A theoretical study of laminar mixed convection from a horizontal cylinder in a cross stream

The problem of laminar mixed convection from a horizontal isothermal cylinder is considered. The free stream direction is assumed to be horizontal and perpendicular to the cylinder axis. The study is based on the solution of the full Navier-Stokes and energy equations for 2-dim. flow of a Boussinesq fluid. The free stream is assumed to start impulsively from rest and the velocity and thermal boundary layers are developed in time until reaching steady conditions. The investigation covered the ranges of Reynolds number 1 < Re < 40 and Grashof numbers up to Gr = 5 Re² while keeping Prandtl number at a constant value of 0.7. Comparison of results with previous experimental correlations shows a good agreement. The streamline and isotherm patterns are plotted and different aspects of the phenomenon are discussed.     

Heat transfer enhancement in a tube using circular cross sectional rings separated from wall

A numerical study was undertaken for investigating the heat transfer enhancement in a tube with the circular cross sectional rings. The rings were inserted near the tube wall. Five different spacings between the rings were considered as p = d/2, p = d, p = 3d/2, p = 2d and p = 3d. Uniform heat flux was applied to the external surface of the tube and air was selected as working fluid. Numerical calculations were performed with FLUENT 6.1.22 code, in the range of Reynolds number 4475–43725. The results obtained from a smooth tube were compared with those from the studies in literature in order to validate the numerical method. Consequently, the variation of Nusselt number, friction factor and overall enhancement ratios for the tube with rings were presented and the best overall enhancement of 18% was achieved for Re = 15,600 for which the spacing between the rings is 3d.     

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%.     

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.     

Total and local heat transfer from a smooth circular cylinder in cross-flow at high reynolds number

The total and local heat transfer from a smooth circular cylinder to the cross flow of air has been measured over the Reynolds number range 3 × 10⁴ < Re < 4 × 10⁶. The interaction between flow and heat transfer is discussed. In particular, the boundary-layer effects on the heat transfer, such as transition from laminar to turbulent flow or boundary-layer separation, are considered in conjunction with the distributions of local static pressure and skin friction.     

Three-dimensional driven-cavity flows with a vertical temperature gradient

Numerical studies of three-dimensional flows in a cubical container with a stable vertical temperature stratification are carried out. Flows are driven by the top lid, which slides in its own plane at a constant speed. The top wall is maintained at a higher temperature than the bottom wall. The end walls and the side walls are thermally insulated. Numerical solutions are obtained over a wide range of physical parameters, i.e. 10² ≤ Re ≤ 2 × 10³, 0 ≤ Ri ≤ 10.0 and Pr = 0.71, where the mixed-convection parameter Ri Gr. Re⁻². Systematical comparison of the three-dimensional numerical solutions with the previously reported two-dimensional results illuminates the impact of thermal stratification on the three-dimensional flow characteristics. When Ri < O(1), the effect of the vertical temperature gradient is minor, and the flow structures are similar to those of the non-stratified fluid flows in a conventional lid-driven cavity flow. Fluids in the primary vortex are well mixed, and the temperature is fairly uniform in the main circulating region. When Ri ≥ O(1), the stable temperature distribution tends to suppress the vertical fluid motion. Much of the fluid motion takes place in the vicinity of the top sliding lid and the bulk of the cavity region is nearly stagnant. When Ri > O(1), the fluid motion exhibits vertically layered vortex structures. The Nusselt number is computed at the top and bottom wall, and this also illustrates the varying flow characteristics as Ri encompasses a broad range. Extensive numerical flow visualizations are conducted. Plots demonstrating the primary flows in the (x−y) plane and the secondary flows in the (y−z) plane are presented. These display the influences of Re and Ri on the basic character of the flow and the three-dimensional effects.     

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.     

