@article{zhang_jing_roberts_fang_2015, title={Effects of Ambient Oxygen Concentration on Soot Temperature and Concentration for Biodiesel and Diesel Spray Combustion}, volume={141}, ISSN={["1943-7897"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84929628830&partnerID=MN8TOARS}, DOI={10.1061/(asce)ey.1943-7897.0000214}, abstractNote={AbstractAmbient oxygen concentration, a key variable directly related to exhaust gas recirculation (EGR) levels in diesel engines, plays a significant role in particulate matter (PM) and nitrogen oxides (NOx) emissions. The utilization of biodiesel in diesel engines has been investigated over the last decades for its renewable characteristics and lower emissions compared to diesel. In an earlier work, we demonstrated that the soot temperature and concentration of biodiesel were lower than diesel under regular diesel engine conditions without EGR. Soot concentration was quantified by a parameter called KL factor. As a continuous effort, this paper presents an experimental investigation of the ambient oxygen concentration on soot temperature and KL factor during biodiesel and diesel spray combustion. The experiment was implemented in a constant volume chamber system, where the ambient oxygen concentration varied from 21 to 10% and the ambient temperature was kept to 1,000 K. A high speed two-color pyrometry...}, number={2}, journal={JOURNAL OF ENERGY ENGINEERING}, author={Zhang, Ji and Jing, Wei and Roberts, William L. and Fang, Tiegang}, year={2015}, month={Jun} }
@article{kailasanathan_zhang_fang_roberts_2014, title={EFFECTS OF DILUENTS ON SOOT SURFACE TEMPERATURE AND VOLUME FRACTION IN DILUTED ETHYLENE DIFFUSION FLAMES AT PRESSURE}, volume={186}, ISSN={["1563-521X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84901250746&partnerID=MN8TOARS}, DOI={10.1080/00102202.2013.878710}, abstractNote={Soot surface temperature and volume fraction are measured in ethylene/air coflowing laminar diffusion flames at high pressures, diluted with one of four diluents (argon, helium, nitrogen, and carbon dioxide) using a two-color technique. Both temperature and soot measurements presented are line-of-sight averages. The results aid in understanding the kinetic and thermodynamic behavior of the soot formation and oxidation chemistry with changes in diluents, ultimately leading to possible methods of reducing soot emission from practical combustion hardware. The diluted fuel and coflow exit velocities (top-hat profiles) were matched at all pressures to minimize shear effects. In addition to the velocity-matched flow rates, the mass fluxes were held constant for all pressures. Addition of a diluent has a pronounced effect on both the soot surface temperature and volume fraction, with the helium diluted flame yielding the maximum and carbon dioxide diluted flame yielding minimum soot surface temperature and volum...}, number={6}, journal={COMBUSTION SCIENCE AND TECHNOLOGY}, author={Kailasanathan, Ranjith Kumar Abhinavam and Zhang, Ji and Fang, Tiegang and Roberts, William L.}, year={2014}, pages={815–828} }
@article{zhang_jing_roberts_fang_2014, title={Soot measurements for diesel and biodiesel spray combustion under high temperature highly diluted ambient conditions}, volume={135}, ISSN={["1873-7153"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84904957615&partnerID=MN8TOARS}, DOI={10.1016/j.fuel.2014.06.071}, abstractNote={Abstract This paper presents the soot temperature and KL factor for biodiesel, namely fatty acid methyl ester (FAME) and diesel fuel combustion in a constant volume chamber using a two-color technique. The KL factor is a parameter for soot concentration, where K is an absorption coefficient and proportional to the number density of soot particles, L is the geometric thickness of the flame along the optical detection axis, and KL factor is proportional to soot volume fraction. The main objective is to explore a combustion regime called high-temperature and highly-diluted combustion (HTHDC) and compare it with the conventional and low-temperature combustion (LTC) modes. The three different combustion regimes are implemented under different ambient temperatures (800 K, 1000 K, and 1400 K) and ambient oxygen concentrations (10%, 15%, and 21%). Results are presented in terms of soot temperature and KL factor images, time-resolved pixel-averaged soot temperature, KL factor, and spatially integrated KL factor over the soot area. The time-averaged results for these three regimes are compared for both diesel and biodiesel fuels. Results show complex combined effects of the ambient temperature and oxygen concentration, and that two-color temperature for the HTHDC mode at the 10% oxygen level can actually be lower than the conventional mode. Increasing