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In this note, a new blackbody radiation fraction function is pro-posed for calculating the emissive power or total emissivity of a surface that has an emissivity depending linearly on wavelength in a wavelength interval. This new fraction function is expressed as a function of the product of wavelength and temperature and the numerical values are tabulated. Based on the new defined fraction function, the emissive power in a given wavelength inter-val can be calculated very conveniently combined with the tradi-tional blackbody radiation fraction function. This new function can be used in many practical applications with good accuracy without numerical integration. [ABSTRACT FROM AUTHOR]

In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word. [ABSTRACT FROM AUTHOR]

Low-temperature compression ignition combustion employing multiple-injection strategies in an optical high-speed direct injection diesel engine was investigated. Heat release characteristics were analyzed. The whole cycle combustion process was visualized by imaging the natural flame luminosity. The NOx emissions were measured in the exhaust pipe. The effects of the pilot injection timing, pilot fuel quantity, main injection timing, operating load, and injection pressure on the combustion and emissions were studied. Low-temperature combustion modes were achieved by using a small pilot injection with an injection timing much earlier than top dead center (TDC) followed by a main injection after TDC. The results were compared with conventional diesel (diffusion) combustion for comparison purposes. A premixed-combustion-dominated heat release rate pattern was seen for all the low-temperature combustion cases, while a typical diffusion flame combustion heat release rate was obtained for the conventional combustion case. A highly luminous flame was observed for the conventional combustion condition while a much less luminous flame was seen for the low-temperature combustion cases. For the higherload and lower injection pressure cases, liquid fuel being injected into low-temperature premixed flame was observed for certain cases. Compared with the conventional diffusion combustion, simultaneous reductions in soot and NOx were obtained for the low-temperature combustion mode under similar operating loads. For high-load conditions, higher NOx emissions were obtained due to higher in-cylinder, temperatures. However, compared with the conventional combustion case, a significant reduction in soot was achieved for the high-load conditions, which shows that increasing injection pressure greatly reduces soot emissions. [ABSTRACT FROM AUTHOR]

In the current work, the 3D boundary layers of wall-bounded flow configurations were extended to the situations with span-wise cross moving boundary and free stream. The unsteady boundary layer is also addressed for the Falkner–Skan wedge flow with a span-wise oscillating wall or oscillating free stream. The span-wise secondary boundary layer equation is obtained using similarity transformation technique and solved analytically in terms of the primary stream-wise boundary layer flow solutions. Different fluid motion behaviors are found for these new solutions. It is found that for the span-wise secondary boundary layer flow there is no flow separation for any wall cross moving velocity, which is different from the primary stream-wise boundary layers with a reverse flow. For the unsteady boundary layer with an oscillating wall or free stream, it is seen that the solution is different from the Stokes oscillating plate or free stream problem. The unsteady wall drag increases with the increase in the oscillating frequency and decreases with increasing the primary span-wise free stream magnitude. The velocity overshooting near the wall is also seen for an oscillating free stream for a large oscillating frequency or a lower primary stream-wise free stream magnitude. [ABSTRACT FROM AUTHOR]

Biodiesel is popularly discussed in many countries due to increased environmental awareness and the limited supply of petroleum. One of the main factors impacting general replacement of diesel by biodiesel is NOx (nitrogen oxides) emissions. Previous studies have shown higher NOx emissions relative to petroleum diesel in traditional direct-injection (DI) diesel engines. In this study, effects of injection timing and different biodiesel blends are studied for low load [2 bar IMEP (indicated mean effective pressure)] conditions. The results show that maximum heat release rate can be reduced by retarding fuel injection. Ignition and peak heat release rate are both delayed for fuels containing more biodiesel. Retarding the injection to post-TDC (top dead center) lowers the peak heat release and flattens the heat release curve. It is observed that low-temperature combustion effectively reduces NOx emissions because less thermal NOx is formed. Although biodiesel combustion produces more NOx for both conventional and late-injection strategies, with the latter leading to a low-temperature combustion mode, the levels of NOx of B20 (20 vol % soy biodiesel and 80 vol % European low-sulfur diesel), B50, and B100 all with post-TOC injection are 68.1%, 66.7%, and 64.4%, respectively, lower than pure European low-sulfur diesel in the conventional injection scenario. [ABSTRACT FROM AUTHOR]

