Increase In Average Nusselt Number Research Articles

Numerical Investigation of Natural Convection from a Horizontal Heat Sink with An Array of Rectangular Fins

This research focuses on the numerical analysis of a rectangular fin array with a horizontal heat sink to examine its performance in natural convection heat transfer. The study uses air as the primary working medium. Steady-state 3D modeling is carried out using the finite volume method (FVM), allowing velocity and temperature distributions to be evaluated by solving equations relating to mass conservation, fluid dynamics, turbulence, and heat transfer. This research details temperature and velocity variations as well as fluid trajectories. It also explores how the intensification of heat flow, varying from 361 W/m2 to 2,527 W/m2, influences the cooling efficiency of the fins. It is observed that the increase in heat flux reduces the formation of vortices and intensifies natural convection by rising the temperature gradient between the radiator and the surrounding. The temperature increases at all parts of the heat sink fin array as heat flux increases. Besides, it is noticed that the maximum temperature is generated at the mid-region of the base plate heat sink and gradually dissipates to the surroundings through the bodies of the fins. Moreover, the study indicates that the average convection heat transfer coefficient (hav) and the average Nusselt number (Nus) increase by 86% and 84%, respectively, when the heat flux is increased from 361 W/m2 to 2,527 W/m2. These observations are corroborated by a comparison with existing experimental data, showing an agreement of less than 9%. The digital model is validated by comparing pre-existing data on radiators with horizontal rectangular louvers, revealing minimal deviations of less than 2%.

The effect of appendages at step on heat transfer in a backward-facing step

The current study analyzes the effect of introduction of an appendage at the step, on forced convection, in a backward-facing step. Two-dimensional turbulent flow over a backward-facing step has been tested numerically. The length and size of the recirculation zone have been observed to vary, by changing the appendage length and Reynolds number. An increase in the average Nusselt number has been observed for an increase in the Reynolds number. In this study, it has been visualized that with the introduction of the appendage, the Nusselt number increases. A vertical fin length of Ya/S = 0.5 has been found to provide the greatest improvement in the heat transfer rate. The average Nusselt number increases by three times for Ya/S = 0.5. However, the Performance Evaluation Criteria (PEC) indicates the appendage of length Ya/S = 0.3 provides consistent values. This arises as the pressure drop increases by 8.75 times for Ya/S = 0.5 when compared with unobstructed case.

Numerical study and multi-optimization of heat transfer performance in counter flow minichannel heat sink with slots on ribs using NSGA-Ⅱ

High temperature and nonuniformity temperature cause thermal failure and thermal deformation for high-heat flux electronic devices. To address this issue, a counter flow minichannel heat sink with slots on ribs is designed. A 3D conjugated heat transfer model based on computational fluid dynamics (CFD) was developed to investigate effect of slots number (i) and growth rate of slot width (j) on average Nusselt number (Nu), local temperature distribution and temperature standard deviation (σ). The results show that design parameters i and j significantly influence heat transfer capability and temperature uniformity. However, there is no clear pattern between design parameters (i and j) and heat transfer performance (Nu and σ) to guide design. Furthermore, a non-dominated sequencing genetic algorithm (NSGA-Ⅱ) multi-objective optimization coupled Artificial Neural Network (ANN) is conducted with the consideration of maximum Nusselt number Nu and minimum temperature standard deviation (σ) as objectives. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is employed to determine the best solution from the Pareto front, i.e., multi-objective optimization solutions set. The optimized solution obtains 2.1 times increase in average Nusselt number and 0.36 times decrease in temperature standard deviation compared with conventional counter flow minichannel heat sink. This work serves as a guideline for designing minichannel heat sinks for thermal management of electronic components.

