Effects of Reynolds and Prandtl numbers on heat transfer from a square cylinder in the unsteady flow regime

The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 ? Re ? 160 and 0.7 ? Pr ? 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.     

Experimental study of heat transfer enhancement with wire coil inserts in laminar-transition-turbulent regimes at different Prandtl numbers

Helical-wire-coils fitted inside a round tube have been experimentally studied in order to characterize their thermohydraulic behaviour in laminar, transition and turbulent flow. By using water and water–propylene glycol mixtures at different temperatures, a wide range of flow conditions have been covered: Reynolds numbers from 80 to 90,000 and Prandtl numbers from 2.8 to 150. Six wire coils were tested within a geometrical range of helical pitch 1.17 < p/d < 2.68 and wire diameter 0.07 < e/d < 0.10. Experimental correlations of Fanning friction factor and Nusselt number as functions of flow and dimensionless geometric parameters have been proposed. Results have shown that in turbulent flow wire coils increase pressure drop up to nine times and heat transfer up to four times compared to the empty smooth tube. At low Reynolds numbers, wire coils behave as a smooth tube but accelerate transition to critical Reynolds numbers down to 700. Within the transition region, if wire coils are fitted inside a smooth tube heat exchanger, heat transfer rate can be increased up to 200% keeping pumping power constant. Wire coil inserts offer their best performance within the transition region where they show a considerable advantage over other enhancement techniques.     

Conjugate unsteady heat transfer from a spherical droplet at low Reynolds numbers

The phenomena of conjugate unsteady heat transfer from a spherical droplet or particle moving in a continuous fluid medium is numerically investigated. The energy equation is solved for a spherical droplet using the implicit, finite-difference method of alternating directions (ADI). In this study, the volumetric heat capacities of the two phases are of comparable magnitude but not necessarily equal to each other and the value of the thermal diffusivities of the two phases are set equal to each other. The range of Péclet numbers investigated are : 50⩽ Pe ⩽ 1000, with ratios of volumetric heat capacities, (interior to exterior) varying between 0.333 and 3.0. The velocities used in the convective terms are those corresponding to low Reynolds number flow. It was found that the dimensionless temperature profile asymptotically approaches a steady-state value that is independent of the initial profile in the droplet.     

Experimental investigation on heat transfer and frictional characteristics of spirally corrugated tubes in turbulent flow at different Prandtl numbers

Corrugated tubes have been experimentally studied in order to obtain their heat transfer and isothermal friction characteristics. The use of water and ethylene glycol as test fluids has allowed to cover a wide range of turbulent fluid flow conditions: Reynolds number from 2000 to 90 000 and Prandtl number from 2.5 to 100.The paper presents a comprehensive experimental study on a family of 10 corrugated tubes which were manufactured by cold rolling. Artificial roughness is characterised by rib height h/d ranging from 0.02 to 0.06 and spiral pitch p/d from 0.6 to 1.2. The results show that a unique dimensionless parameter named severity index (φ=h²/pd) can be used to establish roughness influence on flow.The large amount of experimental data has been correlated in order to obtain easy to use expressions for Fanning friction factors and Nusselt numbers as functions of flow and geometry dimensionless parameters. The real benefits which are offered by corrugated tubes have been assessed by calculating one of the performance evaluation criteria commonly used in the enhanced heat transfer literature. Finally an optimisation study shows the guidelines to choose which roughness geometry offers the best performance for specific flow conditions.     

Momentum and heat transfer phenomena of spheroid particles at moderate Reynolds and Prandtl numbers

The momentum and heat transfer phenomena of spheroid particles in an unbounded Newtonian fluid have been numerically investigated by solving governing conservation equations of the mass, the momentum and the energy. The numerical solution methodology has been benchmarked by performing comparisons between present results with those reported in the literature. Further, extensive new results have been obtained to elucidate effects of pertinent dimensionless parameters such as the Reynolds number (Re), the Prandtl number (Pr) and the aspect ratio (e) on the flow and heat transfer behaviour of spheroid particles in the range of parameters: 1 ? Re ? 200; 1 ? Pr ? 1000 and 0.25 ? e ? 2.5. Regardless of the value of the Reynolds number, the total and individual drag coefficients of oblate spheroids (e < 1) are smaller than those of spheres (e = 1) and opposite trend has been observed for prolate spheroids (e > 1). Irrespective of values of Reynolds and Peclet numbers, the average Nusselt number is large for prolate particles as compared to spheres and opposite trend has been observed for the case of oblate particles. Major contribution of this work is the development of simple correlations for the total drag coefficient and the average Nusselt number of unconfined isolated spheroid particles based on present numerical results which can be used in new applications.     

