Wall Heat Flux Boundary Condition Research Articles

Heat transfer inside a horizontal circular enclosure with a heated semi-circular cylinder at different orientations

Natural convection inside a cylindrical enclosure is important in many industrial applications. Laminar natural convective heat transfer in the annular space between heated semi-circular cylinder in a horizontal concentric cylindrical enclosure, which has relevance to cooling of electronic components, is studied in this work. Constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions are considered on the inner cylinder, whereas the outer cylindrical enclosure is maintained at a fixed lower temperature. The Finite Volume Method (FVM) is used for the computations. The effect of the Rayleigh number ( Ra = 10 2 to 10 5 ) and the angular orientation of the semi-circular cylinder on the convective heat transfer is investigated. The fluid flow, temperature profile, and heat flow are visualized via streamlines, isotherms, and heatlines. Further, the overall heat transfer is explained based on the local and average Nusselt number on the inner cylinder wall. The effect of the angular orientation of the inner cylinder is noticeable for Ra ≥ 10 3 . The angular orientation ϕ = 90 ° greatly enhances the heat transfer as compared to all other orientations for all Ra ≥ 10 3 for both CWT and CWHF boundary conditions. The correlation between the average Nusselt and Rayleigh numbers for a particular orientation is proposed.

Thermal entropy generation and exergy efficiency analysis of rGO/water nanofluid in a tube under turbulent regime using experimental and fully connected neural network

Analyzing entropy generation is one of the most effective methods for examining how well thermal systems operate. To determine the ideal operating conditions, numerous researchers have examined the entropy generation of thermal systems. In this work, the effects of concentrations of reduced graphene oxide (rGO) nanoparticles on the formation of entropy in water-rGO nanofluid flow through a circular pipe with a constant wall heat flux boundary condition in turbulent regimes are investigated experimentally. rGOs were prepared from Hummer's technique. Experiments are conducted at particle volumes from 0.5 % to 2.0 %, mass flow rates from 0.0333 kg/s to 0.25 kg/s, and Reynolds numbers from 1800 to 21,000, respectively. Later, estimated data points were anticipated with a convolutional neural network (CNN). The model was analyzed through several performances like root-mean-square-error (RMSE), mean-square-error (MSE), mean-absolute-percentage-error (MAE), and the coefficient of determination (R2). Results indicated, with used by 2.0 vol% of nanofluid, entropy generation-thermal is reduced to 39.24 %, entropy generation-frictional is higher by 16.92 %, entropy generation-total is decreased by 37.82 %, and second law efficiency is augmented to 34.17 % at Reynolds number of 13,705, against base fluid data. The correlation coefficient R2 evaluated from CNN for thermal entropy generation, frictional entropy generation, total entropy generation, and exergy efficiency are 0.99297, 0.99924, 0.9989, and 0.99273, respectively.

CONVECTIVE HEAT TRANSFER INSIDE A ROTATING HELICAL PIPE FILLED WITH SATURATED POROUS MEDIA

In this paper, we study the hydrothermal characteristics of flow inside a rotating helical pipe filled with saturated homogeneous porous medium. The analysis is being carried out for the case of small curvature and torsion. Using the perturbation approach, velocity and temperature fields are solved for both uniform wall heat flux and uniform wall temperature boundary conditions. Perturbation expansion up to the third order is carried out to investigate the effect of rotation on the flow. The influence of rotation on velocity is noticed as early as the first order, and on temperature solution, it has an effect in the third order. The influence of rotation on the Nusselt number does not appear till third order, and it is discovered that the Nusselt number grows as dimensionless curvature increases. Moreover, the theoretical results have been verified against experimental data from existing literature for the special case of zero rotation and curvature of the pipe. The available experimental data align well with and support the theoretical results in this limiting case.