ambient oxygen and temperature increases soot temperature. Diesel fuel results in higher soot temperature than biodiesel for all three regimes. Results also show that diesel and biodiesel fuels have very different burning and sooting behavior under the three different combustion regimes. For diesel fuel, the HTHDC regime offers better results in terms of lower soot than the conventional and LTC regimes, and the 10% O 2 , 1400 K ambient condition shows the lowest soot concentration while maintaining a moderate two-color temperature. For biodiesel, the 15% O 2 , 800 K ambient condition shows some advantages in terms of reducing soot concentration. Based on these results, the practical implementation of this combustion mode is outlined and a feasible option is proposed.}, journal={FUEL}, author={Zhang, Ji and Jing, Wei and Roberts, William L. and Fang, Tiegang}, year={2014}, month={Nov}, pages={340–351} }
@article{zhang_jing_roberts_fang_2013, title={Effects of ambient oxygen concentration on biodiesel and diesel spray combustion under simulated engine conditions}, volume={57}, ISSN={["1873-6785"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84880702414&partnerID=MN8TOARS}, DOI={10.1016/j.energy.2013.05.063}, abstractNote={This study investigates the effect of ambient oxygen concentration on biodiesel and diesel spray combustion under simulated compression-ignition engine conditions in a constant-volume chamber. The apparent heat release rate (AHRR) is calculated based on the measured pressure. High-speed imaging of OH* chemiluminescence and natural luminosity (NL) is employed to visualize the combustion process. Temporally and spatially resolved NL and OH* contour plots are obtained. The result indicates that AHRR depends monotonically on the ambient oxygen concentration for both fuels. A lower oxygen concentration yields a slower AHRR increase rate, a lower peak AHRR value, but a higher AHRR value during the burn-out stage when compared with higher ambient oxygen concentration conditions. OH* chemiluminescence and NL contours indicate that biodiesel may experience a longer premixed-combustion duration. The 18% ambient O2 condition works better for biodiesel than diesel in reducing soot luminosity. With 12% O2, diesel combustion is significantly degraded. However, both fuels experience low temperature combustion at 10% O2. These results may imply that biodiesel is able to achieve the desired lower soot production under a moderate oxygen level with higher combustion efficiency, while diesel needs to be burned under very low ambient oxygen concentration for low soot production.}, journal={ENERGY}, author={Zhang, Ji and Jing, Wei and Roberts, William L. and Fang, Tiegang}, year={2013}, month={Aug}, pages={722–732} }
@article{zhang_jing_roberts_fang_2013, title={Soot temperature and KL factor for biodiesel and diesel spray combustion in a constant volume combustion chamber}, volume={107}, ISSN={["1872-9118"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84875117595&partnerID=MN8TOARS}, DOI={10.1016/j.apenergy.2013.02.023}, abstractNote={This paper presents measurements of the soot temperature and KL factor for biodiesel and diesel combustion in a constant volume chamber using a two-color technique. This technique uses a high-speed camera coupled with two narrowband filters (550 nm and 650 nm, 10 nm FWHM). After calibration, statistical analysis shows that the uncertainty of the two-color temperature is less than 5%, while it is about 50% for the KL factor. This technique is then applied to the spray combustion of biodiesel and diesel fuels under an ambient oxygen concentration of 21% and ambient temperatures of 800, 1000 and 1200 K. The heat release result shows higher energy utilization efficiency for biodiesel compared to diesel under all conditions; meanwhile, diesel shows a higher pressure increase due to its higher heating value. Biodiesel yields a lower temperature inside the flame area, a longer soot lift-off length, and a smaller soot area compared to diesel. Both the KL factor and the total soot with biodiesel are lower than with diesel throughout the entire combustion process, and this difference becomes larger as the ambient temperature decreases. Biodiesel shows approximately 50–100 K lower temperatures than diesel at the quasi-steady stage for 1000 and 1200 K ambient temperature, while diesel shows a lower temperature than biodiesel at 800 K ambient. This result may raise the question of how important the flame temperature is in explaining the higher NOx emissions often observed during biodiesel combustion. Other factors may also play an important role in controlling NOx emissions. Both biodiesel and diesel temperature measurements show a monotonic dependence on the ambient temperature. However, the ambient temperature appears to have a more significant effect on the soot formation and oxidation in diesel combustion, while biodiesel combustion soot characteristics shows relative insensitivity to the ambient temperature.}, journal={APPLIED ENERGY}, author={Zhang, Ji and Jing, Wei and Roberts, William L. and Fang, Tiegang}, year={2013}, month={Jul}, pages={52–65} }
