Heat Flux Thermal Boundary Condition Research Articles

Forced and mixed convection experiments in a confined vertical backward facing step at low-Prandtl number

In this paper, we present experimental results for a non-isothermal vertical confined backward facing step conducted with a low-Prandtl number fluid. The eutectic alloy gallium–indium–tin is used as the working fluid. We conducted experiments for different Reynolds and Richardson numbers covering both forced and mixed convection regimes. Time-averaged velocity profiles were measured at six streamwise positions along the test section center-plane with so-called permanent magnet probes. The local Nusselt number was measured in streamwise and spanwise directions along the heating plate mounted right after the step. We further ran RANS simulations of the experiment to study the qualitative influence of assuming a constant specific heat flux thermal boundary condition for the experiment heating plate. The measured velocity profiles show the expected behavior for both studied convection regimes, while the measured streamwise local Nusselt number profiles do not. This is explained by how the heating plate thermal boundary condition is defined. We performed an order of magnitude estimate to estimate the forced- to mixed convection transition onset. The estimate shows good agreement with the experimental data, although further measurements are needed to further validate the estimated transition threshold. The measurement of fluctuating quantities remains an open task to be addressed in future experiments, since the permanent magnet probe measurement equation needs further adjustments.Graphical

Diffusion-thermo and heat source effects on the unsteady radiative MHD boundary layer slip flow past an infinite vertical porous plate

The heat and mass transfer characteristics of the nonlinear, unsteady, radiative MHD boundary layer slip flow of a chemically reacting fluid past an infinite vertical porous plate are taken into account in this study. The effect of physical parameters are accounted for two distinct types of thermal boundary conditions namely prescribed uniform wall temperature thermal boundary condition and prescribed heat flux thermal boundary condition. Exact solution of the governing equations for the fluid velocity, temperature and concentration are obtained by using two term perturbation technique subject to physically appropriate boundary conditions. The expressions of skin friction, Nusselt number and Sherwood number are also derived. The numerical values of fluid velocity, temperature and concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. Results are compared with the literature in the limiting case.

Computational analysis of perforation effect on the thermo-hydraulic performance of micro pin-fin heat sink

This paper investigates the hydrodynamic and thermal characteristics of perforated micro pin-fin (MPF) heat sink with different shapes and numbers of perforations under a low range (100–1000) of Reynolds number (Re) and constant base wall heat flux thermal boundary condition with air as the working fluid. The results show that the perforated MPFs provide higher Nusselt number (Nu) values and lower pressure drop levels (ΔP) than a solid MPF. These perforations have also shown higher fin effectiveness compared to solid square-shaped MPFs. Besides, the perforated MPFs show a superior performance (i.e., ≥45%) than solid MPFs. This study also infers that the circular-shaped perforation offers the best system performance (η) amidst the all different perforation shapes irrespective of the perforation number, followed by the elliptical and square-shaped perforation. For the circular-shaped perforation, performance improves by 30% when going from one to two perforations, and it improves up to 28% while moving from two to three perforations. This study reveals that there is a greater potential to employ circular perforation on a solid square MPF heat sink for better thermal management in electronic devices.

Thermal boundary layer structure in convection with and without rotation

Convection occurs in many settings from metal production to planetary interiors and atmospheres. To understand the dynamics of these systems it is vital to be able to predict the heat transport which is controlled by the thermal boundary layers (TBL). An important issue in the study of convective fluid dynamics is then to determine the temperature distribution within these thin layers in the vicinity of the bounding walls. Deviations from the classical Rayleigh-Benard convection paradigm such as the addition of rotation or fixed heat-flux (rather than fixed temperature) boundaries compromise the standard ways of defining the width of the TBL. We propose an alternative method for defining the TBL using the location at which the advective and conductive contributions to the heat transport become equal. We show that this method can be robustly applied to two-dimensional (2D) nonrotating convection between no-slip boundaries with fixed temperature or fixed heat-flux thermal boundary conditions and three-dimensional (3D) rotating convection simulations with free-slip boundaries.