Effect of Magnetic Field on the Developing Thermal Field in a Duct Filled with Porous Media under Local Thermal Non-Equilibrium with a Nonlinear Flow Model

In this article, the numerical study of the influence of a magnetic field at the laminar forced convection in a thermally developing region coming under the influence of local thermal non-equilibrium (LTNE) of parallel plate channels completely immersed in the porous material is investigated. Constant wall heat flux boundary conditions are applied to the walls of the channel. In the nonlinear flow model, the Darcy-Brinkman-Forchheimer equation governs the flow field in the porous region, which is assumed to be unidirectional. The system is defined by certain well-known parameters, these being Darcy number (Da), thermal conductivity ratio (κ), Forchheimer number (F), Hartmann number (M), and Biot number (Bi). Numerical solutions have been obtained by applying a successive accelerated replacement (SAR) scheme. Exact solutions for the dimensionless temperature and the fully developed Nusselt number in the absence of the Forchheimer number (F = 0), for the fully developed thermal field, are obtained for the linear flow model, the Darcy-Brinkman model. Plots are given for the dimensionless temperature profiles in the fluid and solid phases, wall temperature, as well as the local Nusselt number at the parallel plate channel, which has been displayed. The effect of the magnetic field and the thermal conductivity ratio has a significant effect on the local Nusselt number.

Numerical Study on the Heat Transfer Characteristics of Cu-Water and TiO2-Water Nanofluid in a Circular Horizontal Tube

A numerical simulation of convective heat transfer coefficient (hconv) was studied with Cu-Water and TiO2-Water nanofluids flowing through a circular tube subjected to uniform wall heat flux boundary conditions under laminar and turbulent regimes. Four different concentrations of nanofluids (ɸ = 0.5, 1, 1.5 and 2%) were used for the analysis and the Reynolds number (Re) was varied from laminar (500 to 2000) to turbulent flow regime (5000 to 20,000). The dependence of hconv on Re and ɸ was investigated using a single-phase Newtonian approach. In comparison to base fluid, average hconv enhancements of 10.4% and 7.3% were noted, respectively, for the maximum concentration (ɸ = 2%) and Re = 2000 for Cu-Water and TiO2—water nanofluids in the laminar regime. For the same ɸ under the turbulent regime (Re = 20,000), the enhancements were noted to be 14.6% and 13.2% for both the nanofluids, respectively. The random motion (Brownian motion) and heat diffusion (thermophoresis) by nanosized particles are the two major slip mechanisms that have more influence on the enhancement of hconv. In addition, the Nusselt number (Nu) of the present work was validated for water with the Shah and Dittus Boelter equation and found to have good agreement for both the regimes.

Characteristics of Heat Transfer and Turbulent Flow in a Baffled Pipe with Different Arrangements

In the heat transfer, fluid flow and energy fields, baffles are an advanced enhancer to improve heat transfer and fluid mixing by working as an obstacle to the flow particles and then increasing the turbulence. The present paper numerically investigates the thermal performance of a circular pipe with a centralized baffle in two arrangements, with a Reynolds number (Re) (ranging from 10,000-50,000) under constant wall heat flux boundary conditions. Ansys Fluent software is used to solve the flow field considering six conical baffles with different Pitch ratios (PR) (from 1 to 5). Results show that baffles shape, arrangement, and PR have a significant impact on the properties of flow and heat transfer. The obtained results show an effective role for the baffles to promote thermal performance when it is used in heated pipes. Heat transfer rate is increased for the baffled pipe by 1-2 compared with the smooth pipe. Moreover, the best value of friction factor, thermal performance, and Nusselt number is recorded at PR= 5 at Re=30000 in the baffled pipe for the second arrangement.

Transient flow and thermal transport characteristics of wall-bounded turbulent dual jet with heated undulated wall