Influence of Joule heating and magneto-hydrodynamic on double diffusion mixed convection in a cavity with liquid sodium-potassium alloy and discrete thermosolutal source

Researchers in the biomedical field have focused more on the application of magneto-hydrodynamics in recent years. This study examines the steady double-diffusive mixed convection characteristics in a double-sided cavity with liquid potassium alloy that exhibits a magnetic effect and Joule heating. The investigation analyzes the impact of various parameters, including Hartmann number (0 ≤ Ha ≤ 50), Joule Heating (0 ≤ J ≤ 10.0), Reynolds number (102 ≤ Re ≤ 103), Lewis number (1.0 ≤ Le ≤ 10.0), Buoyancy ratio (−4.0 ≤ N ≤ 4.0), Prandtl number (Pr = 0.054), and Richardson Number (Ri = 1.0). The results are obtained using finite volume-based numerical codes. The findings suggest that the heat and mass transfer rates increase as Re and J increase and decrease when there is an increase in Ha and N. There is a significant effect on both the Joule parameter and magnetic field on fluid and heat flow. When Joule heating is present, increasing the Le results in a 0.627 times increase in heat transfer rate and a 1.722 times increase in mass transfer rate. When Re increases, the average Nusselt number (Nuavg) and average Sherwood number (Shavg) increase 0.81 and 0.11 times, respectively.

Numeričko ispitivanje prenosa toplote prirodnom konvekcijom korišćenjem nanofluida TiO₂/Al₂O₃-voda

Recently, nanofluids have been used as an alternative in several industries to improve the heat transfer process. This paper focuses on the numerical modeling of the performance of the natural convection process through TiO₂/Al₂O₃-water nanofluids in a square cavity containing a heated block. The lattice Boltzmann method is used in this study to present the nanofluid heat transfer enhancement. Results are presented in terms of streamlines, isothermal contours, and Nusselt number profiles. The findings demonstrate that by raising the Rayleigh number and solid nanoparticle concentration, the average Nusselt number increases, and they reveal that the heated block enormously affects the flow structure and heat transfer. It is also demonstrated that the type of nanoparticles significantly impacts the natural convection heat transfer.

Entropy generation of Al2O3/water nanofluid in corrugated channels

The flow of nanofluids in a corrugated channel has been shown to have a significant impact on heat transfer performance, and has therefore become an important area of research. The ob- jective of this paper is to understand the thermal behavior of Al2O3/water nanofluid in a sinu-soidal and square channel and to identify ways to optimize heat transfer performance in such configurations. For this purpose, a numerical simulation was conducted using ANSYS-Fluent software 16.0 on entropy generation and thermo-hydraulic performance of a wavy channel with the two corrugation profiles (sinusoidal and square). The analyses were carried out under laminar forced convection flow conditions with constant heat flux boundary conditions on the walls. The influence of various parameters, such as particle concentration (0–5%), particle di-ameter (10nm , 40nm and 60nm), and Reynolds number (200 < Re < 800) on the heat transfer, thermal, and frictional entropy generation, and Bejan number was analyzed. Moreover, the distribution of streamlines and static temperature contours has been presented and discussed, and a correlation equation for the average Nusselt number based on the numerical results is presented. One of the most significant results obtained is that the inclusion of nanoparticles (5% volume fraction) in the base fluid yielded remarkable results, including up to 41.92% and 7.03% increase in average Nusselt number for sinusoidal and square channels, respectively. The sinusoidal channel exhibited the highest thermo-hydraulic performance at Re= 800 and φ= 5%, approximately THP= 1.6. In addition, the increase of nanoparticle concentration from 0% to 5% at Re= 800 and dnp= 10nm, diminishes the total entropy generation by 28.39 % and 22.12 % for sinusoidal and square channels, respectively, but when the nanoparticle diameter decreases from 60nm to 10nm at ϕ= 5% and Re= 800, the total entropy generation in the sinusoidal channel decreases by 34.85%, whereas in the square channel, it decreases by 20.05%. Therefore, rather than using a square channel, it is preferable and beneficial to use small values of nanoparticle diameter and large values for each of ϕ and Re in the sinusoidal wavy channel. Overall, the study of nanofluid flow in a wavy channel can provide valuable insights into the behavior of nanofluids and their potential applications in a variety of fields, including manufacturing, energy produc-tion, mining, agriculture, and environmental engineering.