The mechanism of laminar convective heat transfer enhancement enforced by twisting of elliptical tube

Nusselt number has unique characteristics under uniform wall temperature (UWT) and uniform wall heat flux (UWHF) thermal boundary conditions in twisted elliptical tube. Twisting of elliptical tube produces larger local Nusselt number under UWT than that under UWHF in some regions. In order to discover the mechanisms to form such characteristics in twisted elliptical tube, the velocity contribution and velocity gradient contribution to the transport of the heat flux defined by Fourier's law, q, are numerically investigated in this paper. Velocity gradient under UWHF contributes more greatly to the transport of the heat flux under UWHF than under UWT, which results larger local Nusselt number under UWHF than under UWT in straight elliptical tube. Velocity and its gradient contributions to the transport of the heat flux nearly normal to the wall surface have larger values under UWHF than under UWT in most regions, which produces larger local Nusselt number in twisted elliptical tube under UWHF than under UWT in these regions. In some regions velocity and its gradient contributions to the transport of the heat flux nearly normal to the wall surface have larger values under UWT than under UWHF produces larger local Nusselt number in twisted elliptical tube under UWT than under UWHF in these regions.

Analytical Nusselt number for forced convection inside a porous-filled tube with temperature-dependent thermal conductivity arising from high-temperature applications

The convection heat transfer inside a tube filled with a porous material under the constant heat flux thermal boundary condition which is widely used in practical applications is studied in the present article. The Darcy–Brinkman–Forchheimer model is used to cover a wide range of working mediums from clear fluid flow to slug flow (Darcy flow). The case of temperature-dependent thermal conductivity is considered in the present study and the corresponding Nusselt number is analytically obtained using perturbation techniques for the first time. The change in thermal conductivity with respect to temperature occurs at high-temperature applications wherein high-temperature variations exist as well as the radiation heat transfer. A linear model for the thermal conductivity variation with temperature is considered in the present study. The obtained profile for the Nusselt number can be used for quick calculations as well as validation of numerical and experimental studies, especially at high temperatures wherein the experimental studies are accompanied by higher uncertainties. The results show that the Nusselt number increases linearly with the linear increase in the thermal conductivity and as well the heat transfer rate. Furthermore, results show that the Nusselt number (and the heat transfer rate as well) shows more augmentation to the thermal conductivity enhancement due to the temperature-dependent nature of thermal conductivity (especially arising from the radiation heat transfer) in comparison with the clear fluid flow case.

Effect of thermal boundary condition on forced convection from circular cylinders

Researchers commonly assume that the effect of constant temperature and constant heat flux thermal boundary condition on forced convection from a circular cylinder is negligible. Such claim was assessed using Computational Fluid Dynamics for Reynolds number, Re, ≤ 3,000. The flow was directly solved without modeling for Re ≤ 300, and Large Eddy Simulation was used for Re = 1,000 and Re = 3,000. Constant property simulations were done for Prandtl number of 0.7. Fluid dynamics parameters: drag coefficient, Strouhal number, separation angle and recirculation length, were used to assess the accuracy of the simulations. The main parameter of interest, the Nusselt number, is higher locally for constant heat flux than constant temperature for 60 ≤ Re ≤ 3,000. In addition, the ratio of overall Nusselt number for constant heat flux to that for constant temperature increases for Re < 30 and is ∼1.15 between 30 ≤ Re ≤ 3,000, showing that thermal boundary condition has significant effect on heat transfer from circular cylinder. Finally, the study developed empirical correlations relating overall Nusselt number to studied Reynolds number range.

Effect of isoflux thermal boundary condition on mixed convective heat transfer from a sphere for liquid metals

Numerical simulation is performed for mixed convective heat transfer past a sphere with uniform heat flux (Isoflux) thermal boundary condition for liquid metals. The steady, incompressible, laminar, axisymmetric and Newtonian fluid is considered in a vertically upward direction. A spherical geometry higher order compact scheme is utilised to solve the governing equations in stream function vorticity formulation together with the energy equation. The fourth order convergence of the current scheme is demonstrated. The velocity, streamline, isotherm contour profiles together with vorticity, pressure, local Nusselt number and average Nusselt number on the surface of the sphere are presented for the Reynolds number in the range , Richardson number in the range and Prandtl number in case of 0.020, 0.0208, 0.065 (liquid Gallium, liquid metal alloy , liquid lithium). The critical Richardson number is identified beyond which the recirculation phenomena of the flow are completely suppressed. The rate of isoflux heat transfer is more when compare to the isothermal case for the same range of parameters.

On boundary conditions in liquid sodium convective experiments

Turbulent convection of liquid sodium in a cylindrical cell, heated at one end face and cooled at the other, inclined to the vertical at angle 0 and π/4 is studied experimentally and numerically by solving the Oberbeck-Boussinesq equations with the LES (Large Eddy Simulation) approach for small-scale turbulence. The aspect ratio is one, i.e. cylinder length is equal to diameter L = D = 200 mm. The simulations were done using fixed heat flux thermal boundary conditions for the cylinder faces. To resolve the general problem of boundary condition in convective experiment with low Prandtl number liquids, a special kind of heat exchanger were designed for the experimental setup. Each heat exchanger is a temperature-controlled MHD (magnetohydrodynamic) stirrer, filled with sodium and separated from the convective cell by a thin copper plate. We demonstrate the efficiency of MHD stirring for the temperature control. In convective experiments the Rayleigh number, determined by the cylinder diameter, was in the range from 4.7 · 106 to 1.7 · 107. We show that the structure of the flow and the efficient heat transfer strongly depend on the inclination angle.