The present computational study aims to investigate and improve the turbulent dual jet cooling performance on an undulated surface with varying profiles. This study also aims to highlight the flow and thermal features arising owing to an undulated surface having amplitude (UA) between 0.0 and 0.7. The transient RANS equations are considered to simulate the complex behaviour of turbulent dual jet. Four Reynolds-Averaged Navier-Stokes (RANS) turbulence models, namely, standard k-ω, shear-stress transport (SST) k-ω, renormalization group (RNG) k-ϵ, and realizable k-ϵ models, are used to predict the thermal performance and flow field of a turbulent dual jet for a fixed Reynolds number (Re) of 10,000 and offset ratio of 2. A constant wall temperature and constant wall heat flux boundary conditions are used. For the amplitude between 0.0 and 0.1, a periodic vortex shedding phenomenon near the jet exit is observed. However, two stable counter-rotating vortices are observed with no periodic vortex shedding for higher values of UA ≥ 0.3. The axial position of the merge point reduces with a rise in the amplitude. It is also observed that the velocity profile becomes self-similar and the inflection point in the velocity profile rises near the wall region with amplitude. The time series of U and V velocity signals unveil sinusoidal oscillations and display almost the same peak to peak amplitude for UA ≤ 0.1 at various times. The FFT of U velocity signals displays a solo peak dominant frequency which is the same as shown by V velocity in the FFT plot corresponding to the Strouhal number of the vortex shedding phenomenon. The average Nusselt number is increased up to 63.89% and 65.03% for higher amplitude for the constant heat flux and constant temperature boundary conditions. Correlations have been also proposed for the average Nusselt number, the average heat flux and the merge point. The outcomes of the present research can be implemented for better design in automobile industries and utilization of cooling or heating jets in electronics, metal, and material processing.

Thermally developed electrokinetic bi-layer flows of Newtonian and non-Newtonian fluids in a microchannel

In the present study, thermofluidic characteristics of a combined pressure-driven and electrical field mediated thermally fully developed flow of an immiscible Newtonian and a viscoelastic fluid bi-layer in a microchannel have been analyzed. The simplified Phan-Thien–Tanner model with a linear kernel for the stress coefficient function has been utilized to describe the complex fluid rheology for the non-Newtonian fluid. Disparate zeta potentials have been assumed at the interfaces. Accordingly, distinct zeta potential values have been used at the channel walls and interfaces between the fluids to derive the closed-form analytical expressions for the pertinent velocity, stress, and shear viscosity distributions in the fluid layers. For thermally developed flows, the temperature and entropy distributions are obtained along the microchannel for constant wall heat flux boundary conditions. Major findings from our research show that amplification of the viscoelastic parameter designated by the Weissenberg number exhibits an enhancement in the non-dimensional axial velocity, flow rate, and stress magnitudes. Furthermore, the present study indicates that Joule heating and viscous dissipation significantly vary the dimensionless temperature profiles along the fluid bi-layer. The Nusselt number values are found to decrease with the augmentation of the viscoelasticity, Joule heating, and viscous dissipation parameters. The total entropy generation for the fluid layer systems increases with the increasing Joule heating parameter.

A parametric study of the novel flow divider-type turbulator on heat transfer enhancement in a circular tube

The outcomes of numerical findings on a parametric study of flow divider-type turbulators in forced convection heat transfer mode were presented in this research study. A numerical study has been conducted using air as the working fluid within the Reynolds number range 7000–21000 under uniform wall heat flux boundary conditions. The turbulators were used with a pitch to tube diameter ratio of 0.54, with an alternate angle of twist and the cyclic angle of twist equal to 90°, 45° and, 30°. The CFD simulation outcomes show that the Nusselt number enhances by 2.34–2.40 times, for an alternate angle of twist of 30°. The maximum thermal enhancement efficiency equal to 1.09–1.15 is obtained for turbulators with an alternate angle of twist of 30°. The Nusselt number enhances by 1.67–2.13 times for tubes fitted with a turbulator with the cyclic angle of twist equal to 45°.

CFD study of Convective Heat Transfer of Water Flow Through Micro-Pipe with Mixed Constant Wall Temperature and Heat Flux Wall Boundary Conditions

