Value Of Average Nusselt Number Research Articles

NUMERICAL STUDY FOR A THREE DIMENSIONAL LAMINAR NATURAL CONVECTION HEAT TRANSFER FROM AN ISOTHERMAL HEATED HORIZONTAL AND INCLINED SQUARE PLATE AND WITH A CIRCULAR HOLE

A theoretical study for a three-dimensional natural convection heat transfer from an isothermal horizontal , vertical and inclined heated square flat plates (with and without circular hole) has been done in the present work. The study involved the numerical solution of the transient Navier-Stokes and energy equations by using finite deference method (F.D.M.). The complete Navier-Stokes equation are transformed and expressed in terms of vorticity-vector potential. The Energy and Vorticity equations were solved by using an Alternating Direction Implicit (ADI) method because they are transient equations of parabolic portion, and the Vector potential is solved by using an equations Successive Over-Relaxation (S.O.R) method because it is from elliptic portion. The numerical solution is capable of calculating the Vector potential, three components of Vorticity and temperature field of the calculation domain. The numerical results were obtained in rang of Grashof number (103≤Gr≤5x104 ) with Prandtl number of (0.72) for square flat plate and the other consist a circle hole with ratio 0.6 and 0.8 diameter of the hole to main square side length. The numerical results showed that the main process of heat transfer is conduction for Grashof number less than 103 and convection for Grashof number larger than 103 and the results of local Nusselt number show fairly large dependence on inclination angle. For horizontal plate facing upward and downward, average Nusselt number is proportional to one-fifth power of Rayleigh number, and there is a significant difference in heat transfer rates between the upward and downward cases. For horizontal plate with circle hole facing upward for Grashof number 104 , the effect of core portion caused a limited increment in the heat transfer rate, where as for the facing downward case, the effect was larger and the maximum value of heat transfer rates is be for square flat plate with circle hole by ratio 0.6 for all inclination angles. With the increase of Grashof number to 5x104 heat transfer rates decrease except the square horizontal flat plate with circle hole by ratio 0.6 . The average Nusselt number increases with the increase of inclination of plates facing upward to reach to the higher average Nusselt number at vertical position then decrease with increase of inclination of plates. And the maximum value of average Nusselt number is depended on the ratio of diameter of the hole to main square side length, showed that the maximum temperature gradient occurs at the external edge of the horizontal plate (with and without circle hole) facing upward and at the lower external edge in inclined case. The numerical results was made through comparison with a previous numerical and experimental work, the agreement was good.

Power-Law Nanofluid Magnetohydrodynamics Combined Convection in the Presence of Heat Absorption/Generation: A Lattice Boltzmann Analysis to Compute Thermal Performance Index

Endeavors to improve the performance of thermal systems have always been of great noticed due to their extremely high importance in industrial and engineering applications. For this intention, in the existing simulation, several effective strategies have been evaluated to determine the amount of heat transfer and entropy formation caused by the combined convection of non-Newtonian nanofluid with particles Brownian motion. Based on the findings via LBM simulation, it has been observed that changing the position and speed direction on the chamber wall helps to control the flow characteristics, and thus significantly changes the thermal performance of the system. The least effect of the magnetic field in reducing the value of the Nusselt number in all the positions of applying the speed belongs to the state where the wall direction is aligned with the force of gravity. In the case where the middle part of the vertical wall has speed, the formed flow power inside the chamber is 29% and 45% higher than when the first third and the last third of the wall have speed. The presence of a strong magnetic field leads to the reduction of convection effects, which is more evident for moving up the vertical wall. When the middle part of the wall has speed, if the magnetic field is applied to the middle part of the chamber to the highest value, the reduction of the average Nusselt number is about 35% and 39% more than the case when the magnetic field is applied to the first third and the last third of chamber. To have a higher average Nusselt number value, reducing the fluid power-law index and enhancing the Reynolds number value are effective strategies. To control the effects of the magnetic field, it is very effective to reduce the shear force on the chamber wall and expose the fluid flow to the heat absorption/production phenomenon. By reducing the value of fluid power-law index, the effect of magnetic field and heat absorption/production becomes more evident. In Re=200, the reduction of the thermal performance index for enhancing the Hartmann number value to the highest value is about 39% for n = 0.45, while this effect is about 31% and 24% for n = 0.7 and n = 0.95, respectively. By exposing the current to heat production, the effect of the magnetic field is reported to be about 55% higher than in other cases. Although heat production enhances the amount of Be value by about 66% compared to the heat absorption mode, it leads to an increase in the thermal performance index. The highest value of the system thermal performance index (0.82) can be achieved by upward moving the middle part of the chamber wall in the absence of magnetic field for heat absorption mode at the lowest power-law index and the highest Reynolds number value.

