed Solar Tube Collector (STC) are being analysed analytically and experimentally. Fundamental experiments were performed to simulate a direct contact solar storage system, using two vertical cylindrical concentric tubes with the annular space between them filled Stearic acid (C₁₈H₃₈O₂, melting temperature 70 °C). Experimental testing apparatus has been set up to simulated real system conditions, for an assumed initial and boundary conditions, to provide quantitative information concerning the heat transfer and the timewise evolution of the solid-liquid interface and to identify the role and pattern of natural convection and of the movement of the boundary layer in the liquid phase. For the heat charging mode, the experimental results for different types of fin structures have shown that the effect of melting process is strongly effected by the variation of the imposed conditions, in addition to the different trends of the melting profiles along the axial direction due to the effect of natural convection.     

Vortex structure behind highly heated two cylinders in parallel arrangements

Vortex structures behind twin, highly heated cylinders in parallel arrangements have been investigated experimentally. The experiments were conducted under the following conditions: cylinder diameter, D=4mm; mean flow velocity, U_∞ = 1.0 m/s; Reynolds number, Re=250; cylinder clearance, S/D=0.5 to 1.4; and cylinder heat flux, q=0 to 72.6kW/m². For S/D>1.2, the Karman vortex street is formed alternately behind each cylinder divided on the slit flow. The slit flow velocity increases with a decrease in S/D and decreases with increasing heat flux. For S/D < 1.2, the wake vortexes become asymmetric having small and large scale vortexes divided by the slit flow. In the small scale vortexes, the symmetric counter‐rotating twin vortexes are formed just behind the cylinders. In the large scale vortexes, the generated vortexes have a similar structure to a Karman vortex even though the Strouhal number is approximately half of the ordinary single cylinder vortex. For isothermal conditions, the transition phenomena from symmetric to asymmetric wake structures are observed in the range of 0.9 < S/D <1.2. In addition, the asymmetric vortexes are irregularly switched up and down in the case of isothermal conditions. In the highly heated condition, the switching phenomena and the transition phenomena could not be observed and the small scale vortexes always formed behind the upper cylinder. The critical S/D increases approximately 30% in the heated condition (q=72.6kW/m²). As a result, the increased local kinematic viscosity and S/D play a key role for the vortex structure and formation behind arrangements of two parallel cylinders. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20244     

Effect of Blocked Core-Tube Diameter on Heat Transfer Performance of Internally Longitudinal Finned Tubes

Three-dimensional turbulent flow and heat transfer in an internally finned tube with a blocked core-tube have been numerically studied by the realizable k ? ε turbulence model with the wall-function method. The numerical method is validated by comparing the calculated results with experimental data. The range of ratio of blocked core-tube outside diameter to outer-tube inside diameter (d ₀/D _i ) is from 0.25 to 0.75. The computational results demonstrated that there exists an optimal ratio of (d ₀/D _i ) under both identical mass flow rate and identical pressure drop. The optimal ratio of (d ₀/D _i ), which is reduced with the increase of mass flow rate, is approximately 0.5 to 0.625 at given mass flow rate for both constant wall temperature and uniform wall heat flux. The optimal ratio of (d ₀/D _i ) at a given pressure drop is from 0.44 to 0.50, which is also slightly reduced with the increase of pressure drop. Furthermore, the optimal ratio of (d ₀/D _i ) is not sensitive to the number of cross-section wavy fins of an internally longitudinal finned tube, in the range of a fin wave number of 15–25.     

Investigation of natural convection induced outer side heat transfer rate of coiled-tube heat exchangers

Natural convection induced heat transfer has been studied over the outer surface of helically coiled-tube heat exchangers. Several different geometrical configurations (curvature ratio δ ε [0.035, 0.082]) and a wide range of flow parameters (60 <= T_tank <= 90, T_in = 19 and 60 <= T_in <= 90, T_tank = 20, 4000 <= Re <= 45000) have been examined to broaden the validity of the results gained from this research. A fluid-to-fluid boundary condition has been applied in the numerical calculations to create the most realistic flow configurations. Validity of the numerical calculations has been tested by experiments available in the open literature. Calculated results of the inner side heat transfer rate have also been compared to existing empirical formulas and experimental results to test the validity of the numerical computation in an independent way from the outer side validation of common helical tube heat exchangers. Water has been chosen to the working fluid inside and outside of the coiled tube (3 < Pr < 7). Outer side heat transfer rate along the helical tube axis has been investigated to get information about the performance of the heat transport process at different location of the helical tube. It was found that the outer side heat transfer rate is slightly dependent on the inner flow rate of any helical tube in case of increasing temperature differences between the tank working fluid temperature and the coil inlet temperature. A stable thermal boundary layer has been found along the axial direction of the tube.In addition to this the qualitative behavior of the peripherally averaged Nusselt number versus the axial location along the helical tube function is strongly dependent on the direction of the heat flow (from the tube to the storage tank and the reversed direction). Inner side heat transfer rate of helical coils have also been investigated in case of fluid-to-fluid boundary conditions and the calculation results have been compared with different prediction formulas published in the last couples of decades.     

