Experimental investigation on the heat transfer of an impinging inverse diffusion flame

This paper presents the results of an experimental study on the heat transfer characteristics of an inverse diffusion flame (IDF) impinging vertically upwards on a horizontal copper plate. The IDF burner used in the experiment has a central air jet surrounded circumferentially by 12 outer fuel jets. The heat flux at the stagnation point and the radial distribution of heat flux were measured with a heat flux sensor. The effects of Reynolds number, overall equivalence ratio, and nozzle-to-plate distance on the heat flux were investigated. The area-averaged heat flux and the heat transfer efficiency were calculated from the radial heat flux within a radial distance of 50 mm from the stagnation point of the flame, for air jet Reynolds number (Re_air) of 2000, 2500 and 3000, for overall equivalence ratios (Φ) of 0.8–1.8, at normalized nozzle-to-plate distances (H/d_IDF) between 4 and 10. Similar experiments were carried out on a circular premixed impinging flame for comparison.It was found that, for the impinging IDF, for Φ of 1.2 or higher, the area-averaged heat flux increased as the Re_air or Φ was increased while the heat transfer efficiency decreased when these two parameters increased. Thus for the IDF, the maximum heat transfer efficiency occurred at Re_air = 2000 and Φ = 1.2. At lower Φ, the heat transfer efficiency could increase when Φ was decreased. For the range of H/d_IDF investigated, there was certain variation in the heat transfer efficiency with H/d_IDF. The heat transfer efficiency of the premixed flame has a peak value at Φ = 1.0 at H/d_P = 2 and decreases at higher Φ and higher H/d_P. The IDF could have comparable or even higher heat transfer efficiency than a premixed flame.     

The effect of confinement on the flow and turbulent heat transfer in a mist impinging jet

Numerical study of the effect of confinement on a flow structure and heat transfer in an impinging mist jets with low mass fraction of droplets (M_L1 ? 1%) were presented. The turbulent mist jet is issued from a pipe and strikes into the center of the flat heated plate. Mathematical model is based on the steady-state RANS equations for the two-phase flow in Euler/Euler approach. Predictions were performed for the distances between the nozzle and the target plate x/(2R) = 0.5–10 and the initial droplets size (d₁ = 5–100 μm) at the varied Reynolds number based on the nozzle diameter, Re = (1.3–8) × 10⁴. Addition of droplets causes significant increase of heat transfer intensity in the vicinity of the jet stagnation point compared with the one-phase air impinging jet. The presence of the confinement upper surface decreases the wall friction and heat transfer rate, but the change of friction and heat transfer coefficients in the stagnation point is insignificant. The effect of confinement on the heat transfer is observed only in very small nozzle-to-plate distances (H/(2R) < 0.5) both in single-phase and mist impinging jets.     

Heat transfer characteristics of an array of impinging pre-mixed slot flame jets

An experimental study was carried out to investigate the shape and the heat transfer characteristics of an array of three laminar pre-mixed butane/air slot flame jets impinging upwards normally on a horizontal water-cooled flat plate. The effects of jet-to-jet spacing and nozzle-to-plate distance were examined at the Reynolds number (Re) of 1000 and the equivalence ratio (?) of unity. Comparisons of the heat transfer characteristics between single and multiple slot flame jets, as well as multiple slot and round jets, were made. The between-jet interference decreased with increasing jet-to-jet spacing (s/d_e) and nozzle-to-plate distance (H/d_e). Strong interference was obtained at s/d_e = 1 and H/d_e = 2, at which the central jet was suppressed while the side jets were deflected towards their free sides. In addition, there was no minimum heat flux found in the inter-jet interacting zone, instead, a peak heat flux was obtained. Thermal performance was reduced when H/d_e became smaller than the length of the conical luminous reaction zone of the flame. A maximum average heat flux occurred at the moderate jet-to-jet spacing of s/d_e = 2.5 at Re = 1000, ? = 1 and H/d_e = 2. The resultant heat flux distribution of the central jet of a multiple slot jets system was higher than that of a single slot jet when the jet-to-jet spacing was small, but this advantage in thermal performance diminished when the jet-to-jet spacing was increased. Besides, the area-averaged heat flux of the multiple slot flame jets was higher than that of the multiple round flame jets arranged at the same geometric configuration.     