Enhancing solar air heater efficiency with 3D cylinder shaped roughness elements

Solar air heaters (SAHs) harness solar radiation to warm the air. This study investigates the efficacy of 3D cylindrical roughness features in enhancing heat transfer and reducing friction losses within SAHs. The configuration involves inline and staggered placement of 3D cylindrical roughness elements beneath the absorber surface. Through ASHRAE standard 93–77 testing, heat transfer and friction factors are examined across various cylinder roughness setups, with parameters such as relative roughness pitch (p/h) and gap (w/h) considered. The channel aspect ratio (W/B) is set at 5, and a relative roughness height (h/D) of 0.06 is maintained and flow Reynolds number (Re) is varied from 3000 to 8000. Regression analysis reveals a significant relationship between heat transfer and friction. Notably, at Re = 7910, p/h = 20, and w/h = 8 for staggered cylinder roughness, average friction factor (fav) increases by 171.3 %, and average nusselt number (Nuav) increases by 69.7 %. Similarly, the efficiency index (η) peaks at 0.8192 with inline roughness at Re = 2969, p/h = 20, and w/h = 8. The introduced 3D cylinder roughness elements disrupt the laminar sub-layer, amplifying convective heat transfer while curbing friction losses. This approach optimizes SAH performance within the studied parameter range, showcasing potential improvements for utilizing solar energy. Experimental results, along with expressions for average friction factor (fav) and average Nusselt number (Nuav), underscore the benefits of cylinder-shaped roughness geometries while maintaining h/D = 0.06. These findings introduce an innovative convective heat transfer method, enhancing SAH efficiency. Furthermore, the anticipated average friction factor (fav) and average Nusselt number (Nuav) values align within error limits of ±6.63 % and ±6.62 %, respectively, with improved regression coefficients indicating the stronger relationship and the influence of independent variables on dependent variables.

Thermogravitational Convection in a Multiple Baffled Enclosure Filled with Magneto-Hybrid Nanofluid Subjected to Magnetic Field Dependent Viscosity

This study explores the significant impacts of thin baffles and magnetic field dependent viscosity on magnetohydrodynamic (MHD) thermogravitational convection of Cu-Al2O3 (50%–50%) water hybrid nanoliquid in a cavity. Considering different arrangements of baffle sticks on both the vertical walls, four geometrical configurations (Case-I, Case-II, Case-III and Case-IV) have been analyzed. Numerical simulation has been performed for the governing Navier-Stokes (N-S) equations in streamfunction - vorticity form having energy equation. These coupled equations are solved by proposing a higher-order compact finite difference method. The combination of five important aspects (hybrid nanofluid, multiple baffles, magnetic field dependent viscosity (MFDV), magnetic field and compact computation) signifies the novelty of this work. Fluid flow and transportation of thermal energy within the stipulated domain are presented for various flow pertinent parameters. The outcomes show that the increase in number of baffles diminishes the average Nusselt number values. It is concluded here that an increase in Hartmann number from 0 to 90 leads to a decrease in average Nusselt number up to 23.7% for Case-I, 23.8% for Case-II, 21.2% for Case-III and 28% for Case-IV in presence of MFDV effects.

Thermogravitational magnetonanofluid flow in a square cavity with isotropic heat flow field and viscous dissipation: A compact approach

In this paper, thermogravitational flow in a square enclosure filled with Cu-water nanofluid which is influenced by inclined magnetic induction, has been mathematically modelled. Isotropic heat flow field and viscous dissipation effects are introduced in the modelling as well. The vertical walls of the domain are subjected to finite temperature gradient while the horizontal walls are thermally insulated. The control equations subject to the flow physics of an incompressible, viscous and electrically conducting fluid are the Navier-Stokes equations along with energy equation. These governing equations are solved numerically by proposing a fourth order compact scheme. The influences of diverse effective parameters including Hartmann number, viscous dissipation parameter (Eckert number) and heat generation or absorption parameter on characteristic features of heat transfer and fluid flow with different concentration distributions of nanoparticles are analyzed and addressed in detail. Results show that the presence of viscous dissipation retards the thermal diffusion process. The average Nusselt number values are decreased with the increasing values of Eckert number. In addition, with the increasing values of Hartmann number, the thermal transport is decreased in spite of incorporation of isotropic heat flow.