@article{zhang_jing_fang_2012, title={High speed imaging of OH* chemiluminescence and natural luminosity of low temperature diesel spray combustion}, volume={99}, ISSN={["1873-7153"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84862163802&partnerID=MN8TOARS}, DOI={10.1016/j.fuel.2012.04.031}, abstractNote={This study focused on spray combustion of ultra low sulfur diesel (ULSD) fuel under low oxygen conditions with low temperature combustion (LTC) mode in an optically accessible constant volume combustion chamber. The ambient oxygen concentration was configured as 10% and 15% to achieve low flame temperature. The ambient gas temperature varied from 800 K to 1200 K. High speed imaging of OH* chemiluminescence and natural luminosity (NL) was used to visualize the instantaneous spray combustion process. The heat release rate was analyzed using the transient combustion pressure and the flame structure was studied based on the combustion images. Results show that a higher oxygen concentration case features a shorter ignition delay and higher heat release rate. The LTC mode can be realized by decreasing the oxygen concentration and ambient temperature simultaneously and it features a longer ignition delay, a slower reaction rate, and apparently lower soot radiation heat loss. The visualization results of NL and OH* show that the high temperature reaction occurs mainly in the mid-stream and downstream of the spray combustion, but not in the region very close to the chamber wall. This study validates the LTC process by showing very weak OH* chemiluminescence signal. The results also indicate that in order to realize LTC mode, it is important to control the ambient oxygen and ambient temperature at the same time. By only reducing the ambient oxygen concentration it may not be effective to suppress soot generation.}, journal={FUEL}, author={Zhang, Ji and Jing, Wei and Fang, Tiegang}, year={2012}, month={Sep}, pages={226–234} }
@article{fang_yao_zhang_zhong_tao_2012, title={Momentum and heat transfer of the Falkner-Skan flow with algebraic decay: An analytical solution}, volume={17}, ISSN={["1878-7274"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84855241770&partnerID=MN8TOARS}, DOI={10.1016/j.cnsns.2011.10.021}, abstractNote={In this paper, an analytical solution of the Falkner–Skan equation with mass transfer and wall movement is obtained for a special case, namely a velocity power index of −1/3, with an algebraically decaying velocity profile. The solution is given in a closed form. Under different values of the mass transfer parameter, the wall can be fixed, moving in the same direction as the free stream, or opposite to the free stream (reversal flow near the wall). The thermal boundary layer solution is also presented with a closed form for a prescribed power-law wall temperature, which is expressed by the confluent hypergeometric function of the second kind. The temperature profiles and the wall temperature gradients are plotted. Interesting but complicated variation trends for certain combinations of controlling parameters are observed. Under certain parameter combinations, there exist singular points or poles for the wall temperature gradients, namely wall heat flux. With poles, the temperature profiles can cross the zero temperature line and become negative. From the results, it is also found empirically that under certain given values of the Prandtl number (Pr) and flow controlling parameter (b), the number of times for the temperature profiles crossing the zero line is the same as the number of poles when the wall temperature power index varies between zero and a given value n. The current result provides a new analytical solution for the Falkner–Skan equation with algebraic decay and greatly enriches the understanding of this important equation as well as the heat transfer characteristics for this flow.}, number={6}, journal={COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION}, author={Fang, Tiegang and Yao, Shanshan and Zhang, Ji and Zhong, Yongfang and Tao, Hua}, year={2012}, month={Jun}, pages={2476–2488} }