Heat transfer enhancement in channels with roughened and elastic walls

In this research, a combination of passive and active heat transfer enhancements are used synergistically to assist in the increase of absorbed heat from a channel by roughened and fluctuating walls. To this end, the upper wall is artificially roughened and a fluctuating segment is added to the lower wall. Flow regime is considered to be laminar and Reynolds number is 1000 at the entrance of the channel. Combinations of various roughness geometries and fluctuations are studied. It was found that due the increase of the fluid kinetic energy and its interaction with roughened surface and elastic segment, heat transfer rate is amplified. To investigate the overall efficiency of the system, Nusselt number and friction factor are calculated and a maximum value of 37.5% increase in average Nusselt number of the midsection where elastic wall is placed has been reached by flexible plate displacement. A maximum Nusselt number increase of 167% has been observed when the elastic plate reaches its peak value.

Applying position and time dependent nusselt number and friction factor into 1D model to improve regenerator design for solid-state caloric cooling cycles

Active caloric regenerative cycles have recently attracted much attention as a promising cooling technology that can potentially replace the vapor compression cycle based on its high efficiency and eco-friendly characteristics. The use of modeling is necessary in optimizing the active caloric regenerative cycle due to the system’s complex structure and numerous parameters that need to be taken into account. The cycle uses oscillatory flow to efficiently exchange heat between the caloric material and the heat transfer fluid and to generate a desired temperature gradient in the regenerator. When the oscillatory flow is used, hydrodynamically and thermally developing regions occur all over the regenerator when the direction of the fluid flow changes.To the best of the authors’ knowledge, no previous research has considered the oscillatory developing regions in a 1D model. Therefore, this study incorporated the developing regions generated by the oscillatory flow as well as the entrance developing regions into a regenerator model for the first time. Based on the modeling results, the influence of the oscillatory developing regions and the average Nusselt number increase with higher cycle frequency. Additionally, the new 1D model produces average Nusselt number similar to the 2D model with a maximum error of 4 %. Considering that the 2D model requires very high computational cost to solve the transient condition of the caloric cycle, the advanced 1D model can accurately assess the performance of the caloric cycle and provide a detailed analysis of heat transfer phenomena and fluid dynamics in the regenerator at modest computational cost.The parallel plate type, optimized using the new model, has a hydraulic diameter of 0.1 mm. However, maintaining such a small space between the plates can be challenging from an application standpoint. Therefore, this study proposes the use of a wide rectangular microchannel matrix as the regenerator. The rectangular microchannel matrix, with an aspect ratio of 30, produces a coefficient of performance of 5.65, which is comparable to the parallel plate matrix. Consequently, the wide rectangular microchannel matrix can achieve both high Nusselt number and structural stability simultaneously.

Study on enhanced heat transfer of a phase change material slurry in transverse corrugated tubes

Enhancing the heat transfer of ice slurry is a key to improving its application. The outward transverse corrugated tube (OTCT) presents a better heat transfer enhancement as an effective passive flow control method. In this paper, the thermo-fluidic performance and enhanced heat transfer mechanism of ice slurry in OTCT are numerically studied using Euler-Euler multiphase model. The results indicated that turbulent vortex of ice slurry in OTCT is enhanced with the rise in the ratio of corrugation height to diameter (H/D), and declined with rising the of ratio corrugation pitch to diameter (P/D), and ratio of corrugation pitch to width (W/D). The ice concentration presents a periodic fluctuation along the flow direction. The values of H/D, W/D, and P/D have a significant influence on the mass transfer for ice slurry. And the ice particle concentration displays more even distribution as increasing H/D, and decreasing W/D and the P/D. The average flow resistance (fave) and Nusselt number (Nuave) increase with the increasing H/D and decreasing P/D, and decrease with increasing W/D. Nuave presents a linear increase with Re. For the inlet ice volume fraction of αin = 10%, Nuave enlarges significantly by increasing the Re from 4950 to 9540 for different H/D, P/D, and W/D values. The performance evaluation criterion (PEC) reaches a maximum value for different H/D and P/D at Re = 9540 when W/D = 0.4, αin = 10%. For bigger inlet ice particle concentration, the increment of Nuave of ice slurry in OTCT is more significant at higher Re compared with the smooth tube. Meanwhile, under higher ice concentration, the overall heat transfer performance is more prominent at large Re. Finally, the empirical correlations of the fave and Nuave are established to predict the thermal–hydraulic performance of ice slurry flowing through OTCT.