Effects of plate temperature on heat transfer and emissions of impinging flames

Experiments were conducted to investigate the heat transfer and CO/NO_X emissions of a premixed LPG/air circular flame jet impinging upwards normally to a flat rectangular plate. Temperatures of the impingement plate were controlled by cooling water at 38 °C, 58 °C and 78 °C which was circulating at its back in order to create different plate temperatures. Under each plate temperature, the effects of Reynolds number (Re), equivalence ratio (Ф) and nozzle-to-plate distance (H) on the heat transfer and CO/NO_X emissions were examined. The Re was selected to be 500, 1000 and 1500 to ensure laminar flame jets. The values of Ф were chosen to cover fuel-lean, stoichiometric and fuel-rich conditions. The H varied from 3d to 7d with an interval of 1d.The flame-side temperature of the impingement plate is enhanced when the cooling water temperature increases, but the temperature difference across the impingement plate is reduced. Heat transfer from the flame to the plate is suppressed at higher cooling water temperature. The heat transfer rate is the highest when the cooling water temperature is at 38 °C and the lowest heat flux is obtained at 78 °C. At the highest cooling water temperature of 78 °C, the CO emission is reduced whereas the NO_X emission is enhanced. However, this trend is reversed at the lowest cooling water temperature of 38 °C.     

Velocity field and turbulence effects on heat transfer characteristics from surfaces with V-shaped ribs

The flow field of smooth surfaces and surfaces with V-shaped ribs (V-SR) was studied experimentally with a Laser-Doppler Anemometry (LDA) system. In addition, heat transfer characteristics were experimentally investigated. Heat transfer results from these surfaces under impingement of a circular jet array (5 × 3) using an infrared thermal imaging technique are presented.The velocity profiles were measured at Reynolds number of 10,000 and at H/d equal to 3 and 12. For each H/d position, profiles were collected from x/d = 0 to 6 axial locations. The heat transfer data were obtained at Reynolds numbers equal to 2000, 6000, and 10,000. Along the target plate, different boundary layer profiles were obtained for smooth and V-SR plates at H/d = 3 and 12. Positions of maximum radial and axial velocities and turbulence intensities have been determined for smooth and V-SR plates. For low jet-to-plate spacings, the production of turbulence kinetic energy is higher for the V-SR surfaces as compared to smooth surfaces. For H/d = 3, the radial velocities are higher for the V-SR surfaces as compared to smooth surfaces but for H/d = 12, the radial velocities are not nearly changed all x/d locations. The heat transfer results have also been compared with those of a smooth surface under the same flow conditions to determine the enhancement in the heat transfer coefficient from x/d = 0 to 3 locations. In these locations, the Nusselt numbers are higher for the V-SR surfaces as compared to smooth surfaces. The locations of the peaks and the minima are influenced by cross flow velocities which in turn depend on jet-to-plate spacing and V-SR arrangements. For all results, the Nusselt numbers at the stagnation points decrease with increase in H/d.     

Heat transfer of impinging jet-array over convex-dimpled surface

A detailed heat transfer measurement over a convex-dimpled surface of impinging jet-array with three eccentricities (E/H) between jet-centre and dimple-centre is performed. These surface dimples considerably modify heat transfers from smooth-walled scenarios due to different impinging topologies for jet array with modified inter-jet reactions. Heat transfer variations caused by adjusting jet Reynolds number (Re) and separation distance (S/D_j) over the ranges of 5000 ⩽ Re ⩽ 15,000 and 0.5 ⩽ S/D_j ⩽ 11 with three eccentricities of E/H = 0, 1/4 and 1/2 are examined. A selection of experimental data illustrates the isolated and interactive influences of Re, S/D_j and E/H on local and spatially averaged heat transfers. In conformity with the experimentally revealed heat transfer physics, a regression-type analysis is performed to generate a set of heat transfer correlations, which permit the evaluations of spatially averaged Nusselt numbers over central jet region of dimpled impinging surface.     

