Nusselt Number Decreases Research Articles

Study of rectangular fin heat sink performance and prediction based on artificial neural network

The plate-fin heat sink is a widely used heat dissipation device in thermal management systems, playing a crucial role in maintaining the stable operation of electronic equipment and reducing economic costs. In this study, the wind tunnel experimental device was employed to test the thermal and hydraulic properties of a rectangular fin heat sink. The CFD model was utilized to investigate the Nusselt number and friction factor of the rectangular fin heat sink under varying Reynolds numbers, fin numbers, and fin widths. The results indicate that as Reynolds number increases, the friction factor decreases while the Nusselt number increases. An increase in fin number leads to a decrease in both Nusselt number and friction factor. Moreover, with an increase in fin width, the friction factor increases while changes occur differently for Nusselt number at different Reynolds numbers. Furthermore, a multi-layer feedforward neural network based on a genetic algorithm (GA-BP) is employed to predict both Nusselt number and friction factor; subsequently evaluating these predicted results. The findings demonstrate that GA-BP neural network can accurately and rapidly predict thermal and hydraulic properties of heat sinks under various conditions including different Reynolds numbers, fin numbers, and fin widths.

Magnetized wastewater treatment using Williamson’s triple hybrid nanofluid with variable viscosity and internal heat generation on a permeable surface

PurposeTry to find a way to treat wastewater and achieve its purification from suspended waste, which was removed by examining the magneto-Williamson fluid on a horizontal cylindrical tube while taking advantage of solar radiation and nanotechnology.Design/methodology/approachThe effect of Cattaneo–Christoph law of heat transfer, solar radiation, oblique magnetic field, porosity and internal heat generation on the flow was studied. The control system was solved by the numerical technique of Chebyshev pseudospectrum (CPS) with the help of the program MATHEMATICA 12. The tables comparing the published data results with the existing numerical calculation match exactly.FindingsThe tables comparing the published data results with the existing numerical calculation match exactly. The current simulation results indicate that when using variable viscosity, the Nusselt number and surface friction decrease significantly compared to their value in the case of constant viscosity, and variable viscosity has a significant effect on flow, which reduces speed. Curves and increasing temperature profiles.Originality/valueDeveloping a theoretical framework for the problem of sewage turbidity in a healthier and less costly way, by studying the flow of Williamson fluid with variable viscosity (to describe the intensity of sewage turbidity) on a horizontal cylindrical tube, and taking advantage of nanotechnology, solar radiation, Christoph’s thermal law and internal heat generation to reach water free of impurities. Inclined magnetic force and porous force were used, both of which played an effective role in the purification process.

Numerical Assessment of the Thermal Performance of Microchannels with Slip and Viscous Dissipation Effects.

Microchannels are widely used across various industries, including pharmaceuticals and biochemistry, automotive and aerospace, energy production, and many others, although they were originally developed for the computing and electronics sectors. The performance of microchannels is strongly affected by factors such as rarefaction and viscous dissipation. In the present paper, a numerical analysis of the performance of microchannels featuring rectangular, trapezoidal and double-trapezoidal cross-sections in the slip flow regime is presented. The fully developed laminar forced convection of a Newtonian fluid with constant properties is considered. The non-dimensional forms of governing equations are solved by setting slip velocity and uniform heat flux as boundary conditions. Model accuracy was established using the available scientific literature. The numerical results indicated that viscous dissipation effects led to a decrease in the average Nusselt number across all the microchannels examined in this study. The degree of reduction is influenced by the cross-section, aspect ratio and Knudsen number. The highest reductions in the average Nusselt number values were observed under continuum flow conditions for all the microchannels investigated.