Numerical simulation of flow and heat transfer of n-decane in sub-millimeter spiral tube at supercritical pressure

The flow and heat transfer characteristics of n-decane in the sub-millimeter spiral tube (SMST) at supercritical pressure (p = 3 MPa) are studied by the RNG k − ε numerical model in this paper. The effects of various Reynolds numbers (Re) and structural parameters pitch (s) and spiral diameter (D) are analyzed. Results indicate that the average Nusselt number (Nu¯) and friction factor (f¯) increase with an increase in Re, and decrease with an increase in D/d (tube diameter). In terms of the structural parameter s/d, it is found that as s/d increases, the Nu¯ and f¯ first increase, and then decrease. and the critical structural parameter is s/d = 4. Compared with the straight tube, the SMST can improve Nu¯ by 34.8% at best, while it can improve f¯ by 102.1% at most. In addition, a comprehensive heat transfer coefficient is applied to analyze the thermodynamic properties of SMST. With the optimal structural parameters of D/d = 6 and s/d = 4, the comprehensive heat transfer factor of supercritical pressure hydrocarbon fuel in the SMST can reach 1.074. At last, correlations of the average Nusselt number and friction factor are developed to predict the flow and heat transfer of n-decane at supercritical pressure.

Control of the melting process in a rectangular energy storage chamber filled with phase change material in the presence of an oscillating and rotating cylinder

In the present research, the efficacy of rotating and oscillating cylinders on the melting process in a rectangular chamber has been investigated numerically. Porosity-enthalpy model has been used to model the melting process. The effect of the radius, location, rotational and oscillating speed (amplitude and frequency) of the cylinder, the presence of different arrangements of the cylinder and the temperature changes of the active boundary on the liquifying process have been investigated. As the cylinder has an oscillating motion, the dynamic mesh is employed. The phase change material (PCM) is Lauric acid. The consequences reveal that the existence of the cylinder betters the rate of the melting process, and the best melting process occurs at R = 0.3, and the time required for the complete liquifying of the PCM for this state is lessened by 12.84 % compared to the state with R = 0.01. The rotating cylinder reduces the PCM liquifying rate, so that by selecting the rotational speed of −3 and + 10 rad/s, the average melting fraction of PCM has decreased by 7.96 and 8.67 %, respectively, compared to the fixed cylinder state. The oscillating movement of the cylinder improves the liquifying rate. Increasing the oscillation range and frequency will decrease and increase the liquifying rate, respectively. The temperature changes of the active boundary with time have improved the melting process compared to the constant temperature state. In the cases where the average Nusselt number increases, the melting rate has decreased. Among the arrangements considered for the cylinder arrangement, the best melting performance has been observed when two cylinders are placed horizontally in the chamber.