Effect of jet direction on heat/mass transfer of rotating impingement jet

The objective of this study is to investigate the heat/mass transfer characteristics on various impinging jets under rotating condition. Two cooling schemes related to impingement jet are considered; array impingement jet cooling and impingement/effusion cooling. The test duct rotates at Ro = 0.075 with two different jet orientations and the jet Reynolds number is fixed at 5000. Two H/d configurations of 2.0 and 6.0 are conducted. The detailed heat/mass transfer coefficients on the target plate are measured by a naphthalene sublimation technique. The rotation changes the local heat/mass transfer characteristics due to the jet deflection and spreading phenomenon. For H/d = 6.0, the jet is strongly deflected at the leading orientation, resulting in the significant decrease in heat/mass transfer. At the axial orientation, the momentum of jet core decreases slightly due to jet spreading into the radial direction and consequently, the value of stagnation peak is a little lower than that of the stationary case. However, reduction of heat/mass transfer due to rotation disappears at a low H/d of 2.0. In the averaged Sh, the leading orientation with H/d = 6.0 shows 35% lower value than that of the stationary case whereas the other rotating cases lead to a similar value of the stationary case.     

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel

Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ? w_in ? 0.16 m/s) using a flow rate control valve so that Reynolds number was always about Re = 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10⁷ < Ra¹ < 8 × 10⁸ and Richardson number 0.4 < Ri < 5. Dimensionless fin spacing was varied from S/H = 0.04 to S/H = 0.018 and fin height was varied from H_f/H = 0.25 to H_f/H = 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is S = 8–9 mm and optimum fin spacing depends on the value of Ra¹.     

Influences of nozzle-plate spacing on boiling heat transfer of confined planar dielectric liquid impinging jet

We have investigated the single-phase and boiling heat transfer of dielectric liquid under the Reynolds numbers (2000, 3000 and 5000) and under nozzle-plate spacing (H/W; 0.5, 1.0 and 4.0) in a submerged impinging jet system. The boiling incipience increases in proportion to the Reynolds number and in inverse proportion to the nozzle-to-surface spacing. The critical heat flux at H/W = 1.0 is lower than those of outer spacings, such as H/W = 0.5 and 4.0, due to the characteristics of the jet impingement heat transfer distribution. We suggest a correlation equation of nozzle-plate spacing (H/W) having the lowest CHF for various jet velocities.     

Influence of CuO/water nanofluid concentration and swirling flow on jet impingement cooling

CuO/water nanofluids were applied in swirling impinging jets for heat transfer enhancement. Swirling flow was induced by twisted tape inserts with twist ratios (y/w) of 1.43, 2.86 and 4.28. Impinging jets were injected at three different ratios of jet-to-plate spacing to nozzle diameter (H/d) of 2, 3 and 4. Nanofluids with CuO concentrations of 2.0%, 3.0% and 4.0% by volume were comparatively tested with water (a base fluid) for Reynolds numbers ranging from 1600 to 9400. Experimental results reveal that the nanofluids with concentrations of 2.0 and 3.0% by volume yield higher Nusselt numbers than the base fluid while the one with concentration of 4.0% shows opposite result. At the ratio of jet-to-plate spacing/nozzle diameter (H/d) of 2, Nusselt number slightly increases with decreasing twist ratio (y/w). However, at the ratios of jet-to-plate spacing/nozzle diameter (H/d) of 3 and 4, Nusselt number increases with increasing twist ratio. Over the studied range, the optimum condition is found at H/d = 2, y/w = 1.43, and nanofluid concentration of 2.0% by volume.     

Effects of jet plate size and plate spacing on the stagnation Nusselt number for a confined circular air jet impinging on a flat surface

This work deals with the effects of jet plate size and plate spacing (jet height) on the heat transfer characteristics for a confined circular air jet vertically impinging on a flat plate. The jet after impingement was restricted to flow in two opposite directions. A constant surface heat flux of 1000 W/m² was arranged. Totally 88 experiments were performed. Jet orifices individually with diameter of 1.5, 3, 6 and 9 mm were adopted. Jet Reynolds number (Re) was in the range 10,000–30,000 and plate spacing-to-jet diameter ratio (H/d) was in the range 1–6. Eleven jet plate width-to-jet diameter ratios (W/d = 4.17–41.7) and seven jet plate length-to-jet diameter ratios (L/d = 5.5–166.7) were individually considered. The measured data were correlated into a simple equation. It was found that the stagnation Nusselt number is proportional to the 0.638 power of the Re and inversely proportional to the 0.3 power of the H/d. The stagnation Nusselt number was also found to be a function of exp[−0.044(W/d) − 0.011(L/d)]. Through comparisons among the present obtained data and documented results, it may infer that, for a jet impingement, the impingement-plate heating condition and flow arrangement of the jet after impingement are two important factors affecting the dependence of the stagnation Nusselt number on H/d.     

