Constant Heat Flux Conditions Research Articles

Flow and heat transfer characteristics in the entry and stabilized flow regions of a circular channel rotating about a parallel axis

Abstract Cooling of heavy-duty electrical machines such as generators and motors is crucial for smooth operations without thermal runaway. A commonly employed technique for cooling of rotors in these machines is to place channels at different radial locations for the continuous passage of coolant. These channels are therefore rotating about a parallel axis, and the rotation-induced forces alter the flow and thermal behaviour of the coolant compared to stationary channels. The present study reports a detailed numerical investigation on a long circular channel rotating about a parallel axis. The objective is to analyze the flow, heat transfer, and rotation-induced forces (Coriolis and centrifugal forces) in the entry region as well as in the region where flow is stable (the term ‘stable’ is used rather than ‘developed’ due to the presence of secondary flows in this region). The rotating channel was subjected to constant wall heat flux and constant wall temperature conditions at different Rotation numbers of 0, 0.15, 0.4, and 0.6. The Coriolis force is strong enough in the entry region to influence the flow. In the “stable flow” region, the centrifugal force becomes more dominant and forms counter-rotating secondary vortex pair, which causes circumferential variation in the Nusselt number. The flow and heat transfer characteristics for constant wall heat flux and wall temperature boundaries are the same for conditions with similar values of rotational Grashof number. A correlation is presented for the circumferential variation of the Nusselt number in the stable flow region.

Dynamic thermal performance of cryogenic liquid hydrogen heating from gas-liquid stratification to supercritical under a constant heat flux condition: A two-step simulation

The dynamic thermal performance was significant for safety storage of cryogenic liquid hydrogen in tank. In this work, a numerical simulation was presented to investigate the thermal performance of cryogenic liquid hydrogen in a C-type tank heating from gas-liquid stratification to supercritical state. A two-step simulation using separate model was applied. The results show that a leading rise of absolute pressure was observed due to the uneven temperature distribution in the gas-liquid stratification state. Accordingly, the rise of heat flux will enhance the non-uniformity of temperature distribution and reduce the safety storage time. Meanwhile, the effects of heat flux and thermodynamic state on the safety storage time were discussed. Further, the effects of identification of critical state boundary on the accuracy of the two-step simulation were analyzed. It was found that the boundary condition when local supercritical state occurs was better than other two conditions in this work.

Studies on the melting dynamics of PCM in a semicircular cavity with straight and wavy heating surfaces

Several kinds of curved confinements for phase changing material storages are found application in natural systems, latent heat storages, metal furnaces, and thermal control devices. Semi-circular enclosures have an inherent advantage of decreasing unmelt volume on top with an increase in melt height when heated from bottom. Hence the melt dynamics differs from conventional rectangular enclosures of similar orientation and realizes faster thermal response during the entire regimes of melting. Experimental and numerical studies on Rayleigh Benard convection in a semi-circular enclosure having straight, corrugated, and wavy bottom surface with constant heat flux conditions are presented. Melt front evolution, thermal convection, and unsteady surface heat transfer characteristics of a phase changing material contained in a semicircular confinement are presented in this study. Enthalpy-porosity method based finite volume solver is used to simulate the unsteady thermal convection of PCM in semi-circular enclosure. Experimental thermal response at various locations inside the confinement and shadowgraph images are used to verify the numerical results quantitatively and qualitatively. Present results and correlations (103 < Ra < 109) are useful in design, analysis, and thermal characterization of PCM enclosures of minimum volume and better thermal response finding application in electronic cooling devices and latent energy storages.

Investigation of forced convection of a novel hybrid nanofluid containing NEPCM in a square microchannel: Application of single-phase and Eulerian-Eulerian two-phase models