Investigation on the thermohydraulic performance and entropy-generation of novel butterfly-wing vortex generator in a rectangular microchannel

• A new butterfly-wing vortex generator is introduced on the bottom wall of microchannel. • Thermohydraulic performance and entropy-generation in microchannel are investigated. • The maximum Pf of 1.23 and minimum N s , a of 0.84 are obtained . • The proposed microchannel is advantageous according 1 st & 2 nd law of thermodynamics. In the present study, a 3D numerical analysis is carried out to understand the effect of the butterfly-wing vortex generator on the thermohydraulic performance and entropy-generation in a rectangular microchannel. To validate the numerical model, experiments are carried out in the plain microchannel of width ( W ) = 1 mm, height ( H ) = 0.63 mm, and length ( L ) = 50 mm. Further, the simulation is extended to study the effect of several geometric parameters of the butterfly-wing vortex generator, i.e., height ( h ) = 0.05, 0.1 & 0.2 mm, bigger width ( w ) = 0.24, 0.36 & 0.48 mm, smaller width ( b ) = 0.12, 0.18 & 0.24 mm, length ( l ) = 1, 2 & 3 mm, and number of wings ( n ) = 5, 8 & 11 with varying Reynolds number ( R e ) in the range of 142 to 945. Thus, a total of tweleve different combination of microchannel are formed by varying the geometric parameters of the butterfly-wing to carry out the parametric study. The simulation results reveal that the presence of the butterfly-wing vortex generator enhances the convective heat transfer rate (10-26)% with an increase in pressure drop (3-14)%, and reduces the total entropy-generation (3-16)% when compared to a plain microchannel. It is also found that with an increase in h, n, and w, the friction factor ( f ) increases (7-13)%, (3-8)% and (1-9)%, respectively,while the average Nusselt number ( Nu avg ) increases (4-11)%, (4-9)%, and (5-12)%, respectively, by increasing Re value from 142 to 945. However, the l has no significant effect on f and Nu avg . A decreasing trend of Nu avg is seen for increasing b, whereas f does not vary significantly with b . The total entropy generation ( S G ) decreasing with the increase in h , n , and w and remain invariant for b and l . For the studied geometric parameters and Re values, the maximum increase in performance of 23% and a maximum reduction in total entropy-generation of 16% are obtained for the microchannel with butterfly-wing of w = 0.48 mm, b = 0.24 mm, l = 3 mm, h = 0.1 mm, n = 5 at Re = 945.

Numerical study of nanofluid flow and heat transfer through a non-uniformly heated converging duct

Fundamental understanding on the enhancement of heat transfer rate and decreasing the maximum operating temperature is crucial for proper design of thermal systems. The present study discusses the influence of non-uniform heating on the forced convective flow of nanofluid through converging miniduct. Numerical simulations are performed using the Euler-Lagrangian two-phase flow model by finite volume method to find the effects of Reynolds number (Re), nanofluid volume fraction (φ), and amplitude (A) of sinusoidal heat flux on the heat transfer. The effect of various parameters on the magnitude of crest and trough of local Nusselt numbers is found to be a crucial factor in determining the total heat transfer. The results indicate a considerable increase in average Nusselt number (Nuav) with φ and Re. At Re = 100 the increments in Nuav are 3.4%, 6.7%, and 13.4% when φ is increased from 0 to 1, 3, and 5%, respectively, while it increases by 107%, 114%, and 116% for amplitudes of 0, 0.75, and 1, respectively, when Re is increased from 100 to 800. Increasing A reduces the heat transfer rate. The highest performance factor is found to be 0.945 at Re = 600, φ = 5% and A = 0.

Investigation of the optimum design of magnetic field arrangement to enhance heat transfer performance of Fe3O4-water magnetic nanofluid

In this study, numerical simulations were conducted to explore the best possible magnetic field arrangement that can maximize the heat exchange performance of Fe3O4-water magnetic nanofluid. Orientation of magnets poles, number of magnets, and the distribution of magnetic field intensity over the flow path are studied to obtain the optimum design which is then tested at various values of magnetic nanoparticles volume fraction, magnetic flux density, and Reynolds number. Results indicated that the optimum design is achieved by placing magnets with N–N orientation and adjusting the magnetic flux density to increase by a rate of 100% between each two successive magnets along the path of the flow. Results also revealed that the average Nusselt number and pressure drop increase when the magnetic flux density is increased. Furthermore, it was found that the effect of increasing magnetic nanoparticles volume fraction on the heat transfer performance is higher at low Reynolds number. An increase of the average Nusselt number in the range of 16.44%–24.46% compared to the design without magnetic field was achieved when using the optimum design with an average magnetic flux density of 1000 Gauss, and magnetic nanoparticles volume fraction of 4%.