Thermal study of MHD hybrid nano fluids confined between two parallel sheets: Shape factors analysis

This article discusses the heat and air transfer characteristics of stable magnetohydrodynamic nanofluid flow between two interconnected sheets under the influence of a magnetic field. The nanofluid is a mixture of equal proportions of ethylene glycol and water. This study examined hybrid nanoparticles containing multi-walled carbon nanotubes (MWCNT) and silver (Ag). This research presents, for the first time, a new method for solving nonlinear equations using HPM Python and AGM Python. In addition, the symbolic solution to HPM and AGM has been attained by employing SymPy and SciPy libraries in Python. The results are presented graphically by comparing them with the fourth-order Runge-Kutta number. The final results reflect a high level of agreement between the analytical and numerical methods on the one hand and HPM Python and AGM Python on the other hand. This examination also investigates the effect of various parameters, including magnetic properties, viscosity coefficients, thermophoretic parameters, Brownian parameters, and nanofluid parameters such as velocity, temperature, and concentration. The results prove that velocity and concentration increase as the magnetic field decreases, whereas the temperature displays an opposite trend. As the Schmidt number increases, both the Nusselt number and concentration decrease. The relationship between concentration and temperature with respect to the Prandtl number indicates that when the Prandtl number decreases, the temperature increases while the concentration declines. It is important to note that the employment of hybrid nanofluids leads to an increase in velocity, temperature, and concentration.

Effect of wettability and surface roughness on flow and heat transfer characteristics in nanochannels

The flow and heat transfer processes of liquid argon within nanochannels with random roughness are investigated using the molecular dynamics method. This study explores the effects of surface roughness and wettability on flow and heat transfer performance. The results indicate that both surface roughness and wettability significantly influence temperature jumps, velocity slip, flow resistance, and temperature distribution. Specifically, hydrophilic surfaces can reduce temperature jumps and velocity slip due to their enhanced ability to adsorb liquid atoms, which effectively improves heat transfer while simultaneously increasing flow resistance. The fractal dimension D characterizes the surface roughness, which decreases as D increases. Additionally, both the Nusselt number and drag coefficient decrease with increasing D. In this study, we investigate cases where D ranges from 2.5 to 2.9, with D = 2.5 representing the highest roughness, and the smooth channel corresponding to the lowest roughness. For hydrophilic nanochannels at D = 2.5, the Nusselt number and drag coefficient increased by factor of 2.2 times and 5.2 times compared to smooth channels, respectively. For hydrophobic nanochannels at D = 2.5, the Nusselt number and drag coefficient increased by a factor of 4.5 times and 29.1 times compared to smooth surface channels, respectively. Considering both flow and heat transfer performances, the best comprehensive performance is achieved with D = 2.8 for channels with hydrophilic surfaces and D = 2.6 for channels with hydrophobic surfaces. This work systematically investigates the coupled effects of random roughness and wettability on the flow and heat transfer characteristics in nanochannels, providing new theoretical insights for optimizing nanochannel design.

Flow dynamics and heat transfer characteristics of air/water mist jet impingement using Eulerian-Eulerian approach

The present numerical study focuses on a two-phase Eulerian-Eulerian approach to model the flow structure and heat transfer characteristics of an air/water mist jet emanating from a coaxial jet nozzle and impinging on an isothermal heated flat plate. A detailed parametric numerical study has been performed to investigate the effect of various operating parameters like air Reynolds number (2400-9142), mist Reynolds number(1.87–8.68), mist loading fraction (0 % - 0.96 %), droplet diameter (1 μm – 60 μm), and non-dimensional nozzle to plate spacing (10–42) on the flow structure and heat transfer characteristics of air/water mist jet. The present numerical results are in agreement with the experimental results, within 16 % accuracy. The heat transfer increases with an increase in the air Reynolds number or mist loading fraction. The increase in air Reynolds number provides better heat transfer enhancement as high as 94.5 % compared to 27.6 % in the case of an increment in the mist loading fraction. Additionally, the effect of droplet diameter on the flow structure and heat transfer characteristics of air/water mist jet is analyzed at depth. The increase in nozzle-to-plate distance from 10 to 42 leads to a decrease in stagnation point Nusselt number of the order of 31 %. Further, correlations have been proposed to predict the Nusselt number at the stagnation point, stagnation region, and average Nusselt number for the target plate.