In the present study, laminar forced convection flow and heat transfer of novel hybrid nanofluid of Al 2 O 3 -n-octadecane/water through a horizontal microchannel under a constant wall heat flux condition are investigated. N-octadecane is regarded as a nano-encapsulated phase change material (NEPCM). Simulations are performed utilizing single-phase and Eulerian-Eulerian two-phase models. Governing equations are discretized by finite volume method and then solved using SIMPLE algorithm. Effects of nanoparticles volume fraction ( φ ), Reynolds number ( Re ), and melting range ( T mr ) on thermal and hydrodynamic parameters of hybrid nanofluid are evaluated. It is shown that predictions by Eulerian-Eulerian approach are more accurate than those by single-phase approach when compared to available experimental data. Addition of Al 2 O 3 and n-octadecane nanoparticles to water-based fluid leads to a reduction in fluid and wall temperatures, which is intensified at higher φ and Re . Also, these nanoparticles do not have a significant effect on hydrodynamic development of flow, while they delay its thermal development. NEPCM with a higher T mr only slightly improves thermal performance of hybrid nanofluid, which is more noticeable in single-phase procedure. Total efficiency of hybrid nanofluid ( η hnf ) is amplified by raising φ for both approaches. This augmentation is more evident in Eulerian-Eulerian model due to better thermal and hydrodynamic performances. Maximum increases in η hnf concerning single-phase and Eulerian-Eulerian models are 27% and 60%, respectively, occurring at φ Al 2 O 3 = 1 % and φ n ‐ octadecane = 10 % . Therefore, this type of hybrid nanofluids, because of its enhanced thermo-physical properties, can be considered as a suitable candidate for thermal energy storage, heat transfer, and renewable energy applications.

ENHANCING COOLING PERFORMANCE OF A HEAT EXCHANGER DRIVEN BY WATER/ALUMINA-SILICA HYBRID NANOFLUID: EXPERIMENTAL RESULTS

The application of nanofluids in heat exchangers has been established to be beneficial in augmenting heat transfer performance. This study presents an experimental investigation of the performance of a heat exchanger using a water/Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;-SiO&lt;sub&gt;2&lt;/sub&gt; nanofluid under constant heat flux condition. The nanofluid, consisting of well-stabilized nanoparticles, was applied at concentrations ranging from 0.01 to 0.025 vol.&amp;#37;. By systematically varying the Reynold's number from 6,000 to 24,000, the effects of the Reynold's number and concentration on the average Nusselt numbers and friction factor were analyzed. The results indicate that the addition of nanoparticles significantly enhances both the average Nusselt number and friction factor. At a Reynolds number of 24,000, the hybrid nanofluid with a concentration of 0.025 vol.&amp;#37; exhibited a maximum increase of 13.57&amp;#37; in the average Nusselt number and a 10.08&amp;#37; increase in the friction factor compared to using water alone. Sensitivity analysis revealed that concentration had a more pronounced impact on the average Nusselt number and friction factor than Reynold&amp;apos;s number. Various figures of merits determined the thermal performance of the heated tube. The study proposes new correlations with high accuracies (R&lt;sup&gt;2&lt;/sup&gt; &amp;#62; 99&amp;#37;) to predict these parameters. Based on the findings, the use of hybrid nanofluid is recommended for enhancing heat transfer applications. However, it is important to consider the potential increase in pumping power requirements associated with nanoparticles.

Thermodynamic optimization in laminar and fully developed flow in double pipe heat exchanger with arrow-shaped extended surfaces: A novel design

An innovative design of extended fins in the form of arrow fins is optimized for high performance heat transfer in a double pipe heat exchanger (DPHX). The arrow fins are designed within the trapezoidal fin to save material, weight, cost and making energy-efficient DPH. The arrow fins are investigated for the first time in DPHX. The FEM approach is used for computational simulation of the present work. A thermal boundary condition of constant heat flux is imposed on the arrow fins and inner pipe assembly. The results are computed in terms of fRe, Nusselt number and j-factor. The results dictate that the geometrical configurations of arrow DPHX for a significant rise in the values of the Nusselt number are: 80 % height of arrow fins is recommended when the number of arrow fins varies from 6 to 24, 20 % height for 30 arrow fins in the case of smaller values of radii ratio (Rˆ). For larger values of Rˆ, 20 % height of arrow fins may be selected for M=6&30, while for arrow fins varying from 12 to 24,H*=0.8 is recommended. On comparison of the thermal performance of the arrow-finned DPHX with the trapezoidal-finned DPHX, the maximum rise of the Nusselt number and j-factor are 113.2 % and 124.2 %, respectively. The proposed design of arrow-finned DPHX has advantages over the design of trapezoidal finned DPHX due to the significant decrease both in manufacturing cost and weight, increased thermal performance, and saving energy.

