Heat transfer from a pulsed laminar impinging jet

A numerical investigation has been performed to study the effect of flow pulsations on time-averaged Nusselt number under a laminar impinging jet. The parameters considered are as follows: time-averaged jet Reynolds number (100 ≤ Re ≤ 1000), frequency of pulsation (1 ≤ f ≤ 20 Hz), and nozzle-to-target spacing (4 ≤ H/d ≤ 9). The combination of Re = 300, f = 5 Hz and H/d = 9 was found to give the best heat transfer performance. Interestingly, it was found that the onset of separation at the wall jet region of pulsating impinging jet is associated with the point of constant Nusselt number during the oscillation cycle. Downstream of the separation point in the wall jet region, the Nusselt number waveform fluctuates out of phase with the inlet velocity. Within one oscillation, large vortices existing during the minimum velocity state are broken into two smaller vortices when the flow is accelerated to reach the maximum velocity, after which the two vortices merge again when the flow decelerates back to the minimum velocity.     

Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements

Experimental investigation of heat transfer and friction factor characteristics in a double pipe heat exchanger fitted with regularly spaced twisted tape elements, were studied. The inner and outer diameters of the inner tube are 50.6 and 25.8 mm, respectively and cold and hot water were used as working fluids in shell side and tube side. The twisted tapes were made of the stainless steel strip with thickness of 1 mm and the length of 1500 mm. They were inserted in the test tube section in two different cases: (1) full-length typical twisted tape at different twisted ratios (y = 6.0 and 8.0), and (2) twisted tape with various free space ratios (S = 1.0, 2.0, and 3.0). The results, obtained from the tube with twisted tape insert, were compared with those without twisted tape. The results show that the heat transfer coefficient increased with twist ratio (y). Whereas the increase in the free space ratio (S) would improve both the heat transfer coefficient and friction factor. The results from each case were correlated for Nusselt number and friction factor. Subsequently, the predicted Nusselt number and friction factor from the correlations were plotted to compare with the experimental data. It was found that Nusselt number was within ± 15% and ± 10% for friction factor.     

Analysis of mixed convection in a vertical porous layer using non-equilibrium model

The problem of two-dimensional steady mixed convection in a vertical porous layer is investigated numerically in the present paper using the thermally non-equilibrium model. The vertical porous layer is assumed to have a finite isothermally heated segment on one vertical wall which is otherwise adiabatic and the other vertical wall is cooled to a constant temperature. Non-dimensionalization of the governing equations results in four parameters for both aiding and opposing flows: (1) Ra, Rayleigh number (2) Pe, Péclet number (3) K_r, thermal conductivity ratio parameter, and (4) H, heat transfer coefficient parameter. The numerical results are presented for 0.01  H  100, 0.01  K_r  100, 0.01  Pe  100 and Ra = 10, 50 and 100. The results show that, the thermal equilibrium model cannot predict the average Nusselt number correctly for small values of H × K_r. In both the aiding and opposing flows, the total average Nusselt number is decreasing with increasing the heat transfer coefficient parameter at low values of Pe, while for high values of Pe, higher H will enhance the total heat transfer rate. Increasing the thermal conductivity ratio leads to increase in the total average Nusselt number. It is found also that the total average Nusselt number depends strongly on the thermal conductivity ratio parameter and depends slightly on the heat transfer coefficient parameter.     

Heat transfer in inclined rectangular receivers for concentrated solar radiation

We study heat transfer in inclined rectangular cavities, which may be used as receivers of concentrated solar radiation. One of the active walls is subject to concentrated solar radiation and the other is kept at constant temperature. Continuity, momentum and energy equations are solved by finite difference — control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to10¹², the cavity aspect ratio, A = L/H from 0.5 to 2, the inclination angle, from 30 to 90°.We found that the Nusselt number is an increasing function of the Rayleigh number, the aspect ratio and the inclination angle. Based on the computed data a correlation is derived in the form of Nu = f(Ra, A, ).     