Combined convection heat transfer in a lid driven cavity filled with nanofluids

AbstractA simulation study is performed of laminar steady combined convection heat transfer in a lid‐driven cavity containing various types of nanofluid (CuO–water nanofluid and Al2O3–water nanofluid) at various boundary conditions. The influence of two different types of temperature distributions applied to the cavity's bottom wall is investigated. There are two types of temperature distributions: constant temperature (Th) and a sinusoidal temperature distribution applied to the bottom wall, which has a higher temperature than the top moving wall (Tc). In both circumstances, the sidewalls are kept adiabatic. The finite element method is utilized for the current issue. The influence of the Richardson number, which ranges from 0.01 to 10, and the volume fraction of nanoparticles, which ranges from 0 to 0.1, on the heat transfer rate has been explored. The influence of the sinusoidal temperature distribution's amplitude and phase angle is also examined. The isotherm and streamline patterns within the cavity are diverse with distinct nanoparticle volume fractions, and the Richardson numbers are presented and analyzed. The numerical findings showed that lowering the Richardson number raises the average Nusselt number. Also, the existence of nanoparticles in pure water increases heat transmission. Additionally, raising the sinusoidal temperature's amplitude increases the average Nusselt number. The results show that the increase of average Nusselt number at (φ = 0, Gr = 104, Pr = 1, Ɣ = 3π/2) for amplitude 0.25, 0.5, 0.75, and 1 is 0.53, 0.9, 1.3, and 1.87, respectively.

Direct numerical simulation of film boiling on a horizontal periodic surface in three dimensions using front tracking

This study investigates film boiling on a horizontal periodic surface in three dimensions through direct numerical simulations. To solve the momentum and energy equations in both phases, a finite difference/front tracking method is used that accounts for inertia, viscosity, and interface deformation. The mathematical formulation and numerical method are presented. One of the challenging aspects of the front tracking method is breakup and coalescence of bubbles. Previous works continued the simulations up to the breakup and release of the bubble. We use an innovative topology changing algorithm to overcome this challenge. So, simulations are carried out over sufficiently long times to capture several bubble release cycles and to evaluate the quasi steady-state Nusselt number Nu¯. Effect of the Grashof and Jacob numbers on the interface dynamics, heat transfer, and fluid flow is studied. By increasing the Grashof number, buoyancy suppresses the viscous effect, so the average size of departing bubbles decreases, and the average Nusselt number increases. Wall superheat has direct influence on the Jacob number. At relatively low superheats, the bubbles are released periodically from the vapor film, but as the wall superheat increases, permanent vapor jets are formed and become thicker. However, the bubble size and the average Nusselt number decrease. The effect of unit cell size is investigated. It is observed that Nu¯ does not change much with unit cell size. To examine the effect of initial perturbation, single mode and multimode cases were simulated. The initial perturbation has no significant effect on the Nu¯. The density ratio was studied, and it is observed that the stationary steady state condition is reached at a shorter time.

Magneto-turbulent natural convection and entropy generation analyses in liquid sodium-filled cavity partially heated and cooled from sidewalls with circular blocks

Liquid sodium is a promising candidate working fluid in the new solar system and high-density heat sources in industrial applications. In this study free convective flow, heat transfer, and entropy generation of liquid sodium in a hot square enclosure with 16 and 64 cylindrical solid blocks are studied. The cavity is partially heated and cooled from sidewalls with three different locations of heater and cooler named CONF1–3. The effects of the magnetic field in the form of Hartmann number (Ha = 0 and 100), and flow condition in the form of the Rayleigh number (Ra = 106, and 107) are investigated. For tuning the CFD code primitive parameter, the dimensionless forms of the governing equations are used. The ANSYS Fluent equations solver conjugated with a nondimesionlization scheme are used in the turbulent region due to the behavior of liquid metal. The grid verification and validation tests are carried out to ensure the accuracy of the data. Two correlations for average Nusselt number and entropy generation are proposed to simplify calculations. The results discovered that the average Nusselt number and entropy generation increase with increasing the Rayleigh number for each value of the Hartmann number.