Natural convective non-Newtonian nanofluid flow in a wavy-shaped enclosure with a heated elliptic obstacle

A numerical investigation has been carried out in a wavy-shaped enclosure with an elliptical inner cylinder to find out the effect of an inclined magnetic field and a non-Newtonian nanofluid on fluid flow and heat transfer. Here, the dynamic viscosity and thermal conductivity of the nanofluid are also taken into account. These properties change with the temperature and nanoparticle volume fraction. The vertical walls of the enclosure are modeled through complex wavy geometries and are kept at a constant cold temperature. The inner elliptical cylinder is deemed to be heated and the horizontal walls are considered adiabatic. Temperature difference between the wavy walls and the hot cylinder leads to natural convective circulation flow inside the enclosure. The dimensionless set of the governing equations and associated boundary conditions are numerically simulated using the COMSOL Multiphysics software, which is based on finite element methods. Numerical analysis has been scrutinized for varying Rayleigh number (Ra), Hartmann number (Ha), magnetic field inclination angle (γ), rotation angle of the inner cylinder (ω), power-law index (n), and nanoparticle volume fraction (ϕ). The findings demonstrate that the solid volumetric concentration of nanoparticles diminishes the fluid movement at greater values of φ. The heat transfer rate decreases for larger nanoparticle volume fractions. The flow strength increases with an increasing Rayleigh number resulting in a best possible heat transfer. A higher Hartmann number diminishes the fluid flow but converse behavior is exhibited for magnetic field inclination angle (γ). The average Nusselt number (Nuavg) values are maximum for γ = 90°. The power-law index plays a significant role on the heat transfer rate, and results show that the shear-thinning liquid augments the average Nusselt number.

Experimental Study For a Laminar Natural Convection Heat Transfer From an Isothermal Heated Square Plate With and Without Circular Hole

An experimental investigation of natural convection heat transfer from an isothermal horizontal,vertical and inclined heated square flat plates with and without circular hole, were carried out in two cases, perforated plates without an impermeable adiabatic hole "open core" and perforated plates with an impermeable adiabatic hole "closed core" by adiabatic plug. The experiments covered the laminar region with a range of Rayleih number of (1.11x106 ≤RaLo≤4.39x106 ), at Prandtle number (Pr=0.7). Practical experiments have been done with variable inclination angles from horizon (Ф=0o ,45o,90o,135oand 180o),facing upward (0o≤Ф<90o), and downward (90o≤Ф<180o). The results showed that the temperature gradient increases while the thermal boundary layer thickness decreases when Grashof number and perforation ratio (m) increase . The temperature gradient for inclined position facing upward is less than facing downward,while the thermal boundary layer thickness is greater. The temperature gradient decreases while the thermal boundary layer thickness increases for perforated plates with an adiabatic core as compared with perforated plates without an adiabatic core. The value of average Nusselt number increases with increasing perforation ratio, and Grashof number for all specimens with and without an adiabatic core, also increases by increase in inclination of plates approaching the higher value at vertical position (Ф=90o), then decreases with increasing inclination of plates till horizontal position (Ф=180o). The average Nusselt number values for perforated plates with an adiabatic core are lower than for perforated plates without an adiabatic core for all perforation ratios. Maximum heat transfer rate occurs at perforated plate with perforation ratio of (m=0.1) without adiabatic core for vertical position (Ф=90o), at a range of Grashof number (1.576x106≤GrLo≤6.292x106 ), while the rate of heat transfer decreases with increasing perforation ratio for plates with and without adiabatic core for decrease in heat transfer rate area. The rate of heat transfer forperforated plates with circular hole is more than for perforated plates with square hole at the same perforation ratios (m=0.1,0.16,0.24 and 0.36). It found that the lack of core flow decreases the overall heat transfer rate by (6.477%) . There was a good agreement for the experimental present work results compared with other pervious results .