Transpiration cooling of a porous Nb-based alloy in high heat flux conditions

High heat flux environments, such as those encountered in atmospheric re-entry and nuclear fusion, impose severe thermal gradients and high local temperatures on structural components. Scalable heat transfer methods need to be integrated with structural designs to manage these extreme heat loads. Transpiration cooling is a potential approach for managing localized heating and maintaining structural durability in these environments. Capillary-driven transpiration cooling shows potential to adapt to dynamic heat flux conditions, but has not yet been investigated under high heat flux conditions. In this investigation, a porous structure was tested with active transpiration cooling under multiple heat flux conditions. Additive manufacturing was employed to produce a specimen with a tailored porous geometry using a refractory niobium-based alloy (C103). Water was selected as the coolant due to the high magnitude of energy absorbed during vaporization. To generate high heat flux environments for testing, an experimental apparatus that employs a high powered laser and corresponding characterization equipment has been designed. Coolant flow through the structure was driven by capillary forces, which enabled rapid adaptation to changes in heat flux from 132–330 W/cm2. Stable coolant flow rates and temperatures were observed under a range of constant high heat flux conditions. The C103 porous sample maintained average surface temperatures below 170 °C while subject to heat fluxes up to 330 W/cm2, indicating the transpiration cooling of the printed structure provided effective heat dissipation in these conditions.

Numerical simulation and experimental investigation of bubble behaviour during pool boiling in the coiled wire

Under the computational fluid dynamics (CFD) framework, an interface tracking method has been used to perform several multiple simulations of coiled wire boiling in a pool. This study includes simulations of the boiling regime, including the Critical Heat Flux (CHF), ranging from nucleate boiling to film boiling. The purpose of this research was to investigate using coiled wire to increase the rate of heat transfer under constant heat flux conditions. The range of the applied heat flux is 130–1075 kW/m2. This research delves into the formation of bubble shapes, bubble diameter, and bubble departure frequency. The vapour bubble grows in size as the heat flux increases; with a heat flux of q'' = 600 kW/m2, it reaches its maximum measured diameter of about 9 mm. Additionally, the heat transfer coefficients and wall temperature distribution were determined using the simulation findings. The heat flux was gradually increased in the critical heat flux investigation until burnout of the coiled wire was observed and a bubble layer formed. This led to the conclusion that q'' = 1075 kW/m2 represents the CHF for this particular geometry. It was observed that the CHF conditions occur in the coil portion, which emphasises the importance of considering the critical heat flux more carefully while designing this geometry.

Heat transfer enhancement in finned annulus of elliptic-circular heat exchanger

In this numerical study, a trapezoidal finned elliptic-circular heat exchanger is investigated for thermal performance based on the various geometrical parameters. The inner core of this exchanger is circular and augmented with trapezoidal fins longitudinally, whereas the outer core is elliptic. For the first time, the trapezoidal fins are used in this specific duct configuration. The configuration of the proposed heat exchanger depends on the number of fins, fin height and ratio of the radius of the inner circle to the semi-minor axis of the ellipse The material of the inner circular core and trapezoidal fins is assumed to have infinite thermal conductivity. The constant heat flux condition is imposed on the inner pipe and trapezoidal fins, whereas the adiabatic condition is considered for the outer elliptical core of the heat exchanger. The simulation is performed using the finite volume method based on the software ANSYS Fluent. The friction factor (fRe) and Nusselt number (Nu) have been computed and plotted for various fin configurations. The results suggest that the performance of the heat exchanger can be effectively influenced by the number of fins, fin height and radius of the inner circular pipe. For practical interest, a larger number of trapezoidal fins with a higher height and are recommended.

Evaluating the heat transfer and pressure drop in the transitional flow regime for a horizontal circular tube fitted with wavy-tape inserts