Reliable one dimensional 46-CPWTR model applied to two dimensional heat transfer problem of insulated triangular duct

In this study, the heat transfer characteristics of an insulated long triangular duct are analyzed by using the one dimensional plane wedge thermal resistance (PWTR) and plate thermal resistance (PTR) models. It is found that the errors produced by the PWTR model are all positive, but the errors produced by the PTR model are all negative. Thus, the combined plate wedge thermal resistance (CPWTR) model generated by paralleling PWTR and PTR models with the proportion factors of  = 0.4 vs. β = 0.6 (46-CPWTR model) is capable of neutralizing the positive and negative errors and returning very accurate results in comparison with the two dimensional numerical solutions analyzed by CFD software. The errors generated by the one dimensional 46-CPWTR model are within 1% for practical insulation thickness (t/R₂ < 0.5). In the rare situations of thicker insulation (0.5  t/R₂  2), most of the errors returned by the one dimensional 55-CPWTR model are within 2%. Thus, engineers can obtain very reliable heat transfer results by applying the one dimensional 46-CPWTR or 55-CPWTR models to an insulated triangular duct. Meanwhile, the PTR model can still be used to estimate the highest surface temperature for a hot fluid duct or the lowest surface temperature for a cool fluid duct.     

Experimental study of mixed convection and pressure drop in helically dimpled tubes for laminar and transition flow

This paper presents the experimental results carried out in dimpled tubes for laminar and transition flows and completes a previous work of the authors focused on the turbulent region. It was observed that laminar flow heat transfer through horizontal dimpled tubes is produced in mixed convection, where Nusselt number depends on both the natural convection and the entry region. Employing water and ethylene glycol as test fluids, the following flow range was covered: x^*=10⁻⁴–10⁻² and Ra=10⁶–10⁸.

The experimental results of isothermal pressure drop for laminar flow showed dimpled tube friction factors between 10% and 30% higher than the smooth tube ones. Moreover, it was perceived that roughness accelerates transition to critical Reynolds numbers down to 1400. Correlations for the laminar friction factor f=f(Re,h/d) and for the critical Reynolds Re_crit=Re_crit(h/d) are proposed. The hydraulic behaviour of dimpled tubes was found to depend mainly on dimple height.

In mixed convection, high temperature differences in the cross section were measured and therefore heat transfer was evaluated by a circumferentially averaged Nusselt number. Experimenal correlations for the local and the fully developed Nusselt numbers and are given. Results showed that at low Rayleigh numbers, heat transfer is similar to the smooth tube one whereas at high Rayleigh, enhancement produced by dimpled tubes can be up to 30%.     

Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids

Heat transfer enhancement in horizontal annuli using nanofluids is investigated. Water-based nanofluid containing various volume fractions of Cu, Ag, Al₂O₃ and TiO₂ nanoparticles is used. The addition of the different types and different volume fractions of nanoparticles were found to have adverse effects on heat transfer characteristics. For high values of Rayleigh number and high L/D ratio, nanoparticles with high thermal conductivity cause significant enhancement of heat transfer characteristics. On the other hand, for intermediate values of Rayleigh number, nanoparticles with low thermal conductivity cause a reduction in heat transfer. For Ra = 10³ and Ra = 10⁵ the addition of Al₂O₃ nanoparticles improves heat transfer. However, for Ra = 10⁴, the addition of nanoparticles has a very minor effect on heat transfer characteristics.     