Numerical investigation of thermo-hydraulic features of viscoplastic flow in wavy channels

In the present work, the thermo- hydraulic characteristics are studied for a laminar viscoplastic flow through raccoon and serpentine type wavy channels. The results are presented by varying Bingham number (Bn), power-law index (n), Reynolds number (Re), dimensionless amplitude, and wave number in the physically justified ranges. It is found that the size of the recirculatory zone decreases with Bn and the zone disappears at the higher Bn values. The topology of the yielded-unyielded region highly depends on the geometry and the range of Bn. Moreover, the value of average Nusselt number decreases with n. With the increase in Bn, average Nusselt number gradually decreases up to a critical Bn value and then increases sharply at higher Bn values. Interestingly, the wavy channel is only advantageous at smaller Bn values up to a critical limit. The variation of performance factor (PF) strongly depends on the combined effect of rheological and geometrical parameters. Besides, results for raccoon and serpentine channels are highly dependent on the ranges of amplitude, wave number, Bn, and n.

Performance evaluation criteria and entropy generation of hybrid nanofluid in a shell-and-tube heat exchanger with two different types of cross-sectional baffles

Improving the thermo-hydraulic performance of shell-and-tube heat exchangers is of interest to researchers due to their broad applications in the industry. Thermo-hydraulic behavior and entropy generation of hybrid nanofluid in a shell-and-tube heat exchanger with two different types of cross-sectional baffles are numerically examined using the two-phase Eulerian-Eulerian Model (EEM). The volume fraction of nanoparticles (φ) changes from 0 to 2% and the Reynolds number (ReNumber) varies from 25000 to 45000. EEM, Realizable k-ε turbulence model, finite volume method (FVM), and SIMPLE algorithm are used for modeling. According to the numerical results obtained in terms of pressure drop, total entropy generation, and performance evaluation criteria (PEC), baffle 1 is more appropriate. In terms of heat transfer rate and average Nusselt number values, baffle 2 is more suitable. The PEC maximum change was 5.13% at Re = 45000 and φ = 0% by changing the type of baffle from the second type to the first type. The maximum rise in the total entropy generation was 73.68% for φ = 0% for the first type of baffles.

Numerical Investigation on Natural Convection in Inclined Channels Partially Filled With Asymmetrically Heated Metal Foam

Abstract A numerical study on natural convection in an inclined channel partially filled with open metal foam is investigated in two-dimensional laminar and incompressible and steady-state condition. The upper wall is heated at uniform heat flux, and the lower wall is adiabatic. The governing equations for the metal foam are written assuming the Brinkman–Forchheimer-extended Darcy model and the local thermal equilibrium (LTE) hypothesis. The inclination angle with respect to the horizontal direction ranges between 0 deg and 90 deg. The metal foam structure is homogenous and isotropic and the thermophysical properties are assumed constant with the temperature. The main aim of the present study is to analyze the effect of inclination angle, pore density, and porosity to improve the knowledge on the thermal behaviors of natural convection in partially filled channel with metal foam. Moreover, this study aims to evaluate the possible improvement with respect to the clean inclined channel. Results are presented in terms of velocity and temperature fields, and both temperature and velocity profiles at different significant sections are shown, to obtain a description of the natural convection inside the inclined channel. Finally, average Nusselt number values are evaluated. The presence of metal foam affects the fluid flow in the channel with different motion behaviors. The heat transfer rate increases with the increase in inclination angle, and the average Nusselt number shows different trends for lower and higher Rayleigh numbers, Ra. A significant enhancement is detected for the higher Ra and it depends on the porosity and pore density.

Experimental investigation of flow and thermal characteristics of synthetic jetissuing from sharp-edged orifices