Nozzle effect on heat transfer and CO emission of impinging premixed flames

Experiments were carried out to investigate the heat transfer and CO emission characteristics of a premixed LPG/air circular flame jet impinging upwards normal to a flat plate. The effects of nozzle diameter and nozzle arrangement on the heat transfer and CO emission under different fuel/air mixture flow rates (Q_mix), equivalence ratios (Ф) and normalized nozzle-to-plate distances (H/d) were examined. For the effect of nozzle diameter, burners of nozzle diameters of d = 7.9, 9 and 10 mm were used, and for the effect of nozzle arrangement, a twin-nozzle burner and a triple-nozzle burner, each with a cross-sectional area equal to that of the 9 mm diameter burner, were investigated under different normalized jet-to-jet spacing, S/d, of 3, 5 and 7. The heat transfer rate and CO emission index (EICO) are enhanced significantly with the decrease in the nozzle diameter for the single-nozzle flames. For the twin- and triple-nozzle flames, when the other operational conditions including Q_mix, Ф and H/d are invariant, the moderate S/d of 5 gives the highest heat transfer rate, whereas the EICO increases with increasing S/d. Comparison of the flames from all the burners shows that the highest heat transfer rate and EICO are obtained on the single-nozzle burner with the smallest nozzle diameter while the lowest heat transfer rate and EICO are obtained on the triple-nozzle burner with the smallest S/d.     

Confined,milliscale unsteady laminar impinging slot jets and surface Nusselt numbers

Different modes of unsteadiness which develop within confined, laminar impinging slot jets of millimeter-scale are considered, including experimental measurements and numerical predictions of different flow characteristics, including spatially-resolved distributions of local Nusselt numbers measured on a constant heat flux surface. The effects of Reynolds number, and nozzle-to-plate distance on the local Nusselt number are investigated for a slot nozzle width B of 1.0 mm, Reynolds numbers Re from 120 to 200, nozzle-to-plate distances H/B from 0.75 to 12.5, and a nozzle aspect ratio y/B of 50. Observed are several different types of unsteady slot jet behavior, including: (i) a flow fluctuations/flapping motion mode of unsteadiness which is present for B = 1.0 mm, 4.75 ? H/B ? 5.5, and 120 ? Re ? 140, (ii) an intermittent flapping motion of the jet column which is present for B = 1.0 mm, 9 ? H/B ? 11.25, and 120 ? Re ? 200, and (iii) a continuous sinusoidal oscillation state, which is observed to be present for Re = 160 and H/B = 10. The flow fluctuations/flapping motion mode of unsteadiness, and the intermittent flapping motion of the jet column are both associated with local maxima in local, stagnation point Nusselt number distributions. The variations of these stagnation point Nusselt numbers associated with these two modes of unsteadiness are characterized by correlations which provide the dependence upon Reynolds number and normalized nozzle-to-plate distance ratio, H/B. Also described is the lateral variation of local Nusselt numbers for five nozzle-to-plate distances H/B of 2, 6, 8, 10, and 12, and Reynolds numbers from 120 to 200.     

Experimental and kinetic modeling study of methyl butanoate and methyl butanoate/methanol flames at different equivalence ratios and C/O ratios

Premixed laminar methyl butanoate/oxygen/argon and methyl butanoate/methanol/oxygen/argon flames were studied with tunable synchrotron vacuum ultraviolet (VUV) photoionization and molecular-beam sampling mass spectrometry at 30 torr (4.0 kPa). Three flames were investigated in the experiment: MB (methyl butanoate) flame F1.54 (? = 1.54, C/O = 0.479), MB flame F1.67 (? = 1.67, C/O = 0.511) and MB/methanol flame F1.67M (? = 1.67, C/O = 0.479). By measuring the signal intensities at different distances from the burner surface, the mole fraction profiles of intermediates are derived. Experimental results show that the flame front shifts downstream and peak mole fractions of intermediates increase remarkably with the increase of equivalence ratio for pure MB fuel. When methanol is added, the peak mole fractions of most intermediates including those of soot precursors decrease remarkably at the same equivalence ratio, while peaks of soot precursors vary little (only slightly decreasing) at same C/O ratio. It is concluded that the formation of soot precursors is more sensitive to C/O ratio than to equivalence ratio. Besides, more CO₂ is produced near the burner surface in MB flame than that in MB/methanol flame, and this validates an early production of CO₂ in methyl ester oxidation. In addition, a modified MB detailed mechanism is used to model flame structure, and improved agreements between the experimental and predicted results are realized. Based on the simulation results, reaction flux and sensitivity are analyzed for CO₂ and C₃H₃, respectively.     