Mixed convective nanofluid flow and heat transfer induced by a stretchable rotating disk in porous medium

AbstractEnhancement of “heat transfer” using “nanofluid” has diverse potential applications in heat exchangers, thermal management of electric devices, cooling of tractors, solar thermal systems, manufacturing of paper, and many others. Hence, the aim of the current investigation is to explore the impacts of “mixed convection” on “nanofluid flow” over a permeable rotating disk, which is stretched radially in a porous medium. Variable wall “temperature” and “convective boundary conditions” are also considered here. This makes the present investigation different from others. The suitable “similarity transformations” are imposed to alter the governing partial differential equations into a set of coupled ordinary differential equations (ODEs). Then, these ODEs are solved numerically by the “4th order Runge‐Kutta method” using the “shooting technique” with the help of the bvp4c package in MATLAB software. The effects of fluid controlling “parameters” on “flow and thermal fields” as well as “skin friction coefficient” and “Nusselt number” are presented graphically and explained physically. Due to enhanced rotation of the disk, the radial and azimuthal velocity of the fluid increase and the temperature of the fluid decreases. Most importantly, it is observed that when the disk rotates faster than the stretching rate, the temperature of the nanofluid decreases rapidly, which has wider applications for cooling purposes. It is also noted that when the suction parameter increases its value from −1 to 1, for Ag–water nanofluid, the “skin friction coefficient” decreases by 73.56%, and the Nusselt number also decreases by 24.11%, and for Fe3O4–water nanofluids, the “skin friction coefficient” decreases by 71.25% and the Nusselt number decreases by 24.47%.

Thermal magnetization transport analysis featuring darcian and multi-physical rheological characteristics in chemically reactive dual convective tangent-hyperbolic nanomaterial confined by vertical cone

The Soret-Dufour characteristics elaborate the phenomena of cross-diffusion where solutal gradients yield heat flux (Dufour aspect) and thermal gradients engender mass flux (Soret effect). Such consideration finds significance in multi-component fluid systems, influencing both heat-mass transportation processes. This study evaluates the porous medium characteristics in convectively heated tangent-hyperbolic nanomaterial driven by a magnetized convected cone. The analysis features Buongiorno nanomaterial model which accounts Brownian motion together with thermophoresis. Thermal transport expression which reports heat transfer characteristics is modeled by considering thermal radiation, convective thermal conditions and heat generation while mass transfer considers the chemical reaction effects. Dimensional expressions are converted into dimensionless forms deploying similarity transformations ensuing in a set of ODEs (ordinary differential expressions) which are computed by deploying bvp4c algorithm. Graphical and tabular behavior of velocity, nanoparticles concentration and temperature fields is inspected corresponding to related variables. This research highlights key findings, revealing a decrease in Nusselt number with increasing heat generation, Dufour parameter and thermophoresis parameter values while opposite trends are verified for radiation parameter values. The velocity function declines for escalating Weissenberg number, magnetic field and permeability parameters but it upsurges with material and buoyancy parameters.

Optimal Design Of The Concentric Annulus For The Solar Collectors And Energy Storage

Heat exchangers with uniform heating ensure even heat distribution, improving heat transfer efficiency and lowering thermal stress. It contributes to increasing the effectiveness of solar energy conversion into thermal energy in solar collectors, improving system performance and sustainability. It is essential for enhancing performance in both home and industrial applications because of these advantages. An experimental investigation was conducted to study the natural convective flow between two isothermal concentric cylinders filled with porous media (silica sand) and equipped with annular fins attached to the inner cylinder. The fins varied in length (Hf = 3, 7, and 11 mm), and the radius ratios (Rr) between the cylinders were also considered during the study. This work examines and discusses the effects of independent characteristics, such as fin height (Hf), radius ratio (Rr), and Rayleigh number (Ra) from 10 to 500, on heat transfer outcomes. As the distance between the two cylinders expands, the average Nu remains relatively constant for low values of Ra. However, as Ra approaches 100, the average Nu increases. These values also rose when Rr decreased for the hot cylinder and vice versa for the cold cylinder. The average Nusselt number versus Ra was analyzed in graphical form to show the effect of the fin number on the average Nusselt number. The analysis includes a range of fin numbers. It is found that as the amount of fins increases from n = 12 to n = 23 and eventually to n = 45, there is a decrease in the average Nusselt number. The decrease in average Nusselt number can range from 19.2% to 26.6% for the same value of Ra.