ABSTRACT The present experimental study reports the flow and heat transfer characteristics of a synthetic jet issuing from a sharp-edged orifice (diverging-shaped orifice). The experiments are carried out for a varied range of opening angles of sharp-edged orifices (θ = 0°, 30°, 60°, 90°, and 120°), Reynolds number (Re = 3243–8143), different jet-to-surface spacings (z/d = 1–16), and for two different values of orifice thicknesses, t = 5 mm (t/d = 0.33) and 10 mm (t/d = 0.66). The hot-wire anemometry is used to study the flow characteristics of synthetic jet, while heat transfer characteristics are studied by using a thermal imaging technique. The time-averaged flow fields associated with sharp-edged orifices reveal that orifices with t = 5 mm and 10 mm exhibit saddle-backed and top-hat velocity profile shapes, respectively. The results show that for a square-edge orifice (θ = 0°), the heat transfer rate decreases with an increase in orifice plate thickness from 5 to 10 mm, while the opposite trend in heat transfer is observed with sharp-edged orifice. The heat transfer rate with a 10 mm thick sharp-edged orifice is higher than the 5 mm thick sharp-edged orifice for all the tested opening angles. Furthermore, the results also show that for sharp-edged orifices, the heat transfer rate increases with the increase in opening angle from θ = 0° to 60°, while it decreases with further increasing from θ = 60° to 120°. The maximum value of average Nusselt number (Nuavg) is obtained for θ = 60° for both the orifice thicknesses (t = 5 and 10 mm), and this effect is found to be more pronounced for t = 10 mm orifice. For sharp-edged orifice (θ = 60°), the maximum enhancement in Nuavg is found to be 12.66% and 23% higher for t = 5 mm and 10 mm, respectively, compared to the equivalent square-edged orifice (θ = 0°). The cause for variation in heat transfer rate with sharp-edged orifices is interpreted due to the effect of flow recirculation and mass flow rate. A correlation has been proposed for Nuavg as a function of different opening angles. The present finding is useful for the optimization of the synthetic jet geometrical parameters for the effective heat transfer rate.

Coupled Effects of Using Magnetic Field, Rotation and Wavy Porous Layer on the Forced Convection of Hybrid Nanoliquid Flow over 3D-Backward Facing Step.

In the present study, the effects of using a corrugated porous layer on the forced convection of a hybrid nanofluid flow over a 3D backward facing step are analyzed under the coupled effects of magnetic field and surface rotation. The thermal analysis is conducted for different values of the Reynolds number (Re between 100 and 500), the rotational Reynolds number (Rew between 0 and 2000), the Hartmann number (Ha between 0 and 15), the permeability of the porous layer (the Darcy number, Da between and ) and the amplitude (ax between 0.01 ap and 0.7 ap) and wave number (N between 1 and 16) of the porous layer corrugation. When rotations are activated, the average Nusselt number (Nu) and pressure coefficient values rise, while the increment of the latter is less. The increment in the average Nu is higher for the case with a higher permeability of the layer. When the corrugation amplitude and wave number are increased, favorable impacts of the average Nu are observed, but at the same time pressure coefficients are increased. Successful thermal performance estimations are made by using a neural-based modeling approach with a four input-two output system.

Analysis of conjugate heat transfer for forced convective flow through wavy minichannel

PurposeThe purpose of this paper is to analyze numerically forced convective conjugate heat transfer characteristics for laminar flow through a wavy minichannel.Design/methodology/approachThe mass and momentum conservation equations for the flow of water in the fluidic domain and the coupled energy conservation equations in both the fluid and solid domain are solved numerically using the finite element method. The exteriors of both the walls are subjected to a uniform heat flux.FindingsThe results reveal that the theoretical model without consideration of the effect of wall thickness always predicts a lower value of average Nusselt number () as compared to the case of conjugate analysis, although it varies with the thickness as well as material of the wall. For the low amplitude of the wall (α = 0.2), the performance factor (PF) becomes very high for Re in the regime of 5 (⩽) Re (⩽) 15. For any geometrical configurations, conjugate heat transfer analysis predicts higher PF as compared to that of nonconjugate analysis.Practical implicationsThe present study finds relevance in several applications, such as solar collectors and heat exchangers used in chemical industries and heating-ventilation and air-conditioning, etc.Originality/valueTo the best of the authors’ knowledge, the analysis of combined influences of the thickness and the material of the wall of the channel together with the geometrical parameters of the channel, namely, amplitude and wavelength on the heat transfer and fluid flow characteristics for flow through wavy minichannel in the laminar regime is reported first time in the literature.

Numerical Computations of Non-Newtonian Fluid Flow in Hexagonal Cavity With a Square Obstacle: A Hybrid Mesh–Based Study