Crack propagation rate as a function of crack tip characteristics

The dependence of crack growth rate on various crack tip parameters was studied. Experiments were performed on thin sheets of 6063-T6 Al-alloy having a central notch, to find crack tip opening displacement, total strain range, plastic strain range, crack opening stress and crack growth rate. Crack tip opening displacement and crack opening stress were measured, using a surface measurement technique, with small crack opening displacement gauges. The theoretical predictions of crack tip opening displacement compare fairly well with the experimental values. It is found that crack propagation rate vs total strain range-plastic strain range gives a straight-line fit on a log-log graph and, for positive stress ratios, the fatigue crack growth rates are found to be independent of R.

Experimental results show that the crack opening stress is not affected by the position of the gauge when it is mounted behind and near the crack tip.

The effect of mechanical properties and loading on crack growth were also studied. The specimens were fatigue cracked to a predetermined length and some specimens were annealed and again loaded cyclically. The application of cyclic loads to annealed specimens caused significant increase in crack propagation rates in comparison with the specimens having no heat-treatment. The load-displacement record was found to stabilize in about 10 cycles; the crack then extended slowly as a fatigue crack. Crack propagation rates for different values of R for annealed and work-hardened material were plotted against a crack tip parameter, ΔK*, based on notional crack lengths. Since the results of da/dN vs ΔK* for both states of material (as-received and annealed) seem to lie on the same straight line on a log-log graph, the study provides a hope that the results for a material tested in any state (annealed or work-hardened) for positive values of R (0·0≤R≤0·3) will lie on this line, thus eliminating fatigue tests on the same material under different work-hardening conditions for different values of R. Models for da/dN have been developed using various crack tip parameters.     

Periodic, fully developed, natural convection in a channel with corrugated confining walls

Numerical solutions are obtained for natural convection heat transfer in an open channel with corrugated, isothermal confining walls. The channel is very long so that the fluid temperature approaches the wall temperature and the flow can be assumed to be periodically fully developed. The solutions are obtained by solving the full elliptic governing equations in a transformed coordinate system which maps the channel with corrugated walls onto a channel with flat walls. The periodic, fully developed Nusselt number for the corrugated channel is expressed by the relation Nu = CGrPr/(L/W) where Gr, Pr and L/W are the Grashof number, the Prandtl number and the aspect ratio, respectively, and C is a parameter which is a function of Gr, L/W and the corrugation angle θ. In the limiting case of θ = 0° (two flat walls), the parameter C approaches a constant value. This value is within 1.6% of the exact analytical result.     

Effects of ambient turbulence and fuel properties on the evaporation rate of single droplets

Results of the evaporation of a single liquid fuel droplet in various free-stream turbulence intensities and scales are reported. Experiments are carried out at room temperature by using n-heptane and n-decane fuels at Re_d=100. A low-speed vertical wind tunnel with different turbulence intensities and scales, controlled by using different sizes of disk, is constructed. The free-stream turbulence intensities are varied in the range from 1% to 60% and the integral length scales are from 2.5 to 20 times of the initial droplet diameter. Results show that the time history of droplet diameter follows the d²-law in turbulent environments with generally higher evaporation rates as compared with those in quasi-laminar cases. Combined effects of liquid fuel properties and ambient turbulence properties on the evaporation rate can be reasonably well explained by the correlation of normalized evaporation rate with the effective vaporization Damköhler number, Da_v.     

Finite element based evaluation of stress intensity factors for interactive semi-elliptic surface cracks

A finite thickness plate with two coplanar self-same shallow and deep semi-elliptical surface cracks subjected to remote tensile surface traction is considered for fracture analysis. Based on three-dimensional (3D) finite element solutions, stress intensity factors (SIFs) are evaluated along the entire crack front using a force method. The line spring model has also been used to evaluate crack depth point SIFs using shell finite element analysis. A wide range of geometric dimensions and crack configurations viz. crack shape aspect ratio (0.3≤a/c≤1.2), crack depth ratio (1.25≤t/a≤6), relative crack location (0.33≤2c/d≤0.9) and normalized location on the crack front (0≤2φ/π≤2) are considered for numerical estimation of crack interaction factors. SIFs evaluated at the depth point using the force method from the 3D finite element results are compared with SIFs evaluated using the line spring model. Finally, using finite element results, an empirical relation is proposed for the evaluation of crack interaction factors. For the ranges considered, the proposed empirical relation predicts crack interaction factors at critical locations within ±2% of the 3D finite element solutions.     