The dissipation of heat in tiny engineering systems can be achieved with fluid flow through micro pipes. They have the advantage of less volume to large surface ratio convective heat transfer. There are deep-rooted analytical relations for convective heat transfer available for fluid flow through macro size pipes. But differences exist between the convective heat transfer for fluid flow through macro and micro pipes. Therefore, there is a good scope of work in micro convection heat transfer to study the mechanism of fundamental flow physics. There have been studies with either constant heat flux wall boundary conditions or constant wall temperature boundary conditions with constant and variable property flows. In this article, first, the numerical simulations are validated with the experimental data for 2D axisymmetric conventional pipe with pipe diameter of 8 mm is taken with laminar, steady, and single-phase water flows with constant wall heat flux boundary condition of 1 W/cm2. The computed Nusselt number is compared to the experimental results at different Reynolds numbers of 1350, 1600 and 1700. In the next study, three-dimensional micropipe laminar flow is studied numerically using water with an inlet velocity of 3 m/s and pipe diameter of 100 µm. The mixed wall boundary conditions with upper half pipe surface subjecting to constant wall temperature of 313 K and lower half surface subjecting to 100 W/cm2 are used in the simulations. The focus of research would be to consider the effect of temperature-dependent properties like thermal conductivity, viscosity, specific heat, and density (a combined effect we call it as variable properties) on micro-pipe flow characteristics like Nusselt number at mixed wall boundary conditions and compare it with the constant property flows. The conventional pipe showed no significant difference with variable and constant property flows with different Reynolds numbers. On contrary the flow through 3D micropipe shows that the Nusselt number with variable property flows is less as compared to the constant property flows.

Magnetohydrodynamic and radiation effects on the heat transfer of a continuously stretching/shrinking sheet with mass transpiration of the horizontal boundary

The aim of this paper is the investigation of heat transfer regarding the cases of both stretching and shrinking sheets with a sponge-like horizontal wall that allows for mass transpiration. The effects of Prandtl number, radiation and external magnetic field are extensively examined. The Navier-Stokes equations are reduced to partial differential equations, which are eventually become ordinary differential equations and solved analytically. Furthermore, the power-law wall temperature and heat flux boundary conditions are imposed on the boundary layer energy equation for obtaining exact analytical solutions. The results revealed that in both the stretching and shrinking sheet scenarios the thickness of the thermal boundary layer decreases with either increasing of transpiration as well as the Chandrasekhar and Prandtl number numbers or decreasing radiation number. Additionally, the characteristics of the heat transfer regarding a shrinking sheet and those of a stretching sheet are found not to be similar. In fact, a new solution branch appeared which indicates that multiple solutions may emerge under certain circumstances. Finally, by using the present analytical relationships, theoretical guidelines can be given for regulating the procedure.

3-dimensional CFD simulation and correlation development for circular tube equipped with twisted tape

The current paper represents computatioal fluid dynamics (CFD) investigation and novel correlation development for a round tube having twisted tape inserts with various tape length ratio i.e., 0.29, 0.43, 0.57, and 1.0 at uniform wall heat flux boundary conditions. The different short-length tapes are used as a swirling flow system to produce a powerful swirl flow in the tube. The variations of pressure loss and heat transfer in the form of friction factor and Nusselt number have been investigated and graphically represented. The numerical results show that the tube having twisted tape with tape length ratio (LR) of 0.29, 0.43, 0.57, and 1.0 is more effective than the smooth tube in terms of Nusselt number and friction factor values. The resulting data is reduced into correlations using a linear stepwise regression algorithm. The developed equations for tube having twisted tape predict all the data for friction factor and Nusselt number within ±5% relative absolute deviation. The average deviation between developed and available experimental correlation is of the order of <±9%.

Experimental analysis of heat loss of a non – evacuated parabolic trough collector receiver subjected to uniform and non-uniform wall heat flux condition

ABSTRACT The parameters that largely influence the design and performance of a parabolic trough collector system for delivering process heat are optical efficiency, incidence angle modifier, solar irradiation data, and receiver heat loss. The heat loss and optical properties of a receiver greatly influence the overall efficiency of the solar thermal system. This paper focuses the attention on the experimental investigation of heat loss associated with a non-evacuated receiver subjected to i). Uniform wall heat flux (UWHF) and ii). Non – uniform wall heat flux (NUWHF) boundary condition. A series of heat-loss measurements are carried out in the novel test stand capable of emulating both the boundary conditions, on the indigenous non – evacuated receiver developed for moderate temperature process heat applications. A comparative analysis of natural and forced convection heat loss associated with the bare and glass-covered receiver is performed. The results show that the non – uniform wall heat flux boundary condition has a decisive influence over the forced convection heat loss, especially at higher wind velocities. The work concludes that i) the surface temperature of the receiver associated with natural convection heat loss and subjected to NUWHF boundary condition is1.5– 5% higher than the receiver subjected to UWHF boundary condition. ii) In forced convection mode of heat loss the surface temperature of the receiver is 4–13% higher than the receiver subjected to UWHF. Thus, a more realistic characterization of the thermal behaviour of a non-evacuated receiver for moderate temperature process heat application is possible only by investigating the receiver subjected to non – uniform heat flux distribution. Such a characterization of the receiver will considerably influence the aperture area and thus the cost of the collector to deliver process heat.

