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The heat dissipation of surrounding rock of a non-circular roadway is computed using an equivalent circular roadway approach under three circumstances when the area, perimeter, or hydraulic diameter of the circular roadway is equal to the non-circular roadway to obtain the optimal equivalent radius. The differential equations of heat conduction for unstable surrounding rock are established in cylindrical and rectangular coordinate systems using dimensionless analysis method. The calculation formulas of heat dissipation capacity and heat transfer resistance are derived from differential equations. Based on the method of equivalent radius, the similarities and differences between non-circular and circular roadways in calculating the heat dissipation of surrounding rock are discussed. Using the finite volume method, the calculation models for non-circular and circular roadways in the heat dissipation of surrounding rock are also established, among the non-circular roadways including three circumstances, namely, trapezoid, rectangle, and arch. The relation errors of heat dissipation of the surrounding rock of the three equivalent circular roadway methods are investigated for the three non-circular roadways. Results show that the calculation approach with equal perimeters is the best for the heat dissipation of surrounding rock of non-circular roadways.

Study on the Optimal Equivalent Radius in Calculating the Heat Dissipation of Surrounding Rock