Radiative and Lorentz’s effects on MHD free convective mass and heat transfer time-dependent nanofluid flow across vertical perforated plate

The current study investigates the effects of thermal radiation and Lorentz’s force on heat and mass flow in a nanofluid with a magnetic field and free convection, as it passes over a vertical permeable sheet. The dominant PDEs are turned into linked nonlinear ODEs using an appropriate similarity transformation. Using the MATLAB ODE45 tool, dimensionless ODEs are numerically computed using the finite difference procedure. Four different water-based nanofluids are considered, including copper, titanium dioxide, aluminum oxide, and silver. The influence of emerging dimensionless numbers and other parameters, such as the magnetic force parameter, the radiation parameter, the suction parameter, the Prandtl number, the Schmidt number, the Dufour number, as well as for constant values of the modified local Grashof number and local Grashof number on the concentration, velocity, and temperature profiles is emphasized and mentioned. Moreover, the visual representation of the effects of a volume percentage of up to 4% copper nanoparticles on the distributions of concentration, temperature, and velocity is also shown. The temperature profile, concentration profile, and velocity profile all grow with an increase in the volume percent of copper nanoparticles between 0.00 and 0.04. Furthermore, numerous scenarios are investigated for the distributions of the local Sherwood number, the local Nusselt number, and the local skin friction coefficient. The local Nusselt number decreases, and the local skin friction coefficient and Sherwood number increase about by 30 %, 45 %, and 60 % respectively due to increasing the value of volume fraction from 0 % to 4 %. The local skin friction coefficient increases and the local Nusselt number decreases by about 15 % and 39 % respectively for rising values of the thermal radiation number from 0.5 to 3.5. In addition, for magnetic force parameter values between 0.5 and 4.0, the local skin friction coefficient drops by about 13 %.

Bio-Convective Thermally Radiated Casson Fluid Model PDEs Past over a Darcy-Forchheimer Porous Stretched Sheet via OHAM Strategy

The current study examines the topic of continuous flow of nanofluids over two-directional boundary level employing Casson heat transmission across a linearly stretched sheet. Firstly, the partial differential equations are transformed into non-linear ordinary differential equations with the help of similarity parameters. These non-linear ordinary differential equations are solved with the given boundary conditions by applying the BVPh2.0 method on Mathematica software. The effects of magnetic impact, radiation parameter, porosity number, Brownian motion parameter, thermophoresis parameter, Casson fluid parameter, Schmidt number, Prandtl number, peclet number, bioconvection on Velocity, temperature and concentration profiles is observed. It is noted that the concentration and temperature profiles increase by expanding values of thermophoresis parameter also the temperature increase by increment in Brownian motion while a reverse result obtained on concentration profile. Also, the influence of Casson fluid, thermophoresis and Brownian motion on skin friction, Sherwood number and Nusselt number is noted and check the behavior of these numbers by increasing or decreasing values of thermophoresis parameter, Casson fluid parameter and Brownian motion. And, calculated that by increment in thermophoresis and Brownian motion, the Nusselt number decreases. The graphs of temperature profile, velocity profile and concentration profile are drawn and also other results are tabulated.

Experimental investigation of shell and helical coiled heat exchanger with Al2O3 nano-fluid with wide range of particle concentration

The purpose of this study is to experimentally enhance the heat exchange rate of the shell and helical coil tube heat exchanger by mixing water with aluminum oxide (Al2O3) nanoparticles, as well as to explore the effect of inlet thermal parameters on the performance of the heat exchanger. A test rig was constructed to investigate the influence of particle concentration, and inlet temperatures on the performance of nano-fluid. Parameters such as Nusselt number, pressure drop, performance evaluation criteria (PEC) are considered to rate the performance of the nano-particle with the heat exchanger. In this study a wider range of particle concentration is considered, which varies from 0.0%–0.75%. Experiments with and without nanoparticles are carried out under identical working conditions. By analyzing the experimental data, it was found that nanoparticles significantly improve the coefficient of heat transfer inside the helically coiled tube. From sensitivity analysis, it is obseerved that there is a slight decrease in Nusselt number of the nano-fluid with increase in inlet temperatures of the nano-fluid and the cooling water. Furthermore, it is concluded that an 8.5% increase in PEC value is observed with increase in particle concentration from 0.15% to 0.75%.

