Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate

Transcription

1 European Journal of Scientific Research ISSN X Vol.83 No.1 (212), pp.6-75 EuroJournals Publishing, Inc Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate Mohamed A. Teamah Mechanical Engineering Department, Faculty of Engineering Alexandria University, Egypt, Currently, Visiting Professor Faculty of Engineering and Technology, Arab Academy for Science and Technology Maritime Transport, Alexandria, Egypt M. Khalil Ibrahim Mechanical Engineering Department, Faculty of Engineering Alexandria University, Egypt Mohamed M. Khairat Dawood Faculty of Engineering, Suez Canal University, Ismailia, Egypt El-Sayed Abdel Aleem Arab Academy for Science and Technology and Maritime Transport Alexandria, Egypt Abstract The inclination circular liquid jet impingement on a horizontal target smooth plate has been investigated experimentally. The hydrodynamic flow structure of unique nocircular profile due to oblique jet is studied in the present work. The nozzle inclination angle is varied from [3 o to 9 o from horizontal], while the water flow rate is varied from 2 to 5lpm at constant nozzle-to-target separation distance of 3 mm. The nozzle used during the experiments is of circular shape of 5.5 mm diameter. A circular hydraulic jump symmetrical profile was observed due to normal impinging of free water surface jet, but the radial spreading flow structure due to oblique circular jet was different and the hydrodynamic profile of the jump location having elliptical shape structure. The effect of jet inclination angle and the water flow rate on the dimensionless film thickness and the dimensionless hydraulic jump profile in azimuthal direction. The experimental investigation shows that the thin layer film thickness spreading in radial direction decreases gradually until it reaches its minimum value then increases gradually up to location of hydraulic jump. The results show that for oblique jet impingement the thin layer film thickness is non uniform distribution in azimuthal direction. The experimental results indicate that jet inclination angle has significant effect on dimensionless film thickness and flow structure. The thin liquid film area bounded by the jump increases as the jet inclination angle (with the horizontal) increases, being maximum when the jet impinges normal to the horizontal plate. The area bounded being maximum as jet impinging

2 Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate 61 normally on horizontal plate. The striking difference between the non-circular and circular hydraulic jumps is also considered. Keyword: Inclined jet, hydraulic jump, film thickness, free surface jet 1. Introduction An attractive means of obtaining large heat transfer coefficient at a surface can be achieved by using impinging jets on the surface. The rate of heat transfer from the jet is affected by factors such as, the spacing between the nozzle exit and the target, the jet exit velocity and profile, the nozzle shape, fluid turbulence and the inclination of the nozzle. Jet impingement on a hot surface is widely used in various industrial applications because of the high heat transfer rate. In metal and plastic manufacturing industries, this cooling technique is applied to control the temperature histories during processing. The application of liquid jet impingement heat transfer include localized cooling in internal combustion engines, quenching of metal and other materials in manufacturing process and thermal control of high performance computer components. The circular hydraulic jump can be formed as a consequence of normal impingement of a circular liquid jet on a smooth horizontal surface photo (1-a). The flow spreads radially along the surface forming a thin film. At some radial distance from the impingement point, the film thickness abruptly increases charactering the hydraulic jump. These kinds of hydraulic jumps involve a strongly distorted free surface, a boundary layer region and a subsequent separation of a flow. In many industrial applications, the impinging jet is obliquely inclined with the target plate giving a plethora of interesting fluid flow patterns photo (1-b). Therefore, a number of experimental studies have been performed to predict the heat transfer rate between a free impinging jet and a hot surface [1, 2]. Convective heat transfer between a circular free impinging jet and a solid surface whose temperature is below the boiling one of the liquid has been also studied theoretically by several researchers [3]. Chaudhury [4] studied theoretically the problem of heat transfer to a laminar jet impinging on an isothermal surface. His solution is based on the velocity distribution in the liquid film obtained by Watson [5]. Liu and Lienhard [6] proposed the formula capable of predicting the local Nusselt number in the case where the variation of the surface heat flux was specified.the equation agrees well with the experimental data. Also, theoretical predictions of local Nusselt number have been presented by Wang et al. [7-9]. Flow and heat transfer under freesurface flow conditions have been studied numerically by some researchers. Rahman et al. [1, 11] studied the flow of a thin liquid film on the surface. Rahman and Fraghri [12, 13] analyzed the flow and heat transfer in the thin liquid film over a rotating disk. Finally, Fraghri et al. [14] studied experimentally and numerically the conjugate heat transfer between a hot surface and a liquid film formed by a controlled impinging jet. Fujimoto et al. [15] studied numerically the convective heat transfer between a circular free surface impinging jet and a solid surface. The thin liquid film formed on the surface has been assumed to be in non-turbulent free surface flow. The effects of surface tension, viscosity, gravity and heat transfer between the film flow and the solid surface have been taken into account.