Much research is available to support the thermo-hydraulic characteristics of heat exchanger tubes in laminar and turbulent flow regimes. However, very little work is available to support the thermohydraulic characteristics of heat exchangers in transition flow regimes, especially in turbulators. Therefore, this research experimentally evaluated the heat transfer and pressure drop characteristics of a circular tube fitted with wavy-tape inserts in the transition flow regime. Experiments were conducted in a circular tube having an internal diameter of 20 mm and a length of 2000 mm and the Reynolds number varied from 533 to 7002. The Nusselt number and friction factor for a smooth tube are validated by comparison with published research works in the laminar and turbulent flow regimes. A total of nine wavy tape inserts with different wave and width ratios were investigated. To determine the variation of Nusselt number and friction factor, three constant heat fluxes (q˙= 1, 2, and 3 kW/m2) were applied to the test section. The laminar, transition, and turbulent regimes were marked and identified by using the linear best-fit line method for all the cases considered during the investigation. The results obtained from the study showed a shift in the boundaries of laminar, transition, and turbulent flow regimes. For smooth tube with 1 kW/m2 heat flux, the transition starts and ends at Reynolds number 2202 and 3 804, respectively. It was also revealed that the onset of transition occurred further earlier when tapes were used. The boundaries of transition also shifted with a change in the constant heat flux condition. For wavy tape having w = 0.75, d = 0.8, the transition begins at Reynolds number 2 193, 2 021, 2029 and ends at 4 016, 3 997, 3989 for heat flux 1, 2 and 3 kW/m2, respectively. The transition began earlier for lower values of heat flux, while for higher values, the transition limit was delayed compared with that of lower heat flux. The boundary of transition also shifted with wave ratio and width ratio. An increase in wave and width ratios altogether delayed the start and end of the transition. Correlations were also developed to predict the Nusselt number and friction factor in laminar and turbulent flow regime.

Effectiveness of a tubular heat exchanger and a novel perforated rectangular flow-deflector type baffle plate with opposing orientation

Purpose The purpose of this experimental research was to examine a novel axial heat exchanger featuring swirling air movement over heated tubes. This apparatus is designed with perforated circular baffle plates complemented by rectangular air deflectors operating at different inclination angles. The tubes were arranged in a consistent layout parallel to the longitudinal airflow. The deflector’s heightened air-side turbulence initiates the frenzied motion, escalating the surface heat transfer rate. Design/methodology/approach The tubes maintained a constant heat flux condition over the surface. In each baffle plate, eight deflectors with identical inclination angles were devised in a reverse position, forming a rotation of air inside a circular duct that held tubes (carrying hot water) which elevated air-side turbulence, thereby enhancing the rate of heat transference on the surface. The baffle plates were equally situated from each other at changing pitch ratios. The Reynolds quantity was preserved in the scope of 16,000–30,000. The performance of the heat exchanger considering pitch ratios and inclination angles was examined. Findings The research indicates that when examined under similar conditions, an exchanger with a deflector baffle plate shows a strong dependence on the pitch ratio and inclination angle with a mean rise of 0.19 times in thermal enhancement factor at an inclination angle of 30° and a pitch ratio of 1.2 contrasted with an exchanger with segmental baffle plates. Originality/value The result shows the dependence of pitch ratio, Reynolds number and inclination on the heat transfer and friction factor rate.

Thermo-Hydraulic Performance of Spring Tape Inserts in a Circular Channel in Transitional Flow Regime

In this work, forced convection experiments were carried out to investigate the variation of heat transfer and pressure drop inside a uniformly heated circular duct fitted with full-length spring tape inserts of varying spring ratios in a transition flow regime. Air was used as the working fluid medium, and experiments were conducted for three constant heat fluxes of 2, 3, and 4 kW-m−2 with Reynolds numbers varied from 502 to 10936 to cover all three flow regimes. For a plain channel heated with 2 kW/m2 of heat flux, the transition begins at a Reynolds number of 2897 and terminates at a Reynolds number of 3783 which brings the transition Reynolds number width of 886. For the same heat flux, a channel with spring tape having a spring ratio of 3, the transition begins at Reynolds number 661 and ends at 1734 while for the case of spring ratio 5, the transition begins at 1305 and ends at 2226. For constant heat flux conditions, a decrease in the spring ratio results in the early onset of transition and which in turn increased the transition length. Predictive Nusselt number and friction factor correlations for different flow regimes have also been presented.

Analysis on enhanced turbulent heat transfer and flow characteristic in a twisted and dimpled oval tube

This work reveals the heat transfer and flow characteristic in a twisted and oval tube under turbulent flow and constant heat flux conditions. Numerical analyses were carried out on several twisted and oval tube configurations. In order to clearly reveal the effect of dimples in the swirl flow, the twisted oval tubes with and without dimples are considered. In order to enhance the convective heat transfer, the dimples were placed in the narrowing region of the twisted tube where the heat transfer was inefficient. The results indicate that the dimples on the twisted tube significantly increase the heat transfer, although they cause to slightly increase pressure drop penalty. While the decrease in the pitch length induced to enhance the heat transfer, it significantly and negatively affected the hydraulic performance of the tube. Furthermore, while the dimples on the twisted oval tube induce the average Nusselt number to increase by 14.8%, they cause to the friction factor increase by 18.0%. The best configuration that is the case of dimpled twisted oval tube having pitch length of 200 mm at Reynolds number of 10,000, yields thermo-hydraulic performance criteria of 1.428.