Effect of temperature dependence of electrical resistivity on the cooling performance of a single thermoelectric element

The coefficients of performance (COP) φ₀ and φ for a single thermoelectric (TE) element welded with two metal plates were calculated as functions of temperature difference (ΔT) and thermoelectric figure of merit (ZT) from the conventional thermal rate equations and the new thermal rate ones proposed here, respectively. We made an attempt to take the differences in the Seebeck coefficient , electrical resistivity ρ and thermal conductivity κ of TE materials at the hot and cold sides of a TE element into the thermal rate equations on the assumption that their TE properties change linearly with temperature. However, the difference in κ was neglected even in the new thermal rate equations because its temperature dependence was too small when φ was applied to the high-performance Bi–Te alloys. The normalized temperature dependences at 300 K of and ρ were denoted by A and B, respectively. The term of A in the thermal rate equations was canceled out by the Thomson coefficient, but that of B remained. When B > 0 K⁻¹, φ/φ₀ is enhanced more significantly with an increase of B at larger ΔT and lower ZT, and it reached about 1.20 at ΔT = 80 K for Bi–Te alloys with B ≈ 5 × 10⁻³ K⁻¹. It was thus found that the COP of a cooling module is also affected strongly by B as well as ZT.     

Cooling strategy by mixed convection of a discrete heater at its optimum position in a square cavity with ventilation ports

We studied cooling strategy in a square enclosure with ventilation ports and a discrete heat source at its optimum position. We searched the optimum heater position by maximizing the global conductance at different Rayleigh and Reynolds numbers and considered three different ventilation ports arrangements. We solved the conservation equations of mass, momentum and energy for mixed convection. We found that the heater position is at off center in all cases, its optimum position is insensitive to the variation of Ra and Re; it solely depends on the ventilation ports arrangement. The Nusselt number is dependent on Ri = Ra/Re²: at its low values, Nu is a decreasing function of Ri and at its high values, it is an increasing function of it.     

Thermal performance analysis and optimum design parameters of heat exchanger having perforated pin fins

This paper reports the heat transfer enhancement and corresponding pressure drop over a flat surface equipped with circular cross section perforated pin fins in a rectangular channel. The channel had a cross section area of 100–250 mm². The experiments covered the following ranges: Reynolds number 13500–42,000, clearance ratio (C/H) 0, 0.33 and 1 and interfin spacing ratio (S_y/D) 1.208, 1.524, 1.944 and 3.417. Correlation equations were developed for the heat transfer, friction factor and enhancement efficiency. The experimental results showed that the use of circular cross section pin fins may lead to heat transfer enhancement. Enhancement efficiencies varied between 1.4 and 2.6 depending on clearance ratio and interfin spacing ratio. Using a Taguchi experimental design method, optimum design parameters and their levels were investigated. Nusselt number and friction factor were considered as performance parameters. An L₉(3³) orthogonal array was selected as an experimental plan. First of all, each goal was optimized separately. Then, all the goals were optimized together, considering the priority of the goals, and the optimum results were found to be Reynolds number of 42,000, fin height of 50 mm and streamwise distance between fins of 51 mm.     

Entropy generation due to conjugate natural convection in enclosures bounded by vertical solid walls with different thicknesses

Entropy generation due to conjugate natural convection heat transfer and fluid flow has been studied inside an enclosure with bounded by two solid massive walls from vertical sides at different thicknesses. Enclosure is differentially heated from vertical walls and horizontal walls are adiabatic. Governing equations which are written in streamfunction-vorticity form solved by finite difference technique for the governing parameters as Rayleigh number, 10³ ≤ Ra ≤ 10⁶, length ratio of solid walls as ₁ (for left vertical wall) and ₂ (for right vertical wall) and thermal conductivity ratio of solid to fluid (k), 1 ≤ k ≤ 10. Entropy generation contours due to fluid friction and heat transfer irreversibility, isotherms, streamlines, Nusselt numbers and velocity profiles were obtained. It is found that entropy generation increases with increasing of thermal conductivity ratio and thicknesses of the walls. Entropy generation due to heat transfer is more significant than that of fluid flow irreversibility for all values of thickness of the solid vertical walls.     