3 Mohamed A. Teamah, M. Khalil Ibrahim 62 Mohamed M. Khairat Dawood and El-Sayed Abdel Aleem Photo 1: a hydrodynamic flow structure due to vertical and obliquely inclined jet impinging on flat horizontal plate. (a) Vertical jet impingement (b) Obliquely inclined jet impingement Tong [16] studied numerically the hydrodynamics and heat transfer mechanism of the impingement process of an oblique free liquid jet. Local Nusselt number distributions at the substrate have also been calculated. Uniform and parabolic jets have been considered. Both the maximum Nusselt number location and the maximum pressure location have been found to shift upstream from the geometrical impingement point of the jet, with the extent of the displacements increasing as the inclination increases. Choo and Sung [17] investigated experimentally heat transfer and fluid flow characteristics of two-phase impinging jets were under a fixed pumping power condition. The effects of dimensionless pumping power (P Pump = ) and the volumetric fraction (β =. 1.) on the Nusselt number were considered. Air and water were used as the test fluids. The results showed that the Nusselt number increased with volumetric fraction, attained a maximum value at around.2.3 of the volumetric fraction, and then decreased. Teamah and Farahat [18,19] studied the heat transfer and flow due to the impingement of free surface vertical jet on the horizontal heated surface numerically and experimentally for single jet and experimentally only for multi jets. There study shows the effect of interaction between the jets on heat transfer at jet water flow rates of [1, 2, 4, 5, 6 and 8 LPM]. For multi jets their study showed that the interaction between the jets tend to reduce both segment and average segment Nusselt number but the overall average Nusselt number for multi jets for any arrangement is higher than single jet. M. Khairat [2] studies experimentally the heat transfer between a horizontal heated plate and circular liquid jet impinging vertically downward on the plate. He found that the heat transfer in the shooting area is higher than for the streaming zone since in this area the liquid velocity is higher and the liquid film thickness is lower than for streaming zone. There experiments were carried on single jet and two equal flow rate jets and unequal. The study included the effect of distance between jet nozzle and horizontal plate, the effect of liquid flow rate on heat transfer characteristics. They measure the liquid film thickness distribution for each separation distance and difference Reynolds number. They observed that the average Nusselt number is independent on the separation distance between the nozzle and plate. The study showed that the local and average Nusselt number increase as the jet to jet spacing increased with the maximum increase dimensionless jet to spacing of X/d j =9.9 since the liquid thermal film thickness decreases as the jet spacing increase, and found that by increasing the Reynolds number for one jet the interaction zone shifted toward the weaker Reynolds number jet Kate et al. [21, 22] subsequently advanced the above considerations towards elucidating the interactions of hydraulic jumps formed by two normal impinging circular liquid jets and hydraulic jumps with corners due to obliquely inclined circular liquid jets. Kate et al. [23] investigated