Experimental studies of laminar flow and heat transfer in a one-porous-wall square duct with wall injection

Experiments were conducted to investigate the effect of fluid injection on laminar flow and heat transfer characteristics in a one-porous-wall square duct. Uniform air flow at Re₀ = 400−2000 entered the duct with a cross section of 20 × 20 mm² and a ratio of the active injection length to the hydraulic diameter of 40. Pressurized air was injected through a thick layer of porous material for flow uniformity and a heated porous duct wall at injection rates Re_w = 5−20. All of the measured and deduced data, including the axial velocity profiles, the pressure drops, the friction factors, the porous wall temperatures, the outlet fluid temperatures and the Nusselt numbers, were presented and compared with the previous theoretical results. The deduced friction factors and Nusselt numbers from the experimental data were correlated within differences of ±10% and ±15% respectively.     

Measurements of convective heat transfer from a horizontal cylinder rotating in a tank of water

The present paper deals with measurements of heat transfer from a horizontal cylinder rotating in water. The experimental results have been correlated by the equation Nu = 0.133Re^2/3 · Pr^1/3 for a range of rotating Reynolds numbers from 1000 to 46 000, and Prandtl numbers from 2.2 to 6.4. This equation compares very well with the experimental and theoretical information available for air, water and oil in published works.

The analogy suggested by Anderson and Saunders between natural convection from a horizontal plate and the present type of flow has been used to predict the Nusselt numbers. The analogy solution and the present experimental results have been found to compare very well with each other.     

Forced-convective internal cooling of a horizontal equilateral-triangle cross-sectioned duct

An experimental determination of the steady-state forced convection from the internal surfaces of a horizontal, uniformly heated electrically, equilateral-triangle cross-sectioned duct with sharp corners has been undertaken. The average Nusselt number _D, using the hydraulic diameter as the characteristic physical dimension, is a constant if the flow in the duct is laminar, but a function of the air's Reynolds number, when the flow is turbulent. Non-dimensional correlations, which can be used for predicting the value of the steady-state rate of convective heat transfer from such a triangular duct into the airflow, have been deduced, viz. _D = 3·25 for laminar flows, i.e. Re_D < 1450; and _D = 0·012 Re_D^0·83 for turbulent flows, i.e. Re_D ≥ 1450.     

Numerical Investigation of Flow and Heat Transfer Characteristics of Two Tandem Circular Cylinders of Different Diameters

Unsteady laminar flow and heat transfer characteristics from a downstream cylinder of two tandem circular cylinders of different in diameters are numerically investigated. The working fluid is air, and the downstream cylinder is isothermal while the upstream cylinder is kept adiabatic. Two-dimensional numerical simulations are carried out for Reynolds numbers of 100 and 200. The ratio of the upstream to downstream cylinder diameters (diameter ratio) and the ratio of the gap distance to the downstream cylinder diameter (gap ratio) are considered in the range of 0.3 to 2 and 0.5 to 4, respectively. Numerical solutions are obtained using the FLUENT® software. The flow parameters such as the rms lift/drag coefficients and Strouhal numbers are computed and analyzed for the diameter ratio and gap ratio intervals investigated. The iso-vorticity lines and isotherms are also generated to understand, identify and analyze the flow and heat transport characteristics. Four basic flow structures are observed and classified as (i) over-shoot, (ii) symmetric-reattachment, (iii) front-side reattachment and (iv) co-shedding flow. The critical spacing, which marks the minimum gap spacing for the vortex formation to begin, depends on the diameter ratio and Reynolds number, and it decreases with increasing Reynolds number. The convective heat transfer phenomenon is observed to be strongly influenced by diameter ratio, gap ratio and Reynolds number. The mean and the local Nusselt number along the perimeter of isothermal cylinder are computed and discussed in connection with the flow characteristics.     