Natural convection in a parabolic enclosure with an internal vertical heat source filled with Cu–water nanofluid

The numerical investigation of the natural convection in concave and convex parabolic enclosures with a nanofluid consisting of water and copper nanoparticles is carried out by using the finite volume method. The upper and lower walls of the enclosures are adiabatic while the sidewalls are isothermal at a cold temperature. An internal heat source of constant length (ε = 0.2) and negligible thickness is placed at various vertical positions along the center of the enclosure. It was found that the increase in the location of the heat source leads to a drop in the water and nanofluid flow circulation in both types of enclosures. For both considered Cases I and II, the average Nusselt number increases when the Rayleigh number and solid volume fraction increase. Moreover, it was concluded that Case I with δ = 0.8 is the optimum case for heat transfer enhancement for Ra = 10³ and Ra = 10⁴. Case II with δ = 0.5 is optimum for Ra = 10⁵. Both cases are satisfied when the nanofluid is used with ? = 0.2.     

Mass-transfer to a channel wall downstream of a cylinder

The electrochemical method is used to measure the mass-transfer to a channel wall downstream of a cylinder. For Reynolds numbers based on cylinder diameter Re > 50, the flow is unsteady, and the mass-transfer rate is a function of time. When 50 < Re < 200, the mass-transfer rate is periodic with a frequency in the range of 1–3 Hz. When the ratio of cylinder diameter d to channel height h is 0.25, the Strouhal number is measured to be 0.27±0.02, and when d/h = 0.51, the Strouhal number is 0.49±0.01. The average mass-transfer rate at various positions downstream of the cylinder is reported. Experiments are compared to two-dimensional numerical simulations. The simulated and experimental variations of Nusselt number with position and Re contain similar features, but exact agreement is not found.     

Computation of flow and heat transfer in rotating two-pass rectangular channels (AR = 1:1, 1:2, and 1:4) with smooth walls by a Reynolds stress turbulence model

Numerical predictions of three-dimensional flow and heat transfer are presented for rotating two-pass smooth channels with three aspect ratios (AR = 1:1; 1:2; 1:4). Detailed predictions of mean velocity, mean temperature and Nusselt number for two Reynolds numbers (Re = 10,000 and 100,000) were carried out. A total of fifteen calculations have been performed with various combinations of rotation number, Reynolds number, and coolant-to-wall density ratio. The rotation number and inlet coolant-to-wall density ratio varied from 0.0 to 0.28 and from 0.13 to 0.40, respectively. The focus of this study is to investigate the effect of the channel aspect ratio, the Reynolds number, and the coolant-to-wall density ratio on the nature of the flow and heat transfer. A multi-block Reynolds-averaged Navier–Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure. In the present method, the convective transport equations for momentum, energy, and turbulence quantities are solved in curvilinear, body-fitted coordinates using the finite-analytic method.     

Technical Note Transient behavior of vertical buoyancy layer in a stratified fluid

horizontal length scale of the vertical channelg acceleration of gravityRa Rayleigh number [ ≡ gβT_oD⁴ν]T temperaturew velocity component in the z-directionx horizontal coordinatez vertical coordinate.Greek symbols coefficient of thermometric expansionδ thermal perturbation thermal diffusivityν kinematic viscosityσ Prandtl number [ ≡ νχ].     

Thermo-economics for endoreversible heat-engines

The thermoeconomics of endoreversible heat engines has been studied based on the linear phenomenological heat-transfer law [i.e., the heat flux Q ∝ Δ(1/T), where T is the absolute temperature]. Analytical formulae for profit, the maximum profit and the corresponding efficiency are derived.     