4 Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate 63 experimentally the hydrodynamic structure due to oblique impingement of a circular liquid jet on horizontal target. Hydraulic jumps of two broad categories have been observed. At higher angles of jet inclination, they found that jumps are bounded by a smooth curve, and at lower angles of inclination, a typical jump profiles with corners have been observed. Also they investigate the effect of jet inclination angles on jump profile, and jump area. They measure the stagnation pressure and film thickness for different inclination angles and different flow rate volume. In many industrial applications, the impinging jet is obliquely inclined with the target plate, giving a plethora of interesting fluid flow patterns, most of which might appear to be somewhat intuitive, but are by no means obvious. Oblique impinging jets, as compared to normal impinging jets, have received relatively less attention in fluid mechanics literature. The schematic of a circular liquid jet impinging obliquely on a flat horizontal surface, illustrating the associated flow phenomenon, is depicted in Fig. 2. Following the studies of Beltos [24], Rubel [25,26], Sparrow and Lovell [27] and Tong [28], it can be inferred that the radial spreading flow is, in general, three-dimensional in nature. Cavadas et al. [29] investigated experimentally and numerically the flow field created by a laminar Newtonian liquid jet emanating from a fully-developed rectangular duct and impinging on a flat plate inside a cell confined by inclined plane walls. The experiments, carried out at Reynolds numbers of 136 and 275, measured a separation flow region adjacent to the inclined walls for Re>28 and for Re = 275 there is a helical motion inside this separation region. The length of this recirculation zone decreased for decreasing Reynolds number. Bula et al. [3] analyzed a free jet of high Prandtl number fluid impinging perpendicularly on a solid substrate of finite thickness containing small discrete heat sources on the opposite surface. Both solid and fluid regions have been modeled and solved as a conjugate problem. Equations for the conservation of mass, momentum, and energy were solved taking into account the transport processes at the solid liquid and liquid gas interfaces. The shape and location of the free surface (liquid gas interface) was determined iteratively as a part of the solution process by satisfying the kinematic condition as well as the balance of normal and shear forces at this interface. Vipat et al.[31] characterized experimentally the flow and temperature fields caused by a twodimensional heating air jet obliquely impinging on a flat plate. Whilst the jet flow is discharged at Re Dh = based on the hydraulic diameter of the orifice, D h, and the jet exit-to-plate spacing (separation distance) is fixed at 8D h, the impingement angle (inclination) is systematically decreased from 9 (normal impinging) to 3 (oblique impinging). A separate experiment is carried out for a two-dimensional cooling jet obliquely impinging on a heated plate (constant heat flux). The results demonstrate that the response of local surface temperature to plate inclination behaves in a completely different manner. For impinging jet cooling, the inclination (from normal impinging position) reduces the local effective temperature values at corresponding points about actual stagnation point, inclusive of it. From the previous review it is denoted that the recent researches in free liquid inclined jet is very limited and so, our concern in this study is to analyze the hydrodynamic analysis to add a view for the problem for different parameters affect this phenomena 2. Experimental Apparatus and Measuring Technique A special test rig was designed and constructed for the present work. Photo.1 represents the layout of the experimental test rig The Flow Loop of Jet Water A schematic diagram of the experimental facility is shown in figure (1). A main water storage tank have capacity of 2 m 3 used to store the fresh water received from the main water source. A centrifugal pump (2 hp) is used to feed the header tank with fresh water, the header tank is a cylindrical steel tank have a capacity of 2litres used to create a constant head of 1m above jet level to maintain a consent

