注气条件下煤层透气性系数的快速测定及其计算

煤层透气性系数是评价瓦斯抽采效果的主要指标,也是评价煤层增透效果最直接的技术参数。针对煤层透气性系数原位测定时间长的问题,研究煤层透气性系数的快速测定方法以及与之相应的计算方法。基于“原位、密集、快速”的测定原则,开发了移动式煤层透气性系数快速测量仪,并提出了“顺层钻孔+移动式测量仪+注气”的测量方法。针对“注气”快速测定这一特定条件,以达西定律为基础构筑了煤层透气性系数反演计算方程,通过坐标变换,采用数学物理方法推导出了实际钻孔煤层透气性系数解析解表达式,确定了钻孔压力特征曲线方程。通过现场实测验证了煤层透气性系数快速测定方法的再现性,并与传统透气性系数计算方法进行了比较,结果表明:短时间的测定即可得到钻孔压力特征曲线的变化规律和基本特征,煤层透气性系数快速测定方法是可行的;同一钻孔同一测点重复测定的结果基本一致,具有良好的再现性,证明本文提出的快速测定方法是可靠的;实测钻孔压力曲线经过坐标变换得到的特征曲线是线性的,在形式上与本文推导的特征曲线方程完全一致,证明根据特征曲线求解煤层透气性系数是正确的;煤层透气性系数仅与钻孔压力特性曲线的斜率有关,计算简单;本方法与传统煤层透气性系数计算方法的计算结果基本一致,可以满足实际工程需要。

Solution to the MHD flow over a non-linear stretching sheet by homotopy perturbation method

In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM solution.Comparisons with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy,simplicity and efficiency of this method.

Analytic Solutions of a Polynomial-Like Iterative Functional Equation near Resonance

In this paper existence of local analytic solutions of a polynomial-like iterative functional equation is studied. As well as in previous work, we reduce this problem with the SchrSder transformation to finding analytic solutions of a functional equation without iteration of the unknown function f. For technical reasons, in previous work the constant α given in the Schroder transformation, i.e., the eigenvalue of the linearized f at its fixed point O, is required to fulfill that α is off the unit circle S^1 or lies on the circle with the Diophantine condition. In this paper, we obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.

Unsteady 3D algebraically explicit analytical solutions for bio-heat transfer equations

Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is obtained in this paper.In other cases the temperature would vary monotonously along geometric coordinates as time goes by.There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature.Besides its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat transfer.In addition,some new special methods have been given originally and deserved further attention.