Experimental and numerical study on the occurrence of off-stagnation peak in heat flux for laminar methane/air flame impinging on a flat surface

A combined experimental and numerical study has been conducted to investigate the occurrence of off-stagnation peak for laminar methane/air flame impinging on a flat surface. Experiments were conducted for three tube burners of internal diameter 8 mm, 9.7 mm and 12 mm. Radial heat flux distributions were compared (experimentally) for different burner diameters under identical operating conditions (with firing rates of 0.25 kW, 0.40 kW and 0.50 kW, ? = 1 and H = 40 mm). An off-stagnation point peak in heat flux was observed for some of the configurations in the present study which is in accordance with the previous findings. This off-stagnation point peak is a function of stand-off distance between the exit plane of the burner and the plate and also the distance between flame-tip and the plate. A satisfactory explanation is presented to explain the existence of this off-stagnation peak with the help of results of numerical simulation carried out with commercial CFD code FLUENT. It is concluded that this off-stagnation peak in heat flux is primarily due to the peak in the axial velocity profile close to the impingement surface.     

Effect of confinement on heat transfer characteristics of a microscale impinging jet

This study experimentally investigates the local heat transfer characteristics of a microscale confined impinging air jet on a heated plate. The experimental parameters included the Reynolds number (Re_D = 1600–5600), the nozzle-to-plate spacing (H/D = 1–10), and the degree of confinement of the nozzle (D_C/D = 3, 6, 9, 12, 24, 48). The degree of confinement of the nozzle is a novel parameter. A reduction in the heat transfer rate was found for nozzles whose D_C/D values were 6, 9, 12, 24, and 48 as a result of the confinement effect at small nozzle-to-plate spacings. The confinement effect disappeared beyond H/D values of 2, 3, 4, 8, and 17 for D_C/D values of 6, 9, 12, 24, and 48, respectively. Flow characteristics were investigated by measuring pressure distributions along the wall. Subatmospheric pressure, which is evidence of the confinement effect, was observed for the confined nozzles. Correlations of the stagnation and average Nusselt numbers are proposed on the basis of the experimental results. Finally, a contour map that depicts the ratio of the Nusselt numbers of the unconfined and confined jets is presented. The contour map confirms that the confined jets have a smaller Nusselt number than the unconfined jets whenever the degree of confinement of the nozzle is large and the nozzle-to-plate spacing is small.     

Conjugated heat transfer on leading edge of a wedge-shaped concave wall internally impinged by hot jets from corrugated orifice plate

An experimental and numerical investigation is conducted to study the conjugated heat transfer performance on the leading edge of a wedge-shaped concave wall subjected to external cold flow and internal hot jets impingement. A corrugated impinging plate with an extended front-extended port inside the concave cavity is proposed for the purpose of heat transfer enhancement. The effects of corrugation length-to-diameter ratio (H_j/d) ranging from 5 to 11 and width-to-diameter ratio (W_j/d) ranging from 2.5 to 6 on the conjugated heat transfer performance are examined under some representative jet Reynolds numbers (Re_j) in the range of 7900–31,700. The results show that the corrugated impinging plate has a significant impact on improving the conjugated heat transfer performance in the vicinity of concave wall leading edge. The presence of corrugation plays two roles by reducing the jet impinging distance on one hand and aggravating the jet confinement on the other hand. Therefore, it produces more complicated jet impinging flow and convective heat transfer behaviors than the baseline case without corrugation. According to the tested results, the specified area-averaged heating effectiveness is increased approximately 6.3%–18.8% under Re_j = 7900 and 2.5%–9.4% Under Re_j = 31,700 respectively by increasing the corrugation length when W_j/d is fixed as 2.5. The specified area-averaged heating effectiveness is increased approximately 16.1%–22.1% under Re_j = 7900 and 7.7%–12.7% under Re_j = 31,700 respectively by increasing the corrugation width when H_j/d is fixed as 9. In general, the corrugation with larger length and width seems to perform the better heating effectiveness over the entire concave surface. The enhancement of heating effectiveness related to the baseline case behaves more significantly under a smaller jet Reynolds number.     