@article{fang_zhang_zhong_2012, title={Note on unsteady viscous flow on the outside of an expanding or contracting cylinder}, volume={17}, ISSN={["1007-5704"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84862815663&partnerID=MN8TOARS}, DOI={10.1016/j.cnsns.2011.12.013}, abstractNote={Abstract In this paper, the viscous flow on the outside of an expanding or contracting cylinder is studied. The governing Navier–Stokes equations are transformed into a similarity equation, which is solved by a shooting method. The solution is an exact solution to the unsteady Navier–Stokes equations. Results show both trivial and non-trivial solutions. For trivial solutions, there is no axial flow induced during the cylinder expansion or contraction. However, for the non-trivial solutions which only exist for cylinder expansion, an axial flow is generated and its strength increases with the increase in expansion speed.}, number={8}, journal={COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION}, author={Fang, Tiegang and Zhang, Ji and Zhong, Yongfang}, year={2012}, month={Aug}, pages={3124–3128} }
@article{zhang_yao_patel_fang_2011, title={AN EXPERIMENTAL STUDY ON GASOLINE DIRECT-INJECTION SPRAY AND ATOMIZATION CHARACTERISTICS OF ALCOHOL FUELS AND ISOOCTANE}, volume={21}, ISSN={["1936-2684"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84555203802&partnerID=MN8TOARS}, DOI={10.1615/atomizspr.2011003624}, number={5}, journal={ATOMIZATION AND SPRAYS}, author={Zhang, Ji and Yao, Shanshan and Patel, Himesh and Fang, Tiegang}, year={2011}, pages={363–374} }
@article{zhang_fang_zhong_2011, title={Analytical solution of magnetohydrodynamic sink flow}, volume={32}, ISSN={["0253-4827"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-80855139343&partnerID=MN8TOARS}, DOI={10.1007/s10483-011-1495-9}, number={10}, journal={APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION}, author={Zhang, Ji and Fang, Tie-gang and Zhong, Yong-fang}, year={2011}, month={Oct}, pages={1221–1230} }
@article{fang_zhang_2011, title={Note on the Heat Transfer of Flows over a Stretching Wall in Porous Media: Exact Solutions}, volume={86}, ISSN={["1573-1634"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-79953180000&partnerID=MN8TOARS}, DOI={10.1007/s11242-010-9640-6}, number={2}, journal={TRANSPORT IN POROUS MEDIA}, author={Fang, Tiegang and Zhang, Ji}, year={2011}, month={Jan}, pages={609–614} }
@inproceedings{zhang_fang_2011, title={Simultaneous imaging of OH^{*} chemiluminescence and flame luminosity of diesel and biodiesel spray combustion}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84862580656&partnerID=MN8TOARS}, DOI={10.1115/icef2011-60103}, abstractNote={The research on the spray combustion of diesel and biodiesel is vital to the understanding of emission formation and optimal utilization of fuel. This paper studies the biodiesel and diesel spray combustion in a constant volume chamber under different simulated diesel engine conditions. The ambient temperature at fuel injection varied from 800K to 1200K, while the ambient oxygen concentration was maintained at 21%. Simultaneous high speed imaging of OH* chemiluminescence and flame luminosity was employed to visualize the whole combustion process. Heat release rate was analyzed based on the measured combustion pressure. The apparent heat release rate analysis shows that biodiesel has a shorter ignition delay time than diesel, and biodiesel has a smaller cumulative heat release value due to its lower heating value. The overlaying image of OH* chemiluminescence and flame luminosity clearly identifies the high temperature reaction regions and soot formation regions. The line-of-sight images agree with the published observation that the hydroxyl radical is formed on the lean side of the flame edge. Decreasing ambient temperature greatly reduces the OH* chemiluminescence intensity of the diesel combustion, while the impact is smoother and milder for biodiesel combustion. Biodiesel shows a significantly lower level of flame luminosity than diesel under all conditions. These combined observations lead to a speculation that the soot oxidation process may serve as an important contributor to OH* chemiluminescence intensity for late stage combustion, and biodiesel shows a tendency to produce less soot than diesel under the investigated conditions.}, booktitle={American Society of Mechanical Engineers, Internal Combustion Engine Division (Publication) ICE}, author={Zhang, J. and Fang, Tiegang}, year={2011}, pages={415–421} }