A general implementation of the H1 boundary condition in CFD simulations of heat transfer in swept passages

A methodology has been developed to study laminar flow and heat transfer behaviour in periodic non-straight passages with a heat transfer boundary condition of constant axial heat flux and constant peripheral temperature (H1). The technique uses Newton iteration to determine the wall temperature distribution required to satisfy the H1 boundary condition. The methodology is validated for hydrodynamically developed and thermally developing flow, as well as for hydrodynamically and thermally developed flow in straight ducts with various cross-sections. The methodology is extended to study fully developed flow in a periodic serpentine channel, consisting of a number of bends and straight sections, with a semi-circular cross-section. The results show the existence of a non-monotonic temperature distribution along the serpentine channels which exists because increased rates of heat transfer at bends lead to reductions in the local wall temperature in order to maintain a constant axial heat flux. Hot spots within the passage cross-section, typical of the H2 boundary condition, are removed in the H1 case.     

Optimal research of annular baffle for heat-discharging performance of single thermal storage tank with molten salt

The single thermal energy storage tank (STEST) has been extensively investigated because of the advantage of cost and efficiency. This research presents heat discharging performance of STEST using coil heat exchanger (CHE) with annular baffle at different working conditions. The heat discharging performance, flow field and temperature distribution of different parameters of the annular baffle are presented and discussed. The results show that the heat discharging time decreases with an increase inlet air velocity of the CHE. The heat discharging efficiency is up to 95.7% in this study, and the heat discharging time can reach to 18.7 hours. In addition, optimal dimensionless diameters of annular baffle are D_b/D_t = 0.6, H_s/H_t = 0.075 and H_x/H_t = 0.050 (H_s is the height from the top of baffle to the top of tank. H_t is the height of the tank. H_x is the height from bottom of the baffle to the bottom of the tank). The efficiency of heat discharging process can be enhanced with optimal dimensions of the annular baffle. This study presents a direct practicable guide to design the STEST.     

Thermal performance analysis of a tube finned surface

The present work submits an experimental work on the heat transfer and friction loss characteristic, employing a tube finned heating surface kept at a constant temperature in a rectangular channel. The tube fins attached on the surface (o.d.=29 mm) were arranged as either in‐line or staggered. The parameters for the study were Reynolds number (3700–30 000), depending on hydraulic diameter, the distance between the tube fins in the flow direction (S_y/D=1.72–3.45) and the fin arrangement. The change in the Nusselt number with these parameters was determined. For both tube fin arrangements, it was observed that increasing Reynolds number increased Nusselt number, and maximum heat transfer occurred at S_y/D=2.59. Thermal performances for both arrangements were also determined and compared with respect to heat transfer from the same surface without fins. With staggered array, a heat transfer enhancement up to 25 per cent for S_y/D=3.45 in staggered array was achieved in constant pumping power. Copyright © 2002 John Wiley & Sons, Ltd.     

Study of thermal characteristics of bubble‐driven heat‐transport device

In the present paper, we report on heat transport rates and fluid flow patterns of a bubble‐driven heat‐transport device (BD‐HTD) made of glass, obtained with the working fluids water, soapsuds, ethanol, and R141b. In this type of HTD, the cooling and heating sections are connected to each other by a closed loop of tube meandering between them, and the loop is filled to a certain volume fraction with a working fluid. The present BD‐HTD was set vertically and was heated at the bottom by warm water and cooled at the top by cold water. Experimental parameters were the inner diameter of the tube (D = 1.8, 2.4, 5.0 mm), the total temperature difference of heating and cooling water (ΔT = 20 to 60 K), and liquid volume fraction (α = 18 to 98%). The main results are summarized as follows. Heat transfer coefficient of the working fluid at the heating and cooling sections, h_fi, is not strongly dependent on α and ΔT. Among the present test liquids, the effective thermal conductivity k_ef is the highest for R141b, but the heat transfer coefficient h_fi is the highest for water. As k_ef is sufficiently high even for water, the heat transport rate Q is the highest for water. Q of the present BD‐HTD using water can exceed the maximum heat transport rate of conventional heat pipes of the same geometry. For R141b, the BD‐HTD operated for D/λ₀ = 1.5 to 4.2 (λ₀: the capillary length) and Q is not strongly dependent on the tube diameter. This result indicates that BD‐HTDs are suitable for micro‐HTDs, but the BD‐HTD did not operate with water at D/λ₀ = 0.65. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(2): 167–177, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10082     