Numerical study on the effect of cross-section orientation on fluid flow and heat transfer in a periodic serpentine triangular microchannel

The influence of cross-section orientation on fluid flow and heat transfer in a periodic serpentine equilateral triangular microchannel was investigated by means of computational fluid dynamics (CFD) modeling. Serpentine channels with cross-sections of upward- and left-pointing equilateral triangles were considered. Serpentine channels with twisted sections of different degrees of twisting were also considered and evaluated. The simulations were performed for fully-developed periodic flow with constant properties under constant wall heat flux (H2) thermal boundary conditions at Reynolds numbers of 50, 100 and 150 (corresponding to Dean numbers of 38, 76 and 114). The results showed that the heat transfer performance of the triangular channel is sensitive to the orientation of its cross-section. At all the Reynolds numbers studied, the channel with left-pointing triangular cross-section provided a higher mean heat transfer enhancement than the channel with upward-pointing cross-section, whereas the pressure drop remained the same. It was also found that by employing twisted shapes, it is possible to rotate the cross-section into a more favorable orientation for local heat transfer and thus improve the overall thermal performance further. With a moderate pressure drop increase, mean heat transfer enhancements for the channels with twisted sections were found to be greater than those for non-twisted configurations over almost the whole range of Reynolds numbers considered. However, the mean heat transfer enhancement did not rise with increasing degree of twisting, although the pressure drop increased with the degree of twisting.

Experimental study of heat transfer enhancement with segmented flow in a microchannel by using molecule-based temperature sensors

This paper presents an experimental study of heat transfer enhancement with liquid-gas two-phase segmented microchannel flows by utilizing a novel technique of molecule-based temperature sensors. A serpentine microchannel was constructed and steady liquid and gas segments of ethanol and air were successfully produced at various flow rates. A molecule-based temperature sensor made of Tris(2,2′-bipyridyl) ruthenium was utilized in the liquid segments by dissolving in ethanol as temperature-sensitive fluid and mixing in a dope to produce temperature-sensitive paint in order to retrieve fluid and surface temperature data, respectively. Three cases of different liquid and gas flow rates were tested. The heat transfer enhancements of these three cases were carefully examined under constant heat flux thermal boundary conditions, and the increased heat transfer was evaluated in comparison with the single-phase flow, where only liquid was injected in the microchannel. An improvement of up to 30% in the averaged Nu number of the microchannel flow was determined for Case 3, with a high gas flow rate and short liquid segments. Velocity and vorticity profiles in the liquid segments at different gas and liquid flow rates were also studied using a micro-particle image velocimetry technique. Stronger circulation was observed in Case 3, which confirmed the results from the heat transfer analysis, namely that more efficient heat transfer occurs with strong circulation in short liquid segments when a high gas flow rate is applied. The results of the present study provide detailed temperature profiles in segmented flow as well as the evolution of the Nu number from the entrance to the exit of a serpentine microchannel.

Computational study of entropy generation minimisation in continuous stirred tank reactor

Entropy generation minimisation (EGM) for optimising stirred tank reactor (CSTR) is performed by considering two cases: constant wall temperature and heat flux thermal boundary conditions. Entropy generation is computed from the temperature and velocity gradients which are predicted using CFD simulation. The selected parameters for EGM are inlet Reynolds number, impeller rotation, impeller clearance and impeller blade width. The optimum inlet Reynolds number increases with the wall temperature and heat flux. The effect of impeller rotation is also found on entropy generation. The optimum impeller clearance varies with the wall temperature and is invariant with the wall heat flux. The optimum impeller blade width depends on the magnitude of the wall temperature and heat flux. Bejan number is also determined, and it shows that the entropy generation is mostly dominated by heat transfer over the fluid friction irreversibility in the present study.

