•The concept of multi-dimensional conduction-advection thermal resistance in parallel in fluid domain is proposed.•The advection thermal resistance in the fluid domain is closely related to the magnitude and direction of temperature gradient and velocity.•"Negative thermal resistance" in the advection thermal resistance is found to be equivalent to a "heat source" or a "heat sink" in the fluid domain.•The capability of analysis methodology of conduction-advection thermal resistance in parallel is illustrated and proved. Thermo-electric analogy method and thermal resistance are widely used for heat transfer problems to simplify the analysis process of complex heat transfer network. Traditional thermal resistance is usually applicable to one-dimensional steady state heat conduction problem. However, heat convection problem is always involved in engineering applications such as energy power, petrochemical, aerospace and so on. In order to solve this problem, the concept of multi-dimensional conduction-advection thermal resistance in parallel in fluid domain is proposed, and the conduction-advection thermal resistance network with heat capacity is constructed. The advection thermal resistance in the fluid domain is closely related to the magnitude and direction of temperature gradient and velocity. The higher the velocity, the smaller the advection thermal resistance. Simultaneously, there exists a "negative thermal resistance" in the advection thermal resistance, which is equivalent to a "heat source" or a "heat sink" in the fluid domain. A forced convection problem and a natural convection problem are taken as examples to illustrate the practicality of this thermal resistance analysis methodology. The results show that the conduction-advection parallel thermal resistance network is important to analyze the flow and heat transfer processes and guide the regulation and optimization of the heat transfer processes.