@article{fang_lee_zhang_2011, title={The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer}, volume={46}, ISSN={["0020-7462"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-79957829352&partnerID=MN8TOARS}, DOI={10.1016/j.ijnonlinmec.2011.04.007}, abstractNote={In the current work, the boundary layers of an unsteady incompressible stagnation-point flow with mass transfer were further investigated. Similarity transformation technique was used and the similarity equation group was solved using numerical methods. Interesting observation is that there are multiple solutions seen for negative unsteadiness parameters, β. The influences of mass transfer, unsteadiness parameter, and Prandtl numbers on velocity and temperature profiles, wall drag, and wall heat fluxes were investigated and analyzed. The asymptotic behaviors for the similarity equations in limiting situations were theoretically analyzed. It is found that solutions exist for all mass transfer parameters for β≥−1. For a certain mass transfer parameter, there are two solutions when βc<β<0; there is one solution for (β=βc)∪(β≥0); there is no solution for β<βc, where βc is a critical unsteadiness parameter dependent on mass transfer parameter.}, number={7}, journal={INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS}, author={Fang, Tiegang and Lee, Chia-fon F. and Zhang, Ji}, year={2011}, month={Sep}, pages={942–948} }
@article{tie-gang_ji_yong-fang_hua_2011, title={Unsteady Viscous Flow over an Expanding Stretching Cylinder}, volume={28}, ISSN={["0256-307X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-83455233823&partnerID=MN8TOARS}, DOI={10.1088/0256-307x/28/12/124707}, abstractNote={We study the viscous flow over an expanding stretching cylinder. The solution is exact to the Navier—Stokes equations. The stretching velocity of the cylinder is proportional to the axial distance from the origin and decreases with time. There exists a unique solution for the flow with all the studied values of Reynolds number and the unsteadiness parameter. Reversal flows exist for an expanding stretching cylinder. The velocity decays faster for a larger Reynolds number and a more rapidly expanding cylinder.}, number={12}, journal={CHINESE PHYSICS LETTERS}, author={Tie-Gang, Fang and Ji, Zhang and Yong-Fang, Zhong and Hua, Tao}, year={2011}, month={Dec} }
@article{fang_zhang_yao_2010, title={A new family of unsteady boundary layers over a stretching surface}, volume={217}, ISSN={["1873-5649"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-78650034159&partnerID=MN8TOARS}, DOI={10.1016/j.amc.2010.09.031}, abstractNote={Abstract In this paper, a new family of unsteady boundary layers over a stretching flat surface was proposed and studied. This new class of unsteady boundary layers involves the flows over a constant speed stretching surface from a slot, and the slot is moving at a certain speed. Depending on the slot moving parameter, the flow can be treated as a stretching sheet problem or a shrinking sheet problem. Both the momentum and thermal boundary layers were studied. Under special conditions, the solutions reduce to the unsteady Rayleigh problem and the steady Sakiadis stretching sheet problem. Solutions only exist for a certain range of the slot moving parameter, α. Two solutions are found for −53.55°}, number={8}, journal={APPLIED MATHEMATICS AND COMPUTATION}, author={Fang, Tiegang and Zhang, Ji and Yao, Shanshan}, year={2010}, month={Dec}, pages={3747–3755} }
@article{tie-gang_ji_shan-shan_2010, title={Slip Magnetohydrodynamic Viscous Flow over a Permeable Shrinking Sheet}, volume={27}, ISSN={["0256-307X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-78651086198&partnerID=MN8TOARS}, DOI={10.1088/0256-307x/27/12/124702}, abstractNote={The magnetohydrodynamic (MHD) flow under slip conditions over a shrinking sheet is solved analytically. The solution is given in a closed form equation and is an exact solution of the full governing Navier-Stokes equations. Interesting solution behavior is observed with multiple solution branches for certain parameter domain. The effects of the mass transfer, slip, and magnetic parameters are discussed.}, number={12}, journal={CHINESE PHYSICS LETTERS}, author={Tie-Gang, Fang and Ji, Zhang and Shan-Shan, Yao}, year={2010}, month={Dec} }
@article{fang_yao_zhang_aziz_2010, title={Viscous flow over a shrinking sheet with a second order slip flow model}, volume={15}, ISSN={["1878-7274"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-74449090532&partnerID=MN8TOARS}, DOI={10.1016/j.cnsns.2009.07.017}, abstractNote={Abstract In this paper, viscous flow over a shrinking sheet is solved analytically using a newly proposed second order slip flow model. The closed solution is an exact solution of the full governing Navier–Stokes equations. The solution has two branches in a certain range of the parameters. The effects of the two slip parameters and the mass suction parameter on the velocity distribution are presented graphically and discussed. For certain combinations of the slip parameters, the wall drag force can decrease with the increase of mass suction. These results clearly show that the second order slip flow model is necessary to predict the flow characteristics accurately.}, number={7}, journal={COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION}, author={Fang, Tiegang and Yao, Shanshan and Zhang, Ji and Aziz, Abdul}, year={2010}, month={Jul}, pages={1831–1842} }