Numerical study of convective heat transfer and of turbulent forced of differents Nanofluids in channel

In this study, the flow field and heat transfer of differents nanofluids (AL2O3, CuO, SiO2, ZnO), turbulent forced convection in a channel. The surface of the channel is hot Th= 310 K. Simulations are carried out for constant water Prandtl number of 6.99, Reynolds numbers from 20,000, 30,000, 40,000, 50,000 to 60,000, nanoparticles volume fractions of 0, 0.01, 0.02, 0.03, 0.04 and nanoparticles diameter of 30 nm. The finite volume method and SIMPLE algorithm and k-e are utilized to solve the governing equations numerically. The numerical results showed that with enhancing Reynolds numbers and volume fractions, average Nusselt number increases.

Aerodynamic port-aligned fins to enhance thermal-hydraulic performance of jet impingement arrays

Jet impingement arrays with interspersed fluid extraction ports can suffer degraded heat transfer near outlets due to flow separation. This study explores the potential to integrate aerodynamic port-aligned fins on the impingement surface to maintain wall-jet attachment and increase heat transfer area. Such fins may also enhance local transport under inlet nozzles. Laminar-flow conjugate heat transfer simulations are performed for a range of Reynolds numbers and geometries to characterize this concept for slot jet impingement arrays. The simulation methodology is validated with conventional slot jet data from the literature and demonstrated to achieve mesh convergence. Overall flow characteristics are evaluated for a representative geometry, and results show a significant increase in relative average Nusselt number (Nu∗‾)and a reduction in peak temperature of the cooled surface. Conjugate heat transfer effects are evaluated, and are found to be significant for lower conductivity fin materials. Parametric studies are performed to generate performance maps for relative average Nusselt number and pressure drop as functions of Reynolds number, fin height, base width, and tip radius. Pareto curves are generated for the geometries that optimally trade heat transfer enhancement and pressure drop penalty to guide design. Teardrop shaped fins are found to be optimal for low Re, whereas continuously narrowing fins are preferable for higher Re. This jet impingement enhancement is shown to deliver up to 25% enhancement in Nu∗‾ at baseline pressure drop.

Mixed Convection Heat Transfer and Entropy Generation in a Water-filled Square Cavity Partially Heated from Below: The Effects of Richardson and Prandtl Numbers

In the present study, fluid flow, heat transfer, and entropy generation for mixed convection inside a water-filled square cavity were investigated numerically. The sidewalls of the cavity, which move upwards, are kept at low-temperature Tc while only a part in the center of the bottom wall is kept at high-temperature Th and the remaining parts are kept adiabatic. The governing equations, in stream function–vorticity form, are discretized and solved using the finite difference method. Particular attention was paid to the influence of the Prandtl numbers of 5.534, 3.045 and 2, corresponding respectively to the water temperatures of 303.15 K, 333.15 K and 363.15 K. The numerical results are presented in the form of streamlines, isotherms, and entropy generation contours for different values of the Richardson numbers at an arbitrary Reynolds number Re=102. Besides this, the evolution of the average Nusselt number and the average entropy generation is also reported. The obtained results show interesting behaviors of the flow and thermal fields, which mainly involve stable symmetric and non-symmetric steady-state solutions, as well as unsteady regimes, depending on specific values of the Richardson and Prandtl numbers. It is additionally observed that the average Nusselt number increases and the average entropy generation decreases when both the Richardson and Prandtl numbers increase.