The present work discusses a systematic approach to model grinding parameters of coal in a ball mill. A three level Box-Behnken design combined with response surface methodology using second order model was applied to...The present work discusses a systematic approach to model grinding parameters of coal in a ball mill. A three level Box-Behnken design combined with response surface methodology using second order model was applied to the experiments done according to the model requirement. Three parameters ball charge （numbers 10-20）, coal content （100-200 g） and the grinding time （4-8 rain） were chosen for the experiments as well as for the modeling work. Coal fineness is defined as the dso （80 % passing size）. A quadratic model was developed to show the effect of parameters and their interaction with fineness of the product. Three different sizes （4, 1 and 0.65 mm） of Indian coal were used. The model equations for each fraction were developed and different sets of experiments were performed. The predicted values of the fineness of coal were in good agreement with the experimental results （R2 values of dso varies between 0.97 and 0.99）. Fine size of three different coal sizes were obtained with larger ball charge with less grinding time and less solid content. This work represents the efficient use of response surface methodology and the Box-Behnken design use for grinding of Indian coal.展开更多
The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s ...The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.展开更多
In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hy...In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.展开更多
文摘The present work discusses a systematic approach to model grinding parameters of coal in a ball mill. A three level Box-Behnken design combined with response surface methodology using second order model was applied to the experiments done according to the model requirement. Three parameters ball charge （numbers 10-20）, coal content （100-200 g） and the grinding time （4-8 rain） were chosen for the experiments as well as for the modeling work. Coal fineness is defined as the dso （80 % passing size）. A quadratic model was developed to show the effect of parameters and their interaction with fineness of the product. Three different sizes （4, 1 and 0.65 mm） of Indian coal were used. The model equations for each fraction were developed and different sets of experiments were performed. The predicted values of the fineness of coal were in good agreement with the experimental results （R2 values of dso varies between 0.97 and 0.99）. Fine size of three different coal sizes were obtained with larger ball charge with less grinding time and less solid content. This work represents the efficient use of response surface methodology and the Box-Behnken design use for grinding of Indian coal.
文摘The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.
文摘In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.