Significance of Rarefaction, Streamwise Conduction, and Viscous Dissipation on the Extended Graetz–Nusselt Problem: The Case of Finite-Length Microchannels with Prescribed Wall Heat Flux

The article addresses the extended Graetz–Nusselt problem in finite-length microchannels for prescribed wall heat flux boundary conditions, including the effects of rarefaction, streamwise conduction, and viscous dissipation. The analytical solution proposed, valid for low-intermediate Peclet values, takes into account the presence of the thermal development region. The influence of all transport parameters (Peclet Pe, Knudsen Kn, and Brinkman Br) and geometrical parameters (entry length and microchannel aspect ratio) is investigated. Performances of different wall heat flux functions have been analyzed in terms of the averaged Nusselt number. In the absence of viscous dissipation Br=0, the best heating protocol is a decreasing wall heat flux function. In the presence of dissipation Br&gt;0, the best heating protocol is a uniform wall heat flux.

Numerical Modelling of Fluid Flow and Heat Transfer of (TiO2-Water) Nanofluids in Wavy duct

This paper investigates numerically pressure drop and forced convection heat transfer of TiO2-water nanofluids laminar flow through a horizontal curvilinear form or wavy duct with using four baffle height ratio h/H=0.15, 0.25, 0.35 and 0.45. This flow has been investigated assuming constant wall heat flux boundary condition by using ANSYS-Fluent with the finite volume method to discretize the nanofluids. The study has aimed to show the possibility of intensification of heat transfer by adding nanoparticles to the main coolant. The model employed in this study is a single phase (homogenous and dispersion). The effects of various factors, such as Reynolds number (Re) and nanoparticle concentration (φ), on the flow field and thermal distribution of the Nanofluids, have been analysed. The present results show that nanoparticle concentration and Reynolds number play a prevalent role in the horizontal wavy duct. The Nusselt number has increased by 54 % when using high nanoparticle concentration of (0.4 vol. %) at high Reynolds number of (1250), also the skin friction factor increased by (32%) in the same conditions. The results provide good predictions to enhancement the heat transfer. Predictably, as nanoparticle volume fraction and/or the Reynolds number increases, the heat transfer increases. However, the flow is accompanied by high friction factor and consequently, higher pressure drop.

The Effect of Turbulence Model and Nanofluid on Fluid Flow and Heat Transfer in a Narrow Rectangular Duct

The effect of turbulence model and nanofluid on the heat transfer and fluid flow in a horizontal narrow rectangular duct is numerically studied under constant wall heat flux boundary condition. Numerical study is carried out using ANSYS Fluent 17.0 software. Examined parameters are the type of turbulence model, the type of nanofluid, the volume fraction of nanofluid, and the Reynolds number. Three different k-e and four different k-w turbulence models are employed. Aluminum oxide Al2O3-water and copper oxide CuO-water are used as nanofluids. Volume fractions of nanoparticles used are 0%, 0.1%, 0.5%, 1%, 2% and 4%. Reynolds number changes from 3×103 to 50×103. Results showed that k-ω standard turbulence model with low Reynolds number correction gives better result. It is seen that both the type and volume fraction of nanofluid affect heat transfer and pressure drop. Using Al2O3 and CuO nanoparticles in water increases thermal performance. It is found that the performance of CuO-water nanofluid is better than that of Al2O3-water nanofluid. It is seen that using turbulent fully developed correlations derived for circular ducts may end up with incorrect results for the flow in a two dimensional rectangular duct.