A general correlation for the stagnation point Nusselt number of an axisymmetric impinging synthetic jet

Whereas the heat transfer mechanisms in steady impinging jets are well understood, the available knowledge of heat transfer to impinging synthetic jets remains inconsistent. This paper provides an objective comparison of the stagnation point heat transfer performance of axisymmetric impinging synthetic jets versus established steady jet correlations. Furthermore, a general correlation for the stagnation point Nusselt number is proposed including the effect of all appropriate scaling parameters: Reynolds number (500 ? Re ? 1500), jet-to-surface spacing (2 ? H/D ? 16) and stroke length (2 ? L₀/D ? 40). Based on the ratio of stroke length to jet-to-surface spacing L₀/H, four heat transfer regimes are identified.     

Heat transfer correlations of perpendicularly impinging jets on a hemispherical-dimpled surface

Heat transfer results of an inline array of round jets impinging on a staggered array of hemispherical dimples are reported with the consideration of various parametric effects such as Reynolds number (Re_Dj), jet-to-plate spacing (H/D_j), dimple depth (d/D_d) and ratio of jet diameter to dimple projected diameter (D_j/D_d) for both impinging on dimples and impinging on flat portions. The results were normalized against those from a flat plate. The heat transfer was measured by using transient wideband liquid crystal method. Our previous work (Kanokjaruvijit and Martinez-Botas (2005) [1]) on the effect of crossflow scheme suggested that jet impingement coupled with channel-like flow formed by the crossflow helped enhance heat transfer on a dimpled surface; hence three sidewalls were installed to constrain the spent air to leave in one direction. Throughout the study, the pitch of the nozzle holes was kept constant at 4 jet diameters. The Reynolds number (Re_Dj) ranging from 5000 to 11,500, jet-to-plate spacing (H/D_j) varying from 1 to 12 jet diameters, dimple depths (d/D_d) of 0.15, 0.25 and 0.29, and dimple curvature (D_j/D_d) of 0.25, 0.50 and 1.15 were examined. The shallow dimples (d/D_d = 0.15) improved heat transfer significantly by 70% at H/D_j = 2 compared to that of the flat surface, while this value was 30% for the deep ones (d/D_d = 0.25). The improvement also occurred to the moderate and high D_j/D_d. Thereafter, the heat transfer results were correlated in dimensionless form by using logarithmic multiple regression. The correlations were reported with necessary statistics.     

Numerical thermal analysis and optimization of a water jet impingement cooling with VOF two-phase approach

The fluid flow and heat transfer characteristics of a free-surface liquid jet impingement cooling have been investigated numerically. The slot jet with water impinging normally on a flat plate is employed. To describe the turbulent structure, the turbulent governing equations are solved by a control-volume-based finite-difference method with a power-law scheme and the well-known turbulence model, which are associated with wall function. Numerical computations have been conducted with variations of jet exit Reynolds number (11,000 ≤ Re_d ≤ 17,000), dimensionless jet-to-surface distance (3 ≤ H/d₀ ≤ 12), dimensionless jet width (1 ≤ B/d₀ ≤ 2), and the heat flux (140 kW/m² ≤ q″ ≤ 280 kW/m²). The theoretical model developed is validated by comparing the numerical predictions with available experimental data in the literature. Under the studied ranges, the variations of local Nusselt numbers by hydraulic diameter Nu_d of the dimensionless jet-to-surface distance 3 ≤ H/d₀ ≤ 12 along the flat plate decrease monotonically from its maximum value at the stagnation point. In addition, the shape of the inlet area and jet-to-surface distance are optimized by using the response surface methodology (RSM) and the genetic algorithm (GA) method after solutions are carefully validated with available experimental results in the literature. Based on the optimal results, the optimum condition is in H/d₀ = 7.86 and B/d₀ = 2 for this physical model.