Investigation of natural convection and entropy generation of non-Newtonian flow in molten polymer-filled odd-shaped cavities using finite difference lattice Boltzmann method

This study examines the natural convection heat transfer (NCHT) and entropy generation (EG) of a non-Newtonian (NN) flow inside an odd-shaped cavity filled with molten polymer. The cavity configuration comprises hot internal walls, cold external walls, and insulated remaining walls. The finite difference lattice Boltzmann method (FDLBM) is employed to solve the governing equations involved. The input parameters span a range of values, with Rayleigh number (Ra) varying from 104 to 105, power-law index (n) covering a range from 0.5 to 1.5, and width ratio (WR) ranging from 0.2 to 0.4, while maintaining Prandtl number (Pr) at a constant value of 10. The results revealed that at Ra values of 104 and 105, the overall entropy increases as the WR increases from 0.2 to 0.4 and decreases as the n index increases. In contrast to dilatant fluids, where heat transfer (HT) decreases as the n index increases from 1 to 1.5, pseudo-plastic fluids show an opposite trend with HT increasing as the n index decreases from 1 to 0.5. This trend is attributed to the general decrease in the average Nusselt number (Nu) as the n index increases. Additionally, it is observed that the n index has no significant impact on the average Nu due to low buoyancy force at Ra = 104 and WRs of 0.2 and 0.3. However, it notably influences the Bejan number (Be) across all WRs. Overall, the present model demonstrates excellent agreement with previous numerical results, affirming the FDLBM as a superior, reliable, and well-suited technique for relevant applications. These results suggest the potential to extend the application of the FDLBM approach to various cavity shapes, allowing for a comprehensive exploration of NCHT and EG under various conditions.

Influence of thermal radiation and shape factor on a hybrid nanofluid flow over a permeable flat plate with cross-diffusion effects: An irreversibility analysis

Understanding and controlling the shape factors of nanoparticles in fluid flow problems is crucial for optimizing heat transfer, fluid dynamics, and various applications such as nanofluids, drug delivery systems, catalysis, and nanocomposites. By tailoring the shape of nanoparticles, researchers can manipulate their behavior, dispersion, and interaction with the fluid, thereby optimizing the desired outcomes in various fluid flow problems. The meticulous investigation uncovers the integration of entropy analysis in the investigation of the flow of convective magnetohydrodynamic hybrid nanofluid via a permeable flat surface, by considering the effects of Dufour, viscous dissipation, Soret, and thermal radiation. The governing equations are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved using the bvp4c solver, a MATLAB in-built function. We display the outcomes for three different shape factors: platelet, cylinder, and brick. The skin friction coefficient increases at a rate of 1.5089 for the brick shape, 1.5163 for the cylindrical shape, and 1.5212 for the platelet shape when the mixed convection parameter lies between 1 and 5. In this regard, it is important to point out that there is a direct connection between the increase in temperature transmission rate and a decline in the Dufour number ( Du ). It has been found that when 1 ≤ Du ≤ 2.4 , the Nusselt number decreases by 0.4786, 0.4618, and 0.4512 for brick, cylinder, and platelet shapes, respectively. A decline in the Sherwood number is noticed with an upsurge in the Soret number ( Sr ). There is a noticeable increase of 0.0442 in the Sherwood number for brick shape, 0.0438 for cylinder form, and 0.0435 for platelet form when 1 ≤ Du ≤ 2.4 . Furthermore, we have detected that an increase in the radiation parameter amplifies both the Bejan number and the profiles of entropy formation.