5 Mohamed A. Teamah, M. Khalil Ibrahim 64 Mohamed M. Khairat Dawood and El-Sayed Abdel Aleem head of water above the jet during all experimental test procedure the water flows from the header tank through PVC tube under gravity to jet which fixed on a special designed flexible mechanism to facilitate the direction of jet to any required angle faced the target plate according to test requirements. The jet is fabricated from cupper with 5 mm diameter and 3 mm length, the target horizontal heated plate is manufacture from high quality stainless steel have shape of square box of 96 cm side length and thickness of 6 mm. Figure 1: Experimental apparatus and equipments Photo 2: A schematic representation of the experimental setup 2.2. Nozzle Position System The spray nozzle was mounted to a bracket to provide the rotational movement. A pointer is welded to the jet to indicate the desired angle through a protractor as shown in Photo (2). The adjustment of jet angle can be achieved by turning the jet with the flexible hose to required angle where there is locking nut at the back side of the bracket. Photo (1) shows a translation/rotation of water jet that was used to set the position of the spray nozzle relative to the test surface. The orifice-to-surface distance was

6 Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate 65 adjusted with the aid of a vertical translation stage that was attached to two vertical aluminum rods. The second, horizontal translation stage was made using horizontal screw mounted in a rectangular box. Photo 3: Jet nozzle positioning mechanism 2.3. Film Thickness and Hydraulic Jump Location Measuring Technique The details of water film thickness measuring are showed in Fig.2.and Photo.2. The film thickness of the water flowing over the heated plate is of few millimeters. The micrometer is of.1 mm sensitivity is used for measuring the film thickness. A vernier caliper connected to PVC pipe with two clamps around the PVC pipe. This whole mechanism allow to measure the film thickness at different radius from the jet and different circumference. A special electrical circuit is used. This circuit is manufactured as the free surface of the water is wavy. A D/C power supply exerts 5 volts on 5-kΩ resistance series circuit. An oscilloscope used for showing the position of the stylus with respect to the film thickness. At the beginning of the experiments, the stylus is in the air above the water film. The oscilloscope supposed to read the 5-volt. The micrometer is turned around until the stylus touch the free surface of water. The oscilloscope reading will drop to the reduction of the resistance in the circuit. The micrometer will further turned around and the stylus will go toward the surface of the plate. When the stylus touches the surface, the reading on the oscilloscope is zero. The difference between the two reading of the micrometer indicates the film thickness at the specified location. Figure 2: Details construction for measuring the film thickness

7 Mohamed A. Teamah, M. Khalil Ibrahim 66 Mohamed M. Khairat Dawood and El-Sayed Abdel Aleem Photo 4: A schematic representation of the experimental setup 2.4. Measuring the Area Bounded by Hydraulic Jump The hydraulic jump area through shooting zone was determined depending on the experimental measuring of hydraulic jump radius for each test procedure at different flow rates and jet inclination angles. The film thickness was measured at different radius and at circumference direction. The plate was divided into contour lines in azimuthal plane at increment angle of 1 o. Fig.3 shows a schematic diagram of circular liquid jet impinging obliquily on a flat smooth target plate. The hydraulic jump radius location in (r,θ) directions used as input data for a special software computer program grapher 9 for calculate and plotting the area bounded by the hydraulic jump for both vertical and oblique jet impingement. 3. Comparsion with the Previous Works The location of the hydraulic jump on the wetted surface is an interest physical phenomenon that produced at the end zone of the parallel flow in case of vertical jet ψ=9. In the previous work, Baonga et.al. [32] Showed the influence of the flow rate on the radius of the hydraulic jump. Fig.4. showed the comparison between the present results and with Baonga et.al. [32] For Reynolds number in the range of 7 2. The Reynolds number based on the diameter of the nozzle is calculated as following: Vd Re = j (1) ϑ The comparison show the present work is The Reynolds number is determined using the properties of water at the inlet temperature of the jet at 16 C. The comparison show that the present work is with good agreement with previous work. The experiment results are correlated in an equation for determining the hydraulic jump radius with maximum error of 1% for vertical jet as following: Rhdr Re d = (2) j