Non-thermal equilibrium melting of granular packed bed in horizontal forced convection. Part I: experiment

A series of experiments are conducted to investigate the non-thermal equilibrium characteristics of melting of a packed bed under horizontal forced and mixed convections. This configuration imposes a complex treatment in phase change heat transfer that involves not only the coupled heat, mass and momentum exchanges but also the local geometric change of the packed bed (packing effect). Using visualization observations and measurements, we determine experimentally the volumes and packing patterns of the melting granular packed beds and the time variation of average melting rate per unit bed volume and average heat transfer coefficient for Re=71–2291, Gr/Re²=1.48×10⁻⁵–17.32, and Ste=0.0444–0.385. The effects of water velocity and water temperature on the melting and heat transfer in the melting process are analyzed. The effects of packing patterns on Nusselt number correlations are presented. Using the definition of a terminal velocity, a Reynolds number ratio is developed as the criterion defining the floating, non-floating or transitional packing pattern.     

Experimental study on the unsteady laminar heat transfer downstream of a backwards facing step

The objective of this work is to study experimentally the unsteady heat transfer downstream of a backward-facing step in the 2-D laminar regime when the inlet flow is pulsated. To this aim, an experimental set-up has been prepared with water as the working fluid. The Reynolds number based on the hydraulic diameter of the inlet channel and average inlet velocity is 300. Inlet flow temperature is 30 °C and a region downstream of the step is heated up to 74 °C. Pulsation is achieved using a piston pump and heat transfer is studied up to a maximum pulsation Strouhal number of 1.2. The results obtained confirm previous numerical simulation work in the sense that pulsation could be used to partially recover the heat transfer efficiency that is lost in steady flow conditions downstream of a backward-facing step. It has also been confirmed that the behaviour of the averaged Nusselt number versus pulsation Strouhal number is of the resonant type. That is: the Nusselt number increases from the steady situation up to a certain value of the Strouhal number (0.41 in our case) and, then, it degrades as the frequency of the pulsation is further increased.     

A NUMERICAL INVESTIGATION OF THE CONVECTIVE HEAT TRANSFER IN UNSTEADY LAMINAR FLOW PAST A SINGLE AND TANDEM PAIR OF SQUARE CYLINDERS IN A CHANNEL

The unsteady laminar flow and heat transfer characteristics from square cylinders located in a channel with a fully developed inlet velocity profile were studied numerically. The time-averaged Nusselt number for each face and the time-averaged cylinder Nusselt number (Nu) were determined, as well as aerodynamic characteristics such as cylinder lift, drag, and eddy-shedding Strouhal number (St) . The results show that the cylinder Nu decreases for both the single and the tandem pair of cylinders as they approach the channel wall. The upstream eddy-promoting cylinder significantly reduces the drag of the downstream cylinder as compared with that of the single cylinder. The St decreases as the wall is approached and is larger for the tandem pair than for the single cylinder for all positions.     

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.     

Synthesis of LiCoO2 from cobalt—organic acid complexes and its electrode behaviour in a lithium secondary battery

Well-crystallized, layered LiCoO₂ has been prepared by heating cobalt—organic acid complexes (such as malic acid and succinic acid) at 900 °C in air after preheating at 400 °C (2 h) and at 650 °C (6 h). LiCoO₂ obtained by this method shows a high (003) peak intensity and low (104) or (101) intensities in X-ray diffraction (XRD). The first discharge capacity of LiCoO₂ obtained from this method in ester-based electrolyte is 132 mA h g⁻¹ on cycling between 4.3 and 3.7 V. The value is larger than that obtained by the conventional method. X-ray diffraction studies and open-circuit voltage curves show the presence of at least two types of reaction. A two-phase reaction occurs in the region of 0.71<χ <1.0 in Li_xCoO₂. The lithiation proceeds as a homogeneous reaction together with expansion of the c-axis in the region of 0.47<χ<0.71. The expansion of the c-axis againstΔχ at x=0.56 corresponds well with the voltage jump observed in the charge/discharge curves.