Numerical Investigation of Hybrid Nanofluid Natural Convection and Entropy Generation in a Corrugated Enclosure with an Inner Conducting Block

Current work deals with a numerical analysis of convective heat transfer and entropy generation inside a rectangular cavity with a corrugated bottom filled with MoS2–SiO2-water hybrid nanofluid. Here, a conducting solid body is attached to the top wall, and discrete heaters are attached to the bottom wall of the cavity. The numerical solutions of the governing equations are derived utilizing a higher-order compact (HOC) finite difference scheme and validated with the existing computational and experimental results. Present numerical results are then studied in detail, emphasizing isotherms, streamlines, and local entropy generation with respect to specific parameters like Rayleigh number (103 ≤ Ra ≤ 106), the volume percentage of nanoparticles (0% ≤ Φ ≤ 4%), the thermal conductivity of solid body (1.95 ≤ ks ≤ 16.00) as well as the aspect ratio of heater length (AR = 0.2, 0.4, 0.6, 0.8). The impacts of key factors on the Bejan number, average Nusselt number, and overall entropy generation are also investigated. The results show that an increase in the thermal conductivity of the solid body from 1.95 to 16.00 increases the average Nusselt number and total entropy generation by 9.17% and 40.07%, respectively, for AR = 0.2, Ra = 106, and Φ = 4%. In addition, the average Nusselt number and total entropy generation decrease by 59.11% and 61.99%, respectively, for ks = 16.00, Ra = 106, and Φ = 4% when the aspect ratio of heater length increases to 0.8.

Heat Transfer and Flow Resistance in Crossflow over Corrugated Tube Banks

The engineering of tubes with surface corrugations is recognized as an effective method for enhancing heat transfer within the tube. Yet the impact of surface corrugation on the flow and heat transfer around the tube’s exterior remains inadequately explored. This study investigates the crossflow and heat transfer characteristics in banks of periodically inward-corrugated tubes using computational fluid dynamics. Numerical simulations were performed for both in-line and staggered tube arrangements, covering Reynolds numbers from 1000 to 10,000. The aim was to examine how various corrugation parameters affect heat transfer and flow dynamics in tube banks configured in both in-line and staggered layouts. The results show that the heat transfer and the pressure drop in crossflow across tube banks are substantially influenced by changes in corrugation parameters. Specifically, in the in-line arrangement, both the Nusselt number and Euler number decrease significantly as the corrugation height increases. In contrast, in the staggered arrangement, the Nusselt number and Euler number exhibit less variation in response to surface corrugation. A comparative analysis of performance criteria suggests that a staggered arrangement is more advantageous for improving thermal–hydraulic efficiency in crossflow through corrugated tube banks.

Investigating double-diffusive natural convection in a sloped dual-layered homogenous porous-fluid square cavity

This article investigates natural convection with double-diffusive properties numerically in a vertical bi-layered square enclosure. The cavity has two parts: one part is an isotropic and homogeneous porous along the wall, and an adjacent part is an aqueous fluid. Adiabatic, impermeable horizontal walls and constant and uniform temperatures and concentrations on other walls are maintained. To solve the governing equations, the finite element method (FEM) employed and predicted results shows the impact of typical elements of convection on double diffusion, namely the porosity thickness, cavity rotation angle, and thermal conductivity ratio. Different Darcy and Rayleigh numbers effects on heat transfer conditions were investigated, and the Nusselt number in the border of two layers was obtained. The expected results, presented as temperature field (isothermal lines) and velocity behavior in X and Y directions, show the different effects of the aforementioned parameters on double diffusion convective heat transfer. Also results show that with the increase in the thickness of the porous layer, the Nusselt number decreases, but at a thickness higher than 0.8, we will see an increase in the Nusselt number. Increasing the thermal conductivity ratio in values less than one leads to a decrease in the average Nusselt number, and by increasing that parameter from 1 to 10, the Nusselt values increase. A higher rotational angle of the cavity reduces the thermosolutal convective heat transfer, and increasing the Rayleigh and Darcy numbers, increases Nusselt. These results confirm that the findings obtained from the Finite Element Method (FEM), which is the main idea of this research, are in good agreement with previous studies that have been done with other numerical methods.