8 Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate 67 Figure 3: Elliptical shape profile of hydraulic jump due to obliquely jet impinging on horizontal flat plate Figure 4: Comparison between the present work and previous for dimensionless hydraulic jump radius evolution. 4 3 Baonga et.al.[32] Present work correlation R hyd /d j Re 4. Results and Discussion When a circular liquid jet impinged a flat horizontal target a free distinct regions are identified as shown in fig.5. The first zone is the free jet region where the flow mainly in axial direction is accelerated due to the gravitational force. The second zone is the impingement region (stagnation region) where the interaction between the jet and the target produces a strong deceleration of the flow in the axial direction and accelerated in the radial direction. The thickness of the boundary layer in these regions is very thin and uniform due to radial acceleration of the fluid this results in high heat transfer coefficient. In radial flow region (parallel flow) the radial velocity decreases as it flows outward, these results in a thickening of boundary layer and gradually decreases in heat transfer coefficient along the radial direction. The main objective of the present work is to investigate experimentally the effect of jet inclination angle and fluid flow rate on hydrodynamic flow structure of jet impingement zone since it have a direct effect on mass and heat transfer coefficient.

9 Mohamed A. Teamah, M. Khalil Ibrahim 68 Mohamed M. Khairat Dawood and El-Sayed Abdel Aleem Figure 5: Schematic of flow developing from nozzle to heated disk 1.8 Z/d j.6.4 stagnation region free jet region parallel flow Effect of Jet Flow Rate on Film Thickness and Hydraulic Jump Location Fig.6. represent the dimensionless film thickness at different dimensionless radius due to vertical jet. Vertical impinging jet on flat horizontal target creates a radialy spreading symmetrical liquid film thickness. As increasing the water flow rate, the location which hydraulic jump occur increases. Also, increasing flow rate, the dimensionless water film thickness decreases. Fig.7. represent the effect of increasing the water flow rate at inclined jet angle, ψ=45.the dimensionless water film thickness profile is non-symmetrical as vertical jet. At θ=π, the effect of increasing the water flow rate is more significant on the dimensionless hydraulic jump radius than at θ=.the same observation for vertical jet, as increasing the water flow rate,the dimensionless film thickness decreases.fig.8a.shows the dimensionless hydraulic jump profile for vertical jet at different azimuthal direction. The area bounded by hydraulic jump at the different water flow rates are symmetrical circular shape. As the water flow rate increases, the radius of hydraulic jump increases 23% as the flow rate increases from 2 to 5lpm. Fig.8b. shows the dimensionless hydraulic jump profile for inclination jet angle, ψ=45, at different azimuthal direction. The radial symmetry of the hydraulic jump is lost. The hydraulic jump formed under these conditions assumes an oblate shape. Some of the profiles captured during our laboratory experiments are depicted in Photo. 5. Figure 6: Effect of Flow rate on dimensionless water film thickness distribution at ψ= lpm,θ=π 2lpm,θ= 3lpm,θ=π 3lpm,θ= 4lpm,θ=π 4lpm,θ= 5lpm,θ=π 5lpm,θ= Z/d j

10 Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate 69 Figure 7: Effect of Flow rate on dimensionless water film thickness distribution at ψ=45.8 Z/d j.6.4 2lpm,θ=π 2lpm,θ= 3lpm,θ=π 3lpm,θ= 4lpm,θ=π 4lpm,θ= 5lpm,θ=π 5lpm,θ= Figure 8: Effect of the flow rate on the hydraulic jump profile lpm 3 lpm 4 lpm 5 lpm (a) ψ = lpm 3lpm 4lpm 5lpm (b) ψ =45