Entropy Generation-Based Analysis of Laminar Magneto-Convection in Different Cross-Section Channel Filled with Ferrofluid and Subjected to Partial and Full Magnetic Fields

Heat transfer and entropy generation of laminar flow of a ferrofluid in different cross-section channel subjected to partial and full magnetic field are investigated in this study. A constant heat flux condition was applied on the external surface. The conservation equations (mass, momentum, and energy) are solved numerically via the finite volume method with a second-order precision. The effects of fully or partially applying a magnetic field with different directions and intensities on thermodynamic features, heat transfer, and entropy generation have been investigated. Analyses were carried out in four different cross-section channels, namely triangular, rectangular, circular, and elliptical. Results indicate that the circular cross-section channel provides higher heat transfer rates and lower entropy generation than non-circular cross-section channels.

Performance Analysis of Variable Cross-Section TEGs under Constant Heat Flux Conditions

In this paper, five shapes of thermoelectric generator (TEG) models (cylindrical, barrel shaped, hourglass shaped, cup shaped, and inverse cup shaped) are built under the boundary conditions of heat flux at the hot end and convection at the cold end of the TEGs. Based on the numerical simulation results, the configuration of the variable cross-section can effectively boost the performance of TEGs. Remarkably, the hourglass-shaped TEG generated the maximum output power and efficiency, which were 69.62% and 70.96% higher than that of the conventional cylindrical TEG, respectively. The results indicate that the hourglass shape is beneficial to enlarge the temperature difference between the two ends of the TEG, which results in performance improvement. In addition, the effects of heat flux and convection on the performance of TEGs are explored and discussed. After choosing the appropriate boundary conditions, the relationships between the maximum output power and efficiency and the shape factor of the hourglass-shaped TEG are obtained according to the fitting results. Finally, some conclusions are drawn to provide guidance for TEG applications.

Heat Transfer Enhancement in Laminar Pipe Flow Using Al2O3–Water Nanofluid and Twisted Tape Inserts

Abstract In this study, an attempt has been made to carry out a numerical investigation using water-based Al2O3 nanofluid, flowing through a circular tube under constant inlet temperature and constant heat flux conditions in the laminar flow regime. The water-based Al2O3 nanofluid is used in a circular plain tube first, and then, this process is repeated for the same tube fitted with twisted tape inserts of twist ratio 1.85 at Reynolds numbers ranging from 680 to 2030. For the numerical analysis, ANSYS FLUENT is used to solve three-dimensional conservation equations of mass, momentum, and energy. The simulated results indicate that when twisted tape is used, heat transfer rates increase significantly with the use of nanofluid. In the case of nanofluid with the plain tube, only 10–24% enhancement in heat transfer rate is noted. On the other hand, almost 27–45% increase in heat transfer is observed compared to that with only water when twisted tape is inserted into it. Also, the friction factor increases as the nanoparticle volume fraction increases. However, the effect on the heat transfer rate is more significant than that on the friction factor. The best thermohydraulic performance factor achieved is 2.1 using nanofluids with a 5% volume fraction of the nanoparticles at a high Reynolds number when twisted tape is also inserted.

Artificial intelligence approach for energy and entropy analyses of NiFe2O4/H2O nanofluid flow in a tube with vortex generator

The base purpose of the study is to examine the influence of vortex generator geometry and nanofluid on thermo-hydraulic and irreversibility behavior by using a numerical and predictable approach under a laminar flow regime. The selection of an original magnetic nanofluid, the handling of forced convection in a tube including a vortex generator with the artificial neural network approach, and the 2nd law analysis of thermodynamics reflect the novelty of the study. In this context, it was explored numerically for heat transfer and flow profiles of NiFe2O4/H2O flowing with 1% volume fraction in a tube with different vortex generator geometries. This study has been carried out with the solutions under constant heat flux conditions of 2000 W/m2 along the tube. The analyzes have been applied in the range of 500≤Re≤2000. The Laminar model and single-phase approach in all analyses have been taken into account. Heat convection coefficient, pressure drop, and entropy generation were analyzed for the smooth tube and tube with wave ratio (WR=h/w) of 2, 3, and 4. Levenberg-Marquardt as train algorithm and Learngdm and Tansig as transfer function was used as the MLP network model in the present study. As a result, The highest heat transfer ratio, pressure drop, frictional entropy, and total entropy values are obtained for the tube with a wave ratio of 2. The highest deviation rates between the predicted and numerical results for WT1 and WT2 cases (the supreme among all cases) have been seen as 4.67% and 1.73% for the heat convection coefficient and pressure drop values, respectively.