Periodic state of fluid flow and heat transfer in a lid-driven cavity due to an oscillating thin fin

Results of a computational study of periodic laminar flow and heat transfer in a lid-driven square cavity due to an oscillating thin fin are presented. The lid moves from left to right and a thin fin is positioned normal to the right stationary wall. The length of the fin varies sinusoidally with its mean length and amplitude equal to 10% and 5% of the side of the cavity, respectively. Two Reynolds numbers of 100 and 1000 for a Pr = 1 fluid were considered. For a given convection time scale (t_conv), fin’s oscillation periods (τ) were selected in order to cover both slow (TR = τ/t_conv > 1) and fast (τ/t_conv < 1) oscillation regimes, covering a Strouhal number range of 0.005–0.5. The periodic flow field for the case with Re = 1000 and TR = 10 is distinguished by the creation, lateral motion and subsequent wall impingement of a CCW rotating vortex within the lower half of the cavity. Periodic flow and thermal fields of the other nine cases studied were not as varied. Phase diagrams of the stream function and temperature vs. fin’s length clearly exhibit the synchronous behavior of the system. Amplitude of fluctuations of the kinetic energy and temperature are very intense near the fin. As the fin oscillates slower, a greater portion of the cavity exhibits intense fluctuations. For slow to moderate oscillations, the maximum value of K_amp is observed to be greater for Re = 1000 in comparison to Re = 100. For fast oscillations, this behavior is reversed. The maximum values of the amplitude of fluctuations of temperature increase monotonically as the fin oscillates slower. The maximum values of θ_amp are greater for Re = 1000 compared to Re = 100. The amplitude of fluctuations of the mean Nusselt number on four walls increase as the fin oscillates slower.     

Turbulent heat and mass transfer between wall and fluid streams of large Prandtl and Schmidt numbers

The expression for eddy diffusivity in a previous analysis was revised. By using the revised expression, good agreement was obtained between the predicted and experimental results for mass transfer at Schmidt numbers between 800 and 15,000.     

On the laminar and turbulent free convection heat transfer from a vertical plate over the entire range of Prandtl numbers

In a number of papers, Arpaci et al. (Int. J. Heat Mass Transfer, 29, 1071 (1986); 40, 3819 (1997) obtained equations for the laminar and turbulent heat transfer in free convection from a vertical plate over the entire range of Prandtl numbers. The objective of the present paper is to note that their approach for the laminar case is similar to that of Ruckenstein (AIChE Journal, 26, 850 (1980). Their treatment of the turbulent case differs from that of Ruckenstein and Felske (J. Heat Transfer, 102, 773 (1980) and arguments are brought to demonstrate that the latter is more plausible than the former.     

Unsteady wake dynamics and heat transfer in forced and mixed convection past a circular cylinder in cross flow for high Prandtl numbers

This paper investigates the combined effect of Prandtl number and Richardson number on the wake dynamics and heat transfer past a circular cylinder in crossflow using a SUPG based finite element method. The computations are carried out for 80 < Re < 180, 0.7 < Pr < 100 and $0?\mathrm{Ri}?2$. The results have been presented for both forced and mixed convection flows. In the case of forced convection, crowding of temperature contours with reduced spatial spread is observed for increasing Prandtl numbers. The local and average Nusselt numbers are found to increase with increasing Reynolds number and Prandtl number. The average Nusselt number and Colburn factor are found to vary as Re^0.548 Pr ^0.373 and Re^?0.452, respectively. The extrapolated results of the average Nusselt number for low and high Reynolds numbers are found to match quite well with the available results in literature. Effect of Prandtl number shows various interesting phenomena for the mixed convective flows. Increasing the Prandtl numbers resulted in decreasing deflection and strength in the wake structures. The effect of baroclinic vorticity production during vortex shedding has been demonstrated at the vicinity of the cylinder and near wake. The Strouhal number is found to decrease with increasing Prandtl number, in the case of buoyancy induced flow. The effect of increasing Prandtl number is manifested as the stabilizing effect in the flow. This is, perhaps, the first time that such behavior for the Prandtl number is being reported. Additionally it is observed that the average Nusselt number decreases with increasing Richardson number.     