Thermal Control of Protruding Electronic Components with PCM: A Parametric Study

This work deals with the melting and natural convection in a rectangular enclosure heated from three discrete protruding electronic components (heat sources) mounted on a conducting vertical plate (substrate). The heat sources generate heat at a constant and uniform volumetric rate. A part of the power generated in the heat sources is dissipated to the phase change material (PCM, n-eicosane with a melting temperature T _m  = 36°C) that filled the enclosure. To investigate the thermal behavior of the proposed heat sink, a mathematical model, based on the mass, momentum, and energy conservation equations was developed. The model has been verified and then validated comparing the melting front with available experimental results. Numerical investigations have been conducted in order to examine the effects of the electronic components thickness and the plate thermal diffusivity on the maximum temperature of electronic components. The percentage contribution of plate heat conduction on the total removed heat and temperature profile in the plate have also been analyzed. Correlations for the nondimensional secured working time (time to reach the threshold temperature, T _cr  = 75°C) and its corresponding melt fraction were derived.     

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

The objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 10³–10⁵, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nu_av), drag force (D), and maximum bulk temperature (θ_max). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21002     

The Cooling of PEFC with Pentane Boiling in Minichannels: A Study of Flow Instabilities Using Neutron Radiography Visualization

Polymer electrolyte fuel cells (PEFC) operate best at a steady temperature of about 80°C and have a very low heat flux compared to other heat transfer applications. Two-phase pentane cooling of bipolar plates is studied in order to optimize fuel cell cooling in transport applications. High-speed visualizations of boiling pentane in a circular steel tube (D _i = 1.1 mm, D _o = 2 mm) have been performed in a Neutrograph instrument at the Institut Laue-Langevin in Grenoble, France. The heat and mass flux were both very low and appropriate for cooling of PEFC. The spatial resolution of the images is approximately 0.15 mm and the maximum frequency is 154 Hz. In the images, the liquid-vapor differentiation is clearly visible. Time resolved measurements of the outer pipe wall temperature, synchronized with the images, show that at low mass flow rates, the pipe wall is high above the saturation temperature and the pipe filled with vapor and liquid slugs. At higher flow rates, the wall is superheated when filled with liquid, and at saturation temperature during boiling when exposed to a liquid-vapor mixture. An irregular switch between these two states was observed. The superheated wall is shown to be consistent with the superheated liquid in the pipe in both stable and time-dependent states. Unfortunately, the strong γ-radiation produced by the neutrons has a substantial effect on the onset of boiling, which is why comparisons with non-irradiated systems might be difficult. Simplified steady and time-dependent models are proposed to explain the measured wall temperature instabilities and superheat.     

Fluid flow and heat transfer of mixed convection adjacent to vertical heated plates placed in uniform horizontal flow of air

Experiments have been carried out for mixed convective flows of air adjacent to the vertical heated plates in uniform horizontal forced flows to investigate relationships between the flow and the heat transfer. The experiments cover the ranges of the Reynolds and modified Rayleigh numbers: Re_L = 160 to 2300 and Ra_L^* = 4.3 × 10⁵ to 2.0 × 10⁸. The flow fields over the plates are visualized with particles and smoke. The results show that a stagnation point moves downward away from the center of the plate when the surface heat flux is beyond a critical value. The condition where the stagnation point begins to move is expressed with non‐dimensional parameters as: Gr_L^*/Re_L^2.5 = 0.15. Profiles of measured local heat transfer coefficients are smooth even at the stagnation points in all the cases examined. When buoyancy effect is sufficiently weak, the coefficients agree well with those of the wedge flow. With increasing the surface heat flux, the coefficients are augmented to approach asymptotically the boundary layer solution of natural convection along a vertical heated plate. Finally, forced, mixed, and natural convection regimes are classified by the non‐dimensional parameter (Gr_L^*/Re_L^2.5). © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20256     

DNS of turbulent heat transfer in a channel flow with a varying streamwise thermal boundary condition

Direct numerical simulation (DNS) was performed for the turbulent heat transfer in a channel flow. In the present study, the effect of the thermal boundary condition was examined. DNS was carried out for varying streamwise thermal boundary conditions (Re_τ = 180) with Pr = 0.71 to obtain statistical mean temperatures, temperature variances, budget terms, and time scale ratios. The results obtained indicate that the time scale ratio varies along the stream direction. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(4): 265–278, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20114     

Numerical studies of simultaneously developing laminar flow and heat transfer in microtubes with thick wall and constant outside wall temperature

The effects of wall axial heat conduction in a conjugate heat transfer problem in simultaneously developing laminar flow and heat transfer in straight thick wall of circular tube with constant outside wall temperature are numerically investigated. The results show that the heat transfer process is most sensitive to wall-to-fluid conductivity ratio k_sf, and when k_sf ? 25 the increasing tube thickness and the decreasing k_sf could make the inner wall surface approaching the uniform heat flux condition. It turns out that the basic function of the wall axial heat conduction for the cases studied is to unify the inner wall surface heat flux.