The system of equations of one-dimensional unsteady fluid motion in a viscous heat-conducting medium is considered. The mathematical model is based on the equations of conservation of mass for liquid and solid phases, Darcy’s law, rheological relation, the law of conservation of balance of forces and the equation for the temperature of the medium. The transition to Lagrange variables in the case of an incompressible fluid allows us to reduce the initial system of governing equations to a third-order equation for porosity and a second-order equation for temperature, respectively. A calculation algorithm is proposed and a numerical study of the obtained initial - boundary value problem is carried out.

考虑粘性导热介质中的一维非定常流体运动方程组。数学模型基于液相和固相质量守恒方程、达西定律、流变关系、力平衡守恒定律和介质温度方程。在不可压缩流体的情况下，向拉格朗日变量的转变使我们能够将控制方程的初始系统分别简化为孔隙度的三阶方程和温度的二阶方程。提出了一种计算算法，并对得到的初-边值问题进行了数值研究。