The asymptotic equivalence of fixed heat flux and fixed temperature thermal boundary conditions for rapidly rotating convection

The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that whereas the leading-order system satisfies fixed temperature boundary conditions implicitly, a double boundary layer structure is necessary to satisfy the fixed heat flux thermal boundary conditions. The boundary layers consist of a classical Ekman layer adjacent to the solid boundaries that adjust viscous stresses to zero, and a layer in thermal wind balance just outside the Ekman layers that adjusts the normal derivative of the temperature fluctuation to zero. The influence of these boundary layers on the interior geostrophically balanced convection is shown to be asymptotically weak, however. Upon defining a simple rescaling of the thermal variables, the leading-order reduced system of governing equations is therefore equivalent for both boundary conditions. These results imply that any horizontal thermal variation along the boundaries that varies on the scale of the convection has no leading-order influence on the interior convection, thus providing insight into geophysical and astrophysical flows where stress-free mechanical boundary conditions are often assumed.

Constructal design and thermal analysis of microchannel heat sinks with multistage bifurcations in single-phase liquid flow

Based on constructal theory, five different cases with multistage bifurcations are designed as well as one case without bifurcations, and the corresponding laminar fluid flow and thermal performance have been investigated numerically. All laminar fluid flow and heat transfer results are obtained using computation fluid dynamics, and a uniform wall heat flux thermal boundary condition is applied all heated surfaces. The inlet velocity ranges from 0.66 m/s to 1.6 m/s with the corresponding Reynolds number ranging from 230 to 560. The pressure, velocity, temperature distributions and averaged Nusselt number are presented. The overall thermal resistances versus inlet Reynolds number or pumping power are evaluated and compared for the six microchannel heat sinks. Numerical results show that the thermal performance of the microchannel heat sink with multistage bifurcation flow is better than that of the corresponding straight microchannel heat sink. The heat sink with a long bifurcation length in the first stage (Case 1A) is superior. The usage of multistage bifurcated plates in microchannel heat sink can reduce the overall thermal resistance and make the temperature of the heated surface more uniform (Case 3). It is suggested that proper design of the multistage bifurcations could be employed to improve the overall thermal performance of microchannel heat sinks and the maximum number of stages of bifurcations is recommended to be two. The study complements and extends previous works.

A Numerical Study of the Thermal Performance of Microchannel Heat Sinks with Multiple Length Bifurcation in Laminar Liquid Flow

A rectangular, straight microchannel heat sink with multiple length bifurcation has been designed, and the corresponding laminar flow and thermal performance have been investigated, numerically. Five different cases with multiple length bifurcation and various arrangements are investigated, as well as one case without bifurcations. All laminar fluid flow and surface heat transfer results are obtained using computation fluid dynamics, and a constant heat flux thermal boundary condition is applied to the heated surfaces. The inlet velocity ranges from 0.6 m/s to 1.4 m/s, with the corresponding Reynolds number from 220 to 520. The local pressure, velocity, temperature distributions, and averaged heat transfer coefficient are presented. The overall thermal resistances subjected to inlet Reynolds number are evaluated and compared for six different microchannel heat sinks. Numerical results show that the thermal performance of the microchannel heat sink with bifurcation flow is better than that of the corresponding straight microchannel heat sink, especially the heat sink with longer length bifurcation. The usage of multiple length bifurcated plates in microchannel heat sink can reduce the overall thermal resistance by a factor of up to 2, and make the temperature of a heated surface more uniform, especially for the heat sink having a short bifurcation in the center and two bifurcations near the sides (case 4). It is suggested that proper design of the multiple length bifurcation could be employed to improve the overall thermal performance of microchannel heat sinks.

A numerical study of flow structure and heat transfer in a square channel with ribs combined downstream half-size or same-size ribs

The present study employs square cross-section ribbed channels with different arrangements of downstream half-size ribs to determine the most optimal configurations for augmenting heat transfer rates with minimized pressure drop penalties. The channel inlet Reynolds number ranges from 20,000 to 160,000. The influence of downstream ribs arrangement on the overall performance characteristics of ribbed duct is observed with six different cases. A case of an array of six big continuous ribs installed on one wall with a pitch ratio of P/e = 20, is first designed (Case A). Four cases are then designed with inserting half-size and same-size ribs downstream the big ribs (Case B, Case C, Case D and Case E, respectively). The last case has a different pitch ratio and half-size ribs in the middle of two neighbor big ribs (Case F). The details of turbulent flow structure temperature fields, local heat transfer, normalized heat transfer, and thermal performance factor were obtained using Computation Fluid Dynamics (CFD) with the v2f turbulence model and constant heat flux thermal boundary conditions applied to all surfaces. The overall performances of six ribbed channel are evaluated and compared. The results reveal that the usage of downstream ribs is a suitable way to decrease the pressure loss and improve the flow structure, while keeps comparable enhancement in heat transfer as expected. Compared with Case A, all other cases yield the lower friction factor except for Case B. Case D and Case F present the prominent effect of their thermal enhancement factor, suggesting that the two cases exhibit individual advantage when different performances are taken into account to augment the heat transfer of ribbed channels.

