The temporal evolution of the initial shock front and the low Mach regime produced behind the front due to the sudden introduction of a spherical, finite-size, low Biot number, uniformly heated energy source in a variable property gas is investigated. While the sphere is of physical interest, analogous problems of a uniformly heated infinitely long cylindrical wire and an infinite plate are also studied. Compressibility, finite-size, and nonlinear heating effects are studied without constraining the temperature of the source. Shortly after the energy source is introduced, compressibility is significant and a strong shock wave forms which weakens as it moves away from the source eventually becoming an acoustic wave. Behind it, fluid motion occurs at a much lower speed (low Mach regime), where the resulting nonlinear heating problem is solved analytically using the method of homotopy perturbation expansion leading to weak decoupling of finite-size effects and nonlinear heating effects.

中文翻译：

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气体中局部均匀热源的低马赫数、可压缩性和有限尺寸效应

研究了由于突然引入球形、有限尺寸、低比奥数、均匀加热的能量源在可变特性气体中引起的初始激波前沿和前沿后面产生的低马赫区域的时间演变。虽然球体具有物理意义，但也研究了均匀加热的无限长圆柱线和无限板的类似问题。在不限制源温度的情况下研究了可压缩性、有限尺寸和非线性热效应。引入能量源后不久，可压缩性就很显着，并且会形成强烈的冲击波，当它远离能量源时会减弱，最终变成声波。在它后面，流体运动以低得多的速度发生（低马赫数），