Dropwise Condensation Heat Transfer on Plasma-Ion-Implanted Small Horizontal Tube Bundles

Stable dropwise condensation of saturated steam was achieved on stainless-steel tube bundles implanted with nitrogen ions by plasma ion implantation. For the investigation of the condensation heat transfer enhancement by plasma ion implantation, a condenser was constructed in order to measure the heat flow and the overall heat transfer coefficient for the condensation of steam on the outside surface of tube bundles. For a horizontal tube bundle of nine tubes implanted with a nitrogen ion dose of 10¹⁶ cm^{? 2}, the enhancement ratio, which represents the ratio of the overall heat transfer coefficient of the implanted tube bundle to that of the unimplanted one, was found to be 1.12 for a cooling-water Reynolds number of about 21,000. The heat flow and the overall heat transfer coefficient were increased by increasing the steam pressure. The maximum overall heat transfer coefficient of 2.22 kW · m^?2· K^?1 was measured at a steam pressure of 2 bar and a cooling-water Reynolds number of about 2,000. At these conditions, more dropwise condensation was formed on the upper tube rows, while the lowest row received more condensate, which converted the condensation form to filmwise condensation.     

Parametric study on turbulent heat transfer and flow characteristics in a circular tube fitted with louvered strip inserts

In the present work, characteristics of heat transfer, flow resistance, and overall thermo-hydraulic performance of turbulent airflow in a circular tube fitted with louvered strip inserts were investigated through numerical simulation. Our main attention was paid to the effects of the slant angle and pitch of the turbulators. The results show that the Nusselt number is augmented by 2.75–4.05 times (Nu = 108.71–423.87) as that of the smooth tube. The value of performance evaluation criterion (PEC) lies in the range of 1.60–2.05, which demonstrates that the louvered strip insert has a very good overall thermo-hydraulic performance. Moreover, the computational results indicate that larger slant angle and small pitch can effectively enhance the heat transfer rate, but also increase the flow resistance. Furthermore, it is noted that the Nusselt number and friction factor are more sensitive to the slant angle than the inserts pitch. Comparatively steady and good overall thermo-hydraulic performance can be obtained at a moderate slant angle together with a small pitch. All these data show that the louvered strip is a promising tube insert which would be widely used in heat transfer enhancement of turbulent flow.     

Chimney effect in a “T” form cavity with heated isothermal blocks: The blocks height effect

In this paper, a numerical study of natural convection from a two dimensional “T” form cavity with rectangular heated blocks is conducted. The blocks are identical, and the domain presents a symmetry with respect to a vertical axis passing through the middle of the opening. The governing equations are solved using a control volume method, and the SIMPLER algorithm for the velocity–pressure coupling is employed. Special emphasis is given to detail the effect of Rayleigh number and block height on the heat transfer and the flow rate generated by the chimney effect. The results are given for the parameters of control as, 10⁴Ra3×10⁶, Pr=0.71, opening diameter (C=l^′/H^′=0.15), blocks gap (D=d^′/H^′=0.5) and blocks height (1/8B=h^′/H^′1/2). These results show that the heat transfer variation with Ra is in the same manner as those met in the case of the vertical smooth or ribbed channels.     

Thermochemical hydrogen production from a two-step solar-driven water-splitting cycle based on cerium oxides

A new thermochemical cycle for H₂ production based on CeO₂/Ce₂O₃ oxides has been successfully demonstrated. It consists of two chemical steps: (1) reduction, 2CeO₂ → Ce₂O₃ + 0.5O₂; (2) hydrolysis, Ce₂O₃ + H₂O → 2CeO₂ + H₂. The thermal reduction of Ce(IV) to Ce(III) (endothermic step) is performed in a solar reactor featuring a controlled inert atmosphere. The feasibility of this first step has been demonstrated and the operating conditions have been defined (T = 2000 °C, P = 100–200 mbar). The hydrogen generation step (water-splitting with Ce(III) oxide) is studied in a fixed bed reactor and the reaction is complete with a fast kinetic in the studied temperature range 400–600 °C. The recovered Ce(IV) oxide is then recycled in first step. In this process, water is the only material input and heat is the only energy input. The only outputs are hydrogen and oxygen, and these two gases are obtained in different steps avoiding a high temperature energy consuming gas-phase separation. Furthermore, pure hydrogen is produced (it is not contaminated by carbon products like CO, CO₂), thus it can be used directly in fuel cells. The results have shown that the cerium oxide two-step thermochemical cycle is a promising process for hydrogen production.