In this work, an exact solution for the steady state Navier–Stokes equation in cylindrical coordinates is presented. The solution is an extension of the well-known von Kármán viscous pump problem to the configuration with a stretchable disk with or without rotation. The results also offer new examples for three-dimensional computation code validation. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic (MHD) flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated. [ABSTRACT FROM AUTHOR]

We investigate a viscous flow over a cylinder with stretching and torsional motion. There is an exact solution to the Navier--Stokes equations and there exists a unique solution for all the given values of the flow Reynolds number. The results show that velocity decays faster for a higher Reynolds number and the flow penetrates shallower into the ambient fluid. All the velocity profiles decay algebraically to the ambient zero velocity. [ABSTRACT FROM AUTHOR]

Soot formation process was investigated for biomass-based renewable diesel fuel, such as biomass to liquid (BTL), and conventional diesel combustion under varied fuel quantities injected into a constant volume combustion chamber. Soot measurement was implemented by two-color pyrometry under quiescent type diesel engine conditions (1000 K and 21% O2 concentration). Different fuel quantities, which correspond to different injection widths from 0.5 ms to 2 ms under constant injection pressure (1000 bar), were used to simulate different loads in engines. For a given fuel, soot temperature and KL factor show a different trend at initial stage for different fuel quantities, where a higher soot temperature can be found in a small fuel quantity case. but a higher KL factor is observed in a large fuel quantity case generally. Another difference occurs at the end of combustion due to the termination of fuel injection. Additionally, BTL flame has a lower soot temperature, especially under a larger fuel quantity (2 ms injection width). Meanwhile, average soot level is lower for BTL flame, especially under a lower fuel quantity (0.5 ms injection width). BTL shows an overall low sooting behavior with low soot temperature compared to diesel; however, trade-off between soot level and soot temperature needs to be carefully selected when different loads are used. [ABSTRACT FROM AUTHOR]

Soot formation process was investigated for biomass-based renewable diesel fuel, such as biomass to liquid (BTL), and conventional diesel combustion under varied fuel quantities injected into a constant volume combustion chamber. Soot measurement was implemented by two-color pyrometry under quiescent type diesel engine conditions (1000K and 21% O2 concentration). Different fuel quantities, which correspond to different injection widths from 0.5ms to 2ms under constant injection pressure (1000 bar), were used to simulate different loads in engines. For a given fuel, soot temperature and KL factor show a different trend at initial stage for different fuel quantities, where a higher soot temperature can be found in a small fuel quantity case. but a higher KL factor is observed in a large fuel quantity case generally. Another difference occurs at the end of combustion due to the termination of fuel injection. Additionally, BTL flame has a lower soot temperature, especially under a larger fuel quantity (2ms injection width). Meanwhile, average soot level is lower for BTL flame, especially under a lower fuel quantity (0.5ms injection width). BTL shows an overall low sooting behavior with low soot temperature compared to diesel; however, trade-off between soot level and soot temperature needs to be carefully selected when different loads are used. [ABSTRACT FROM AUTHOR]

Ambient 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 technique was used to measure transient soot temperature and the KL factor of the spray flame. The soot temperature of biodiesel is found to be lower than that of diesel under the same conditions, which follows the same trend from our previous results found when the ambient temperature changes to 21% oxygen conditions. A reduction in ambient oxygen concentration generally reduces the soot temperature for both fuels. However, this is a complicated effect on soot processes as the change of oxygen concentration greatly affects the balance between soot formation and oxidation. The KL factor is observed to be the highest at 12% O2 for diesel and 18% O2 for biodiesel, respectively. On the other hand, the 10% O2 condition shows the lowest KL factor for both fuels. These results can provide quantitative experimental evidences to optimize the ambient oxygen concentration for diesel engines using different fuels for better emissions characteristics. [ABSTRACT FROM AUTHOR]