Single-phaseexperimental analysis of heat transfer in helically finned heat exchanger

A methodology for designing helically serrated finned tube heat exchanger based on the logarithmic Mean Temperature Difference (LMTD) method is validated with experimental tests. The method uses semi-empirical correlations for calculating convective coefficients both inside and outside staggered tube bundles. Equipment was designed, built, and installed in a paper factory in order to validate the methodology. Comparisons between predictions and experimental data show a precision of approximately 96% in heat transfer and approximately 90% in pressure drop for Reynolds numbers upper to 10,000.     

Laminar natural convection in a square cavity: Low Prandtl numbers and large density differences

Steady natural convection at low Prandtl numbers caused by large density differences in a square cavity heated through the side walls is investigated numerically and theoretically. An appropriate dimensionless parameter characterizing the density differences of the working fluid is identified by the Gay-Lussac number. The Boussinesq assumption is achieved when the Gay-Lussac number tends to zero. The Nusselt number is derived for the ranges in Rayleigh number 10 ? Ra ? 10⁸, in Prandtl number 0.0071 ? Pr ? 7.1 and in Gay-Lussac number 0 ? Ga < 2. The effects of the Rayleigh, Prandtl and Gay-Lussac numbers on the Nusselt number are discussed on physical grounds by means of a scale analysis. Finally, based on physical arguments, a heat transfer correlation is proposed, valid for all Prandtl and Gay-Lussac number ranges addressed.     

Computational study of unsteady mixed convection heat transfer of nanofluids in a 3D closed lid-driven cavity

Mixed heat convection of three-dimensional unsteady flow of four different types of fluids in a double lid-driven enclosure is simulated by a two-phase mixture model in this project. The cubic cavity with moving isothermal sidewalls has uniform heat flux on the middle part of the bottom wall, and the other remaining walls forming the enclosure are adiabatic and stationary. The relevant parameters in the present research include Reynolds number Re (5000–30,000), nanoparticle diameter (25 nm–85 nm), and nanoparticle volume fraction (0.00–0.08). In general, remarkable effects on the heat transfer and fluid patterns are observed by using nanofluids in comparison to the conventional fluid. Different types of nanofluids or different diameters of nanoparticles can make pronounced changes in the heat convection ratio. In addition, increasing in either volume fraction of nanoparticles or Reynolds number leads to increasing in the Nusselt number, fluctuation kinetic energy and root mean square velocity of the fluid in the domain. It is also found that both URANS and LES methods have shown good performance in dealing with unsteady flow conducted in this project. However, the comparisons have elucidated clearly the advantages of the LES approach in predicting more detailed heat and flow structures.     

Prediction of turbine blade heat transfer and aerodynamics using a new unsteady boundary layer transition model

The effects of periodic unsteady flow on heat transfer and aerodynamic characteristics, particularly on the boundary layer transition along the suction and the pressure surfaces of a typical gas turbine blade, are experimentally and theoretically investigated. Comprehensive aerodynamic and heat transfer experimental data are collected for different unsteady passing frequencies that are typical of gas turbines. To predict the effect of the impinging periodic unsteady flow on the heat transfer and the aerodynamics of turbine blades, a new unsteady boundary layer transition model is developed. The model is based on a universal unsteady intermittency function and utilizes an inductive approach that implements the results of comprehensive experimental and theoretical studies of unsteady wake development and the boundary layer flow. Three distinct quantities are identified as primarily responsible for the transition of an unsteady boundary layer: (1) the universal relative intermittency function, (2) maximum intermittency, and (3) minimum intermittency. The analysis of the experimental results and the comparison with the model prediction confirm the validity of the model and its capability to accurately predict the unsteady boundary layer transition.     

Parametric study of unsteady flow and heat transfer in a pin-fin heat exchanger

A numerical study has been carried out to analyze the unsteady three-dimensional flow and heat transfer in a parallel-plate channel heat exchanger with in-line arrays of periodically mounted rectangular cylinders (pins) at various Reynolds number and geometrical configurations. The three-dimensional unsteady Navier-Stokes and energy equations are solved using higher order temporal and spatial discretizations. The simulations have been carried out for a range of Reynolds number based on cylinder width (180-600) and a Prandtl number of 6.99 (corresponding to water). Conjugate heat transfer calculations have been employed to account for the conduction in the solid cylinder and convection in the fluid. The thermal performance factor (TPF) increases significantly when the flow becomes unsteady. The choice of aspect ratio of the cylinders is judged by their relative increase in friction factor and heat transfer at transitional Reynolds number. The TPF is found to increase with the increase in pitch of the cylinders. The increase in channel height enhances the TPF though the heat transfer decreases at higher channel height.     