11 Mohamed A. Teamah, M. Khalil Ibrahim 7 Mohamed M. Khairat Dawood and El-Sayed Abdel Aleem Photo 5: Profiles of the hydraulic jumps at ψ =45 at different flow rate (a) Q=2lpm (b) Q=3lpm (c) Q=4lpm (d) Q=5lpm 4.2. Effect of Jet Inclination Angle on Hydrodynamic Flow Structure Figures [9, 1] represent the effect of jet inclination angle on dimensionless hydraulic jump profile for oblique jet impingement at different inclination jet angles at two different flow rate. 2 and 5 lpm. The dimensionless film thickness is not symmetrical profile. For the same jet water flow rate, at θ=π direction, the dimensionless film thickness increases as jet inclination angle with horizontal decreases to reach its minimum value at [ψ =9 ].Also, the dimensionless film thickness at θ=π, is higher than the dimensionless film thickness at θ=.as the jet inclination angle decreased (with respect to horizontal), the difference between the dimensionless film thickness in θ=π and θ= increased for the same flow rate. The increase of jet inclination angle also induces a non uniform distribution of the film in the azimuthal direction. Fig.11 represent the effect of jet inclination angle on dimensionless area bounded by hydraulic jump radius profile for oblique jet impingement at different inclination jet angles at two different flow rate. 2 and 5 lpm. For the same flow rate, as the jet inclination angle decreases, the dimensionless hydraulic jump radius increased in θ=π and decreased in the direction of θ=, and the area bounded by hydraulic jump elongates. The area bounded by hydraulic jump changed from circular shape at ψ=9 to non-circular shape. Some of the profiles captured during our laboratory experiments are depicted in Photo. 6, showing the effect of decreasing the jet inclination angle.

12 Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate 71 Figure 9: Effect of Jet Inclination angle on dimensionless water film thickness distribution at Q=2lpm.8.6 ψ=8,θ=π ψ=8,θ= ψ=6,θ=π ψ=6,θ= ψ=4,θ=π ψ=4,θ= Z/d j Figure 1: Effect of Jet Inclination angle on dimensionless water film thickness distribution at Q=5lpm.8.6 ψ=8,θ=π ψ=8,θ= ψ=6,θ=π ψ=6,θ= ψ=4,θ=π ψ=4,θ= Z/d j Figure 11: Effect of the Jet Inclination angle on the hydraulic jump profile at different flow rate ψ=8 ψ=7 ψ=6 ψ=5 ψ=4 ψ= (a) Q=2lpm

13 Mohamed A. Teamah, M. Khalil Ibrahim 72 Mohamed M. Khairat Dawood and El-Sayed Abdel Aleem Figure 11: Effect of the Jet Inclination angle on the hydraulic jump profile at different flow rate - continued ψ=8 ψ=7 ψ=6 ψ=5 ψ=4 ψ= (b) Q=5lpm Photo.6: Profiles of the hydraulic jumps at Q =2 lpm at different Jet Inclination angle (a) ψ=9 (b) ψ=8 (C) ψ=6 (d) ψ=4

14 Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate Comparison Between the Circular and Non-Circular Hydraulic Jump Profile The experimental results for area ratio are correlated as shown in fig.12 at different jet inclination angle and flow rate. It is noted that for both low and high jet water flow rate as jet inclination angle decreased the hydraulic jump profile take unique non- circular shape (elliptical) and for the same jet water flow rate the area bounded by hydraulic jump profile increases as jet inclination (with horizontal) increases and being maximum when [ψ =9 ]. The ratio, A inclined /A normal, is observed to be independent of the volume flow rate of the liquid for a fixed value of ψ. The Area of the jump can be correlated with the jet inclination angle (in degree) as follows: Ainclined 2 = φ φ (3) A normal Figure 12: Change in the thin film area bounded by the jump with the jet inclination angle lpm 3 lpm 4 lpm 5 lpm correlation Ainclined/Anormal Jet inclination angle,ψ 5. Conclusion From the present work results the following conclusions can be summarized: 1. A circular hydraulic jump profile is created due to normal impingement of free water jet on smooth horizontal surface. As the jet inclination angle changes from vertical to any angle the circular profile changed to non circular shape. 2. An elliptical area bounded by hydraulic jump has been observed due to impinging of obliquely liquid jet on horizontal smooth surface. The hydraulic jump location increased as the jet inclination angle decreased in the direction of downstream flow [θ=π] while decreased in the upstream flow [θ=]. 3. The effect of increasing the flow rate at fixed inclination jet angle is significant on the film thickness and the hydraulic jump location. As increasing the flow rate, the film thickness decreases and the location of the hydraulic jump increased at different azimuth direction. Also it was observed that the inclination angle have a direct effect on film thickness and hydraulic jump location. As increasing the jet inclination angle, the film thickness and the hydraulic jump location decreased to reach minimum value as the jet is vertical. 4. The area bounded by hydraulic jump profile have been calculated for both vertical and oblique jet impingement for different jet inclination angle from 3 to 8 for different flow rate. The result shows that for the same test conditions the area being maximum when jet inclination angle is ψ= 9 and decreased as jet inclination angle decreases. The ratio of A inclined / A vertical is depended only on the angle of jet inclination.