Numerical Predictions of Heat Transfer and Flow Structure in a Square Cross-Section Channel with Various Non-Spherical Indentation Dimples

The present study employs arrays of different shapes of surface dimples to determine the most optimal configurations for augmenting surface heat transfer rates, as pressure drop penalties are minimized. Six different dimple shapes are investigated (spherical indentation (case A), super-ellipse (case D), two ellipse-spherical arrangements with the long axis oriented both parallel and normal to the bulk flow direction (cases B1 and B2, respectively), and two egg-spherical arrangements with the half ellipse with longer axis pointed both away and towards the bulk flow direction (cases C1 and C2, respectively). The dimples in these arrays are aligned with each other, as they are located on one surface of a square cross-section channel in six different streamwise rows. All turbulent fluid flow and surface heat transfer results are obtained using computation fluid dynamics with a k−ϵ RNG turbulence model, and constant heat flux thermal boundary conditions applied to all channel surfaces. Flow development is provided, both before and after the middle channel section, which contains each dimple array. Numerically predicted results are qualified using grid-independent predictions of experimental data for one baseline dimple array arrangement. The channel inlet Reynolds number ranges from 8,000 to 24,000. The dimple shapes with the best overall performance (depending upon the Reynolds number and performance criteria considered) are the spherical indentation arrangement (case A), and the ellipse-spherical arrangement with the long axis oriented normal to the bulk flow direction (case B2). Overall, the most optimal heat transfer augmentations seem to occur when the largest indented cross-section area is oriented perpendicular to the streamwise direction, since larger areas are then available for shear layer re-attachment over downstream portions of the associated dimples. Also important for such augmentations are dimple surface geometry transitions and surface curvature diameters, as illustrated by thermal performance which decreases as surface shapes have more numerous or more significant discontinuities, or when local surface curvature diameters are too small. Overall, the present results also show that such configuration sensitivities appear to increase with Reynolds number.

Heat Transfer Properties of Nanodiamond–Engine Oil Nanofluid in Laminar Flow

This study investigates the effects of utilizing nanodiamond as an additive to engine oil on the heat transfer enhancement in laminar pipe flow. A plain tube with internal diameter of 6 mm was used as the test section and heated by an electrical coil heater to produce a constant heat flux thermal boundary condition. Thermal conductivity, specific heat, and viscosity of nanofluids were measured for various volume fractions and temperatures. In addition, convection heat transfer coefficients and Nusselt numbers of nanofluids were obtained for different nanoparticle concentrations as well as various Peclet and Reynolds numbers. Experimental results clearly indicate the heat transfer enhancement due to the presence of nanoparticles in the fluid. However, pressure-drop measurements showed significant increase due to addition of nanopowder to engine oil.

Second law analysis of nanofluid flow

This paper analytically examines the effects of adding nanoparticles on the entropy generation of water–Al 2O 3 and ethylene glycol–Al 2O 3 nanofluid flows through a circular pipe under uniform wall heat flux thermal boundary condition in both laminar and turbulent regimes. Approved formulations of mixtures are used for density and specific heat of the nanofluids, and a model developed by Maiga et al. [9] based on experimental studies is used for viscosity and conductivity of the nanofluids. It is found that adding nanoparticles improves the thermal performance of water–Al 2O 3 flow with Re numbers less than 40,000 and ethylene glycol–Al 2O 3 flow with Re < 11. It is shown that adding nanoparticles leads to increased entropy generation in the cases that fluid flow (pressure drop) irreversibility is dominant. Moreover optimum conditions (based on the entropy generation sense) for both laminar and turbulent nanofluid flows are obtained.

Convective heat transfer in the thermal entrance region of finned double-pipe

Numerical simulation of the steady and laminar convection in the thermal entry region of the finned annulus is carried out for the case of hydrodynamically fully developed flow when subjected to uniform heat flux thermal boundary condition. Finite difference based marching procedure is used to compute the numerical solution of the energy equation. The results to be presented include Nusselt number, as a function of dimensionless axial length and thermal entrance length for various configurations of the finned double-pipe. The numerical results show that Nusselt number has complex dependence on the geometric variables like ratio of radii, fin height, and number of fins. A comparison of the computed results for certain limiting cases with the results available in the literature validates the numerical procedure used in this work.