Thermal flow phenomena in a double lid–driven enclosure have many potential applications in numerous engineering domains. The present article theoretically investigates the heat transfer analysis of power-law fluid in a hexagonal cavity embedded with a square obstacle. The upper and lower lid walls of the cavity are considered heated along with the walls of the centered embedded square, while the rest of the cavity walls are thermally insulated. In addition, the horizontal lid walls of the cavity are uniformly moving in opposite horizontal directions. The mathematical modeling of the nonlinear fluid has been developed considering the continuity, momentum, and energy equations subjected to the appropriate boundary conditions. Due to the nonlinearity of the governing partial differential equations and of the viscosity models, we use the numerical scheme based on the finite element method The stable finite element pair (ℙ2/ℙ1) has been selected for the discretization purpose. The discretized nonlinear system is solved with the Newton method in conjunction with a direct linear solver in the inner iterations. The thermal flow features are exposed via streamlines and temperature contours for a set of governing parameters such as Reynolds number (Re), Prandtl number (Pr), and Grashof number (Gr) along with the power-law index (n). The values of local and average Nusselt numbers are calculated for the involved parameters. It is noted that the square obstacle has a strong impact for the formulation of streamlines and isotherms. Moreover, the power-law index has a strong impact on the values of the average Nusselt number and kinetic energy. The kinetic energy of the system increases with an increasing value of Gr and n, while Reynolds number has opposite effects on kinetic energy.

Optimization of a high-temperature recuperator equipped with corrugated helical heat exchanger for improvement of thermal-hydraulic performance

The main aim of present study is to optimize a high-temperature recuperator equipped with corrugated helical heat exchanger numerically. This heat exchanger has inner corrugations and/or outer blades. Different geometrical parameters are analyzed according to thermal-hydraulic performance (THP) of the studied helical heat exchanger. The model with the maximum THP evaluation criteria index is introduced as the optimum model. Moreover, the effects of ash fouling characteristics on THP of recuperator are presented. The ash particles material is chosen K2SO4 with the density of 2665 kg/m3. As it is realized in this paper, in case of simulating the problem in steady-state condition, employing the two-phase model achieves to higher average Nusselt number (Nu) values versus all considered mass flow rates. However, it should be noted that in these two approaches the ash fouling characteristics are not determined. By transient solving, the ash fouling characteristics are applied on the outer wall of helical heat exchanger and therefore the convectional heat transfer coefficient is reduced. Hence, in case of employing two phase approach (with ash fouling characteristics) model, lower average Nu values are achieved and it is clear that these values are more validated than attained values from two other approaches. Usage of inner and/or outer corrugations has a substantial influence on THP of recuperator and increases the PEC index values versus all considered mass flow rates sharply. The recuperator equipped with finned helical heat exchanger with a = 3 mm, b = 7 mm, H = 8 mm, g = 2 mm and f = 3 mm is introduced as the optimum model in present work.

Mathematical modeling of unsteady flow with uniform/non-uniform temperature and magnetic intensity in a half-moon shaped domain

The mathematical modeling of two-dimensional unsteady free convective flow and thermal transport inside a half-moon shaped domain charged in the presence of uniform/non-uniform temperature and magnetic effects with Brownian motion of the nanoparticles has been conducted. Thirty-two types of nanofluids in a combination of various nanoparticles and base fluids having different sizes, shapes, and solid concentrations of nanoparticles are chosen to examine the better performance of heat transfer. The circular boundary is cooled while the diameter boundary is heated with uniform/non-uniform temperature. An external uniform/non-uniform/periodic magnetic field is imposed along diameter. The powerful partial differential equations solver, finite element method of Galerkin type, has been engaged in numerical simulation. The numerical solution's heat transfer mechanism reaches a steady state from the unsteady situation within a very short dimensionless time of about 0.65. The thermal transport rate enhances for increasing buoyancy force whereas decreases with higher magnetic intensity. The uniform thermal condition along the diameter of half-moon gives a higher thermal transport rate compared to non-uniform heating conditions. The non-uniform magnetic field provides greater values of the mean Nusselt number than the uniform field. In addition, the outcomes also predict that a better rate of temperature transport for kerosene-based nanofluid than water-based, ethylene glycol-based, and engine oil-based nanofluid. The heat transfer rate is observed at about 67.86 and 23.78% using Co-Kerosene and Co-water nanofluids, respectively, with an additional 1% nanoparticles volume fraction. The blade shape nanoparticles provide a better heat transfer rate than spherical, cylindrical, brick, and platelet shapes. Small size nanoparticles confirm a higher value of average Nusselt number than big size. Mean Nusselt number increases 22.1 and 5.4% using 1% concentrated Cu-water and Cu-engine oil nanofluid, respectively than base fluid.