Fundamental Study of Laminar Low-Subsonic Micro-Convective Air-Flow with Density Variations Due to Temperature Gradients

Examining non-rarefaction effects in laminar micro-convective low subsonic (with negligible compressibility effects) gas flows is as important as the well-explored rarefaction effects. This study numerically analyzes one of the important non-rarefaction effects arising from steep density variations due to the steep temperature-gradients, in micro-convective air-flow. For the constant wall heat flux boundary condition with air-heated along the flow, density-variation over the cross-section sharpens the radial mass flux profile. This sharpening of radial mass flux profile is reduced along the flow by the flattening of axial velocity profile along the flow. Net sharpening of radial mass flux profile relative to the constant properties case reduces the axial advection, which reduces the Nusselt number. The varying radial mass flux profile along the flow induces a weak radially outward flow i.e. induces a radially outward advection that is not weak, which also degrades Nusselt number. The low Nusselt number values in this study relative to its value of the case of all constant properties (including density), highlight the significant role of density variations in laminar micro-convective gas flow.

Effect of Density Variation on Rarefied and Non-rarefied Gaseous Flows in Developing Region of Microtubes

The present study analyzes the rarefaction and non-rarefaction effects on heat transfer characteristics of hydrodynamically and thermally developing air flow through microtubes having a constant wall heat flux boundary condition. The problem is especially simulated with two microtubes having diameters 50 µm and 150 µm. The rarefaction effect is taken into consideration using Maxwell slip flow and temperature jump boundary conditions. The fluid property variation is considered as a non-rarefaction effect which plays a significant influence on convection through a microtube. It is observed that the rarefaction and non-rarefaction effects significantly affect the convective heat transfer. The non-rarefaction effect decreases the Nusselt number (Nu) as compared to constant property solution; however, the rarefaction effect increases the Nu compared to constant property solution.

Empirical correlation of laminar forced convective flow in trapezoidal microchannel based on experimental and 3D numerical study

In this paper, the fluid flow and heat transfer characterizations in trapezoid shaped microchannel with H1 (axially constant heat flux and circumferentially constant temperature) and H2 (constant axial and circumferential wall heat flux) boundary conditions are studied. A three-dimensional numerical model is developed for trapezoidal geometries with side-angles of 30° and 60° with different aspect ratios ranging from 0.1 to 10 to evaluate the Nusselt number and Poiseuille number for fully-developed and developing flow conditions. Experiments are performed on a trapezoidal microchannel and experimental results are compared with the three-dimensional conjugate heat transfer numerical model. It is found that the experimental results are close to the H1 boundary condition. The Nusselt number and Poiseuille number are found to be increasing with the side-angle and aspect ratio of trapezoidal channel. Generalized correlations for Poiseuille number, Nusselt number and entrance length are developed for trapezoidal channel with side angles in the range of 30°–60° and aspect ratios of 0.1–10. These correlations can be used for designing of trapezoidal microchannel in future heat transfer applications.

Experimental study of buoyancy and inclination effects on transient mixed convection heat transfer in a channel with two symmetric open cubic cavities with prescribed heat flux

An experimental study in a recirculating water channel with a square cross section is carried out to study the transient laminar opposing mixed convection heat transfer from two symmetric open cubic cavities. The walls of the cavities facing the openings are subject to a constant wall heat flux boundary condition, the other bounding walls of the cavities and the channel are insulated and adiabatic. The experiments are done under different values of buoyancy strength or modified Richardson number, Ri* = Gr*/Re2 from 32.17 to 300.77, channel inclination of 0∘≤γ≤90∘, Reynolds number of 500 ≤Re≤ 1500, and a fixed Prandtl number of Pr = 7. Mean surface temperature distributions and averaged Nusselt numbers have been obtained. Results indicate that depending on the channel orientation and buoyancy strength, the flow and temperature distributions experience an oscillatory behavior and are not symmetric with respect to the channel centerline. In addition, at high Ri* numbers, spanwise and axial variation of the heat transfer rates has been reported elucidating the strong three-dimensional (3D) nature of the flow. Empirical correlations for the overall Nusselt number of each cavity are also developed for relations using the Reynolds and modified Grashof numbers over the range of physical parameters considered in this study.