15 Mohamed A. Teamah, M. Khalil Ibrahim 74 Mohamed M. Khairat Dawood and El-Sayed Abdel Aleem 5. For inclined jets, considerable variations in the liquid film thickness in azimuthal direction are observed. 6. Nomenclature A : Area, m 2 d j : Nozzle diameter, m Q : water volume flow rate, m 3 /s R : hydraulic jump radius m r : radial coordinate, m Re : Reynolds number based on nozzle diameter : dimensionless radial distance. V : jet velocity, m/s Z : film thickness, m Z/d j : dimensionless water film thickness Greek Letters θ : contour line angle in azimuthal direction degree φ : jet inclination angle, degree : kinematic viscosity m 2 /s Subscripts inclined: inclined jet normal: normal jet Reference [1] Vader DT; Incropera FP; Viskanta R, 1991, '' Local convective heat transfer from a heated surface to an impinging, planar jet of water ''. Int. J Heat and Mass Transfer 34: [2] Hall DE; Incropera FP; Viskanta R, 1996, ''Jet impingement boiling from circular free-surface jets during Quenching Experiments.'' Proc of the ASME Heat Transfer Division HTD 332: [3] Webb BW; Ma CF,1995, ''Single-phase liquid jet impingement heat transfer.'' Advances in Heat Transfer 26: , Hartnett JP et al. (Eds) Academic Press, San Diego [4] Chaudhury ZH, 1964, ''Heat transfer in a radial liquid jet''. J Fluid Mech 2: [5] Watson EJ,1964, '' the radial spread of a liquid jet over a horizontal plane''. J Fluid Mech 2: [6] Liu X; Lienhard JHV; Lombara JS, 1991, Convective heat transfer by impingement of circular liquid jets. Trans ASME J Heat Transfer 113: [7] Wang XS; Dagan Z; Jiji LM,1989, ''Heat transfer between a circular free impinging jet and a solid surface with non uni-form wall temperature or wall heat flux-1. Solution for the stagnation region''. Int. J Heat and Mass Transfer 32-7: [8] Wang XS; Dagan Z; Jiji LM,1989, ''Heat transfer between a circular free impinging jet and solid surface with non uniform wall temperature or wall heat flux-2. Solution for the boundary layer region.'', Int. J Heat and Mass Transfer 32: [9] Wang XS; Dagan Z; Jiji LM, 1989, ''Conjugate heat transfer between a laminar impinging liquid jet and a solid disk''. Int. J Heat and Mass Transfer 32: [1] Rahman MM; Faghri A; Hankey L, 199, ''Computation of the free surface flow a thin liquid film at zero and normal gravity''. Numerical Heat Transfer 17 part A: [11] Rahman MM; Faghri A; Hankey L, 1992, ''Fluid flow and heat transfer in a radially spreading thin liquid film''. Numerical Heat Transfer 21 Part A: 71-9