Flow and heat transfer over an unsteady stretching surface with non-uniform heat source

The non-uniform heat source/sink effect on the flow and heat transfer from an unsteady stretching sheet through a quiescent fluid medium extending to infinity is studied. The boundary layer equations are transformed by using similarity analysis to be a set of ordinary differential equations containing three parameters: unsteadiness parameter (S), space-dependent parameter (A?) and temperature-dependent parameter (B?) for heat source/sink. The velocity and temperature fields are solved using the Chebyshev finite difference method (ChFD). Results showed that the heat transfer rate, − θ′(0) and the skin friction, − f″(0) increase as the unsteadiness parameter increases whereas decrease as the space-dependent and temperature-dependent parameters for heat source/sink increase.     

Numerical modelling of heat and mass transfer in finned dehumidifier

In several heat exchange devices, phase transition occurs in a small region adjacent to the wall, and the secondary phase is present only in a thin layer running along the wall, allowing for decoupling between the fluid dynamic computation of the core flow and the numerical analysis of the secondary phase. This happens in finned dehumidifier, but also in spray cooling or defogging problems. In a finned dehumidifier, or in air conditioning evaporators, the secondary phase is provided by moist air condensation, and may consist of discrete droplets, continuous film or a collection of rivulets. Several levels of approximation may be adopted, depending on the specific problem: perfect drain assumption requires only the addition of a heat source in the energy equation, otherwise the water layer behaviour has to be taken into account. Furthermore, a heat and mass transfer analogy may or may not be appropriate; in the latter case, the solution of the diffusion equation of humidity is required.Here, different levels of approximation are compared with literature experimental data for condensation over a vertical fin. Results show that thermal resistance and gravity effects, in the considered geometry, are negligible, and the condensate takes the form of a collection of still droplets, rather than a flowing film. This has an effect on the actual heat transfer and water layer build-up, and the variation of temperature along the fin induces some discrepancy with respect to the straightforward application of the heat and mass transfer analogy.     

Experimental study of convective heat transfer on a finned rotating cylinder

In this study, the local convective heat transfer from a rotating finned cylinder to the surrounding air was evaluated using an infrared thermographic experimental set up. Solving the inverse conduction heat transfer problem allows the local convective heat transfer coefficient to be identified. We used the specification function method, along with spatio-temporal regularization, to develop a model of local convective heat transfer in order to take lateral conduction and 2D geometry into account. This model was tested using rotational Reynolds numbers (based on the cylinder diameter and the peripheral speed) between 4300 and 17 900. The local heat transfer on the fin surface was analyzed to determine the influence of the rotational Reynolds number and the influence of the height and spacing of the fins. In this paper, we propose an efficiency definition that allows the optimal geometrical configuration of the finned cylinder to be identified for the given operating conditions.     

Correlations for combined heat and mass transfer from an open cavity in a horizontal channel

Combined heat and mass transfer from a horizontal channel with an open cavity heated from below is numerically examined in this paper. Air is the fluid considered (Pr = 0.7). The main focus of the study is mass-transfer driven flows (|N| > 1). The governing parameters considered are the buoyancy ratio N, Lewis number Le, Reynolds number Re, and Grashof number Gr. Based on the scale analysis, correlations for the entire convection regime, from natural, mixed, to forced convection, were proposed.     

Thermophoresis particle deposition on unsteady two-dimensional forced convective heat and mass transfer flow along a wedge with variable viscosity and variable Prandtl number

In this paper, the effects of thermophoresis particle deposition on an unsteady two dimensional forced convective heat and mass transfer flow past a wedge taking into account the variation of fluid viscosity and fluid Prandtl number with temperature are studied. The local similarity equations are derived and solved numerically using Nachtsheim–Swigert shooting iteration technique along with the sixth order Runge–Kutta integration scheme. Comparisons with previously published work are performed, and the results are found to be in excellent agreement. Results for the non-dimensional velocity, temperature, concentration, Prandtl number and thermophoretic velocity are displayed graphically whereas thermophoretic deposition velocity is shown in the tabulated form for various values of the pertinent parameters. The obtained numerical results show that in modeling the thermal boundary-layer flow with a temperature-dependent viscosity, consideration of the Prandtl number as a constant within the boundary layer produces unrealistic results, and therefore, it must be treated as a variable rather than a constant within the boundary layer. The results also show that the thermophoretic particle deposition velocity decreases as the thermophoretic coefficient increases.