@article{fang_zhang_yao_2009, title={Slip MHD viscous flow over a stretching sheet - An exact solution}, volume={14}, ISSN={["1878-7274"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-67349181009&partnerID=MN8TOARS}, DOI={10.1016/j.cnsns.2009.02.012}, abstractNote={Abstract In this paper, the magnetohydrodynamic (MHD) flow under slip condition over a permeable stretching surface is solved analytically. The solution is given in a closed form equation and is an exact solution of the full governing Navier–Stokes equations. The effects of the slip, the magnetic, and the mass transfer parameters are discussed. Results show that there is only one physical solution for any combination of the slip, the magnetic, and the mass transfer parameters. The velocity and shear stress profiles are greatly influenced by these parameters.}, number={11}, journal={COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION}, author={Fang, Tiegang and Zhang, Ji and Yao, Shanshan}, year={2009}, month={Nov}, pages={3731–3737} }
@article{fang_zhang_yao_2009, title={Viscous flow over an unsteady shrinking sheet with mass transfer}, volume={26}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-66149140214&partnerID=MN8TOARS}, DOI={10.1088/0256-307x/26/1/014703}, abstractNote={The unsteady viscous flow over a continuously shrinking surface with mass suction is studied. The solution is fortunately an exact solution of the unsteady Navier–Stokes equations. Similarity equations are obtained through the application of similarity transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the mass suction parameters and the unsteadiness parameters. Results show that multiple solutions exist for a certain range of mass suction and unsteadiness parameters. Quite different flow behaviour is observed for an unsteady shrinking sheet from an unsteady stretching sheet.}, number={1}, journal={Chinese Physics Letters}, author={Fang, Tiegang and Zhang, J. and Yao, S.-S.}, year={2009} }
@article{fang_zhang_2008, title={An exact analytical solution of the Falkner-Skan equation with mass transfer and wall stretching}, volume={43}, ISSN={["0020-7462"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-53949123916&partnerID=MN8TOARS}, DOI={10.1016/j.ijnonlinmec.2008.05.006}, abstractNote={In this paper, an exact analytical solution of the famous Falkner-Skan equation is obtained. The solution involves the boundary layer flow over a moving wall with mass transfer in presence of a free stream with a power-law velocity distribution. Multiple solution branches are observed. The effects of mass transfer and wall stretching are analyzed. Interesting velocity profiles including velocity overshoot and reversal flows are observed in the presence of both mass transfer and wall stretching. These solutions greatly enrich the analytical solution for the celebrated Falkner-Skan equation and the understanding of this important and interesting equation.}, number={9}, journal={INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS}, author={Fang, Tiegang and Zhang, Ji}, year={2008}, month={Nov}, pages={1000–1006} }
@article{fang_zhang_2008, title={Flow between two stretchable disks - An exact solution of the Navier-Stokes equations}, volume={35}, ISSN={["0735-1933"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-56349127272&partnerID=MN8TOARS}, DOI={10.1016/j.icheatmasstransfer.2008.04.018}, abstractNote={Abstract In this work, an exact solution for the steady state Navier–Stokes equations in cylindrical coordinates is presented by similarity transformation technique. The solution involves the flow between two stretchable infinite disks with accelerated stretching velocity. The similarity equation was solved numerically and the effects of disk stretching parameter and stretching Reynolds number were studied. With the increase of the stretching Reynolds numbers, the fluid begins with a creeping type flow at R = 0 to a typical boundary layer type flow for large Reynolds numbers. The pressure parameter β changes from a positive number to a negative value with the increase of non-zero stretching parameter. The upper wall stretching parameter also greatly affects the velocity distribution between the two disks with a downward net flow for γ ≠ 1. The results are also useful as a benchmark problem for the validation of three-dimensional numerical computation code.}, number={8}, journal={INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER}, author={Fang, Tiegang and Zhang, Ji}, year={2008}, month={Oct}, pages={892–895} }