16 Experimental Investigation for Hydrodynamic Flow Due to Obliquely Free Circular Water Jet Impinging on Horizontal Flat Plate 75 [12] Rahman MM; Faghri A,1992, ''Numerical simulation of fluid fl ow and heat transfer in a thin liquid film over a rotating disk''. Int. J Heat and Mass Transfer 35-6: [13] Rahman MM; Faghri A, 1992, ''Analysis of heating and evaporation from a liquid film adjacent to a horizontal rotating disk''. Int. J Heat and Mass Transfer 35-1: [14] Faghri A; Thomas S; Rahman MM,1993,''Conjugate heat transfer from a heated disk to a thin liquid film formed by a controlled impinging jet''. Trans ASME Heat J Transfer 115: [15] H. Fujimoto, N. Hatta, R. Viskanta, 1999, ''Numerical simulation of convective heat transfer to a radial free surface jet impinging on a hot solid'', Heat and Mass Transfer 35: [16] Albert Y. Tong, 23,''On the impingement heat transfer of an oblique free surface plane jet'', International Journal of Heat and Mass Transfer 46: [17] Kyosung Choo, Sung Jin Kim, 21, '' Heat transfer and fluid flow characteristics of two-phase impinging jets'', International Journal of Heat and Mass Transfer 53: [18] M.A. Teamah and S. Farahat, 23,''Experimental heat transfer from impinging single freesurface liquid jet'' Alexandria engineering Journal, Vol. 42 (5), pp [19] M.A. Teamah and S. Farahat, 26,''Experimental heat transfer due to impinging of water from multi jets on heated surface '' Alexandria engineering Journal Vol. 45(1), pp [2] M. Khairat,27,''Heat transfer due to double free water impingement jets over horizontal heated plate.'' Ph.D. Thesis, Alexandria University. [21] R.P. Kate, P.K. Das, S. Chakraborty, 27, ''An experimental investigation on the interaction of hydraulic jumps formed by two normal impinging circular liquid jets''. J. Fluid Mech. 59: [22] R.P. Kate, P.K. Das, S. Chakraborty, 27,''Hydraulic jumps with corners due to obliquely inclined circular liquid jets''. Phys. Rev. E 75, :1 6. [23] R.P.Kate, P.K. Das, Suman Chakraborty, 28, ''An investigation on non-circular hydraulic jumps formed due to obliquely impinging circular liquid jets'', Experimental Thermal and Fluid Science 32 : [24] S. Beltos, 1975,''Oblique impingement of circular turbulent jets.'' J. Hydraul. Res. 14: [25] A. Rubel, 1981,''Computations of the oblique impingement of round jets upon a plane wall'', AIAA 19 : [26] A. Rubel, 1982, ''Oblique impingement of a round jet on plane surface, AIAA 2: [27] E.M. Sparrow, B.J. Lovell, 198, "Heat transfer characteristics of an obliquely impinging circular jet", Trans. ASME J. Heat Trans. 12 : [28] A.Y. Tong, 23,"On the oblique impingement heat transfer of an oblique free surface plane jet", J. Heat Mass Trans. 46: [29] A.S. Cavadas, F.T. Pinho, J.B.L.M. Campos, 212,"Laminar flow field in a viscous liquid impinging jet confined by inclined plane walls", International Journal of Thermal Sciences xxx :1-16 [3] Antonio J. Bula, Muhammad M. Rahman,, John E. Leland, 2,"Axial steady free surface jet impinging over a flat disk with discrete heat sources", International Journal of Heat and Fluid Flow 21 () [31] O. Vipat, S.S. Feng, T. Kim, A.M. Pradeep, T.J. Lu, 29,"Asymmetric entrainment effect on the local surface temperature of a flat plate heated by an obliquely impinging two-dimensional jet", International Journal of Heat and Mass Transfer 52 : [32] J.B. Baonga, H. Louahlia-Gualous,M. Imbert, 26, "Experimental study of the hydrodynamic and heat transfer of free liquid jet impinging a flat circular heated disk", Applied Thermal Engineering 26 :