Numerical Study of Eccentric Jet Impingement Cooling on a Heated Cylindrical Surface

Abstract This article presents a comprehensive numerical analysis of the effects of cooling a cylinder using an eccentric slot jet impingement cooling (SJIC). The study focuses on examining the thermal and fluid behavior when the slot jet is offcenter, during impingement cooling. Several turbulence models from the k–ε and k–ω families were compared by evaluating the local Nusselt number profiles at different locations around the cylinder, and these results were compared to experimental data. The findings indicate that the SST k–ω model outperforms the other turbulence models in estimating the Nusselt number in the stagnation region, while the standard k–ω model shows improved performance elsewhere on the cylinder. Furthermore, this study reveals a decrease in the maximum local Nusselt number and a shift in the direction of the nozzle displacement. The presence of swirling/recirculating fluid at the trailing end of the cylinder enhances heat transfer near the back end of the cylinder. The separation and the reattachment of the fluid stream differ depending on the Reynolds number, with low Reynolds numbers resulting in reattachment on the side of the slot jet and higher Reynolds numbers leading to reattachment in the opposite direction. Additionally, the length of the recirculation and swirling zones increases as the nozzle-to-cylinder spacing (H/S) increases. However, as the eccentricity (E/S) increases, the size of the swirl circulation zones decreases and completely vanishes for E/S = 4. This study provides valuable insights for optimal cooling design.

Modeling of Opposing Mixed Convection of Air in Partially Cooled Vertical Channels

in this paper opposing laminar mixed convection in partially cooled vertical channel is investigated numerically. Temperature profiles, Nusselt number and velocity profiles at various axial locations in the cooled part of opposing buoyancy flow are presented. Streamlines and isotherms have been also plotted for different values of Grashof number, Gr. Conservation equations of continuity, momentum and energy were solved simultaneously using Finite volume method. The effect of the cooled section on the flow pattern and heat transfer performance is investigated for given Grashof numbers. The influence of axial diffusion and it's relevant to flow reversal at the entrance region of the channel was taken into account in the governing equations and particular attention is given to the ratio │Gr / Re2│. The effect of opposing bouncy forces on the hydrodynamic and thermal fields was examined for air with Re = 500, 105 ≤ │Gr ≤ │ 3*105. Reversal flow was observed near the channel wall for this opposing buoyancy flow. It was noticed that the friction factor, f•ReL ,for the ratio │Gr / Re2 │≥ 1.2 was unstable over the cooled length, becomes negative and then increases to an asymptotic value of 16 over the insulated section. The presented numerical results revealed some interesting features which may be summarized as: (i) Globally Nusselt number decreases and reaches asymptotic value at the end of the cooling section. However for Gr = -3*105 Nusselt decreases and reach a minimum value approximately equal to 3.12. (ii) For Gr up to │3ₓ105│ the Boussinesq approximation still predicts reasonably the heat transfer rate.

Numerical Analysis on Stagnation Point Flow of Micropolar Nanofluid with Thermal Radiations over an Exponentially Stretching Surface

Several industrial developments such as polymer extrusion in metal spinning and continuous metal casting include energy transmission and flow over a stretchy surface. In this paper, the stagnation point flow of micropolar nanofluid over a slanted surface is presenting also considering the influence of thermal radiations. Buongiorno’s nanoliquid model is deployed to recover the thermophoretic effects. By using similarity transformations, the governing boundary layer equations are transformed into ordinary differential equations. The Keller-box approach is used to solve transformed equations numerically. The numerical outcomes are presented in tabular and graphical form. A comparison of the outcomes attained with previously published results is done after providing the entire formulation of the Keller-Box approach for the flow problem under consideration. It has been found that the reduced sherwood number grows for increasing values of radiation parameter while, reduced Nusselt number and skin friction coefficient decreases. Furthermore, the skin-friction coefficient increases as the inclination factor increases, but Nusselt and Sherwood's numbers decline.