Effect of amplitude of walls on thermal and hydrodynamic characteristics of laminar flow through an asymmetric wavy channel

In this work, we investigate the hydrothermal characteristics for laminar forced convective flow of water through sinusoidal asymmetric wavy channel of three types: linearly increasing amplitude channel (LIAC), linearly decreasing amplitude channel (LDAC) and constant amplitude channel (CAC). The computed velocity and temperature fields are analyzed by varying the Reynolds number (Re) and slope (A) of the linearly varying amplitude in the following ranges: 5 ≤Re≤ 200 and 0.02≤A≤ 0.04. The value of average Nusselt number is almost independent on the geometry of the channel at lower values of Re and A. At higher Re values, the average Nusselt number is the highest for LIAC followed by LDAC, and CAC. The combined effects of heat transfer increase in the wavy channel compared to plane channel and the associated pumping power is assessed using performance parameter (PF). For lower Re values the highest PF is obtained for CAC. For higher values of Re the PF is the largest for LDAC at A = 0.02 and 0.03, and the value of PF for A = 0.04 is the highest for CAC.

Coupling of BGK lattice Boltzmann method and experimental rheological/thermal behavior of Al2O3–oil nanolubricant for modeling of a finned thermal storage

PurposeThe purpose of the present work is to investigate the hydrodynamic and thermal performance of a thermal storage based on the numerical and experimental approaches using the lattice Boltzmann method and the experimental observation on the thermo-physical properties of the operating fluid.Design/methodology/approachFor this purpose, the Al2O3 nanoparticle is added to the lubricant with four nanoparticle concentrations, including 0.1, 0.2, 0.4 and 0.6Vol.%. After preparing the nanolubricant samples, the thermal conductivity and dynamic viscosity of nanolubricant are measured using thermal analyzer and viscometer, respectively. Finally, the extracted data are used in the numerical simulation using provided correlations. In the numerical process, the lattice Boltzmann equations based on Bhatnagar–Gross Krook model are used. Also, some modifications are applied to treat with the complex boundary conditions. In addition, the second law analysis is used based on the local and total views.FindingsDifferent types of results are reported, including the flow structure, temperature distribution, contours of local entropy generation, value of average Nusselt number, value of entropy generation and value of Bejan number.Originality/valueThe originality of this work is combining a modern numerical methodology with experimental data to simulate the convective flow for an industrial application.

The effect of Nusselt number on the bi-viscosity fluid subjected to the discrete heating effect

Discrete heating action has been established as an energy efficient method. Nusselt number plays a significant role in the heat transfer rate. Local Nusselt number is useful in analyzing the heat transfer rate along the sections of the side walls with different or same temperature in a heated enclosed cavity. Whereas the average Nusselt number quantifies the total heat change in the closed cavity. While the path of the trajectory of the heat flow is being analyzed by heat function. In the current work, multiple heaters of length , and are assembled at each side of the isosceles triangle. The numerical simulations of the modeled system along with boundary conditions are carried out by using the standard Galerkin Finite Element Method. The nonlinear algebraic system is solved by Newton method. The behavior of fluid inside the closed triangle with is observed. The results are reported in terms of the graphs of the temperature contours, streamlines, average and local Nusselt numbers. The maximum heat transfer rate is observed in convection dominant case. By increasing the magnitude of a bi-viscosity parameter, secondary circulation is observed for The rate of heat transfer has a direct relation with the bi-viscosity parameter. The maximum values of average and local Nusselt numbers are achieved by using the heat generation parameter against the Grashof number.

Numerical investigation of circular porous fins effect on natural heat transfer enhancement in an annulus cavity

An asymmetric numerical study has been performed to investigate the effect of utilizing circular porous fins on heat convection inside of an annulus enclosure. The walls are considered to be at a constant temperature. The porous fins are installed on the outer wall, and other walls are insulated. Governing equations discretized using the FVM based on the second-order upwind scheme. The effect of different parameters on heat transfer enhancement inside the annulus, such as annulus inclination angle, annulus aspect ratio, Darcy number, Rayleigh number, thermal conductivity, the position of fins, number, and length of fins, has been investigated. Results declared that increasing Darcy number from a certain value would enhance the average Nusselt number dramatically at both aspect ratios, even though annulus with an aspect ratio of 3:1 has a higher value of average Nusselt number compared to the aspect ratio of 2:1. It has been illustrated utilizing low relative solid to fluid phase thermal conductivity nullify the effect of the increasing number of porous fins on heat transfer enhancement but, by increasing relative thermal conductivity to Ke=100, installing four porous fins on the inner cylinder increases the average Nusselt number by 7 percent compared to using only one fin.