The study of COMPRESSIBLE FLOW plays a fundamental role in the design of heat exchangers at high temperature and pressure. COMPRESSIBLE FLOW is used to design the aerodynamic structure, engines, and high-speed vehicles. In view of these utilities, this paper is deliberated to acquire the analysis of the unsteady COMPRESSIBLE FLOW of a viscous FLUID through an inclined asymmetric channel with thermal effects. Special attention is paid to convective heat transfer with impact of viscous dissipation, source/sink, and joule heating effects. In addition, thermal FLOW is analyzed through slip boundary conditions. The current problem is modeled through the laws of energy, momentum, and mass with the help of a FLUID’s response towards compression. As a result, the coupled nonlinear partial differential equations are obtained, which are investigated through a well-known numerical approach, the explicit finite difference method. The study examines impact of several parameters on the FLOW rate, velocity, and temperature with the help of graphical representations. The behavior of FLOW rate is intended to change with time.