Melting process of RT-25 as a phase change material by placing innovative rectangular and parallelogram fins: Effect of shape and angle of fins

This numerical research used innovative fins that mix parallelogram and rectangular fins to look at the melting of the phase change material (PCM). This paper analyzed, in 2D and using a numerical solution, the melting behavior of several fin models with various angles under constant flux circumstances in a rectangular cavity. The left wall of the storage was subjected to a heat flux of 2500 W/m2. The major objective of the current research was to introduce fins with novel models, which are a mix of rectangular and parallelogram fins, in order to further enhance the melting performance of PCM. For this purpose, the effect of different fin models (with different angles:15°, 30°, 45°, 60°, 75°, and 90°) in the condition of constant heat flux in a rectangular cavity was studied. The results show that among various geometries studied by fin, proposed geometry of model E was selected among the models. Changing the fin model reduces the melting time, which led to a higher energy charging rate. Moreover, by examining different melting angles, the maximum and minimum melting times occurred at 0° and 60°, respectively. The heat flux had an inverse relationship with the melting time; the higher the heat flux, the shorter the melting time. E model with an angle of 60° had the best performance. Because it had reached complete melting in the shortest time, in this model, after 52.25 min, the PCM completely melts. The stored energy for PCM at 60° was less than other angles, and equal to 236.04 MJ. The average power for angles from 15° to 90° was almost equal, and at angle 0°, it was less than other angles.

Arbitrary temperature gradient in thermal-postbuckling behavior of polymer nanocomposites reinforced by boron nitride nanotubes

Polymer nanocomposites reinforced by boron nitride nanotubes (BNNTs) have great potential for use in a wide variety of thermal environments. A closed-form solution for nonlinear bending and thermal-postbuckling behavior of BNNT-reinforced nanocomposite beams under arbitrary temperature gradient in the thickness and length directions is presented for the first time. The uniform and functionally graded (FG) distributions of BNNTs through the thickness of macro-or micro-sized beams are considered. For constant temperature or constant heat flux conditions at two ends of the beam, thermal analysis is carried out to obtain temperature field ΔTx,z using the two-dimensional heat conduction equation and the assumption of arbitrary variation in the z direction. The governing equations of modified couple stress Timoshenko beam theory with von Kármán geometric nonlinearity are derived for BNNT-RC beams subjected to thermomechanical loads. Applying change of variable technique, the governing equations are exactly solved to develop closed-form expression for nonlinear transverse deflection. Finally, parametric study is performed to investigate the effects of length scale parameter, aspect ratio (L/h), distribution of BNNTs, and temperature gradient on the nonlinear bending and postbuckling equilibrium paths. It is shown that the thermal-buckling behavior of clamped and cantilever beams is completely different. Under thermomechanical loading, an initial snap-through buckling behavior is observed in the cantilever beam, while there exist both stable and unstable configurations in the static equilibrium path of clamped beam. Moreover, it is found that the assumption of parabolic variation of temperature through thickness is not compatible with real situations, since the temperature field is obtained as harmonic functions with very short wavelengths in the length direction.

Multiparameter optimization of the thermoelectric module under the constant heat flux condition

Thermoelectric (TE) technology enables direct heat-to-electricity conversion and offers an alternative way to carbon neutralization. Conventional TE device design is usually conducted under the constant temperature difference (CTD) condition. However, the constant heat flux (CHF) condition dominates in realistic applications. Here, using finite element simulation, we investigate the relationship between the geometric parameter and the TE performance under the CHF condition. Our results reveal that the thermal properties are the governing factors under the CHF condition. The simulations suggest that both the maximum output power and conversion efficiency increase with the height, decrease with the fill factor, and share a parabolic tendency as the cross-sectional area ratio changes. Instead of using the module parameters optimized under the CTD condition, the TE performance can be enhanced by 43% after geometric optimization under the CHF condition, suggesting that the optimization under the CHF condition is of significance for realistic applications.