Low Mach, compressibility, and finite size effects of localized uniform heat sources in a gas

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.