Modeling of a continuous superradiant laser on the sub-mHz <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:msup><mml:mrow/><mml:mn>1</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">S</mml:mi><mml:mn>0</mml:

Continuous superradiance using a narrow optical transition has the potential to improve the short-term stability of state-of-the-art optical clocks. Even though pulsed superradiant emission on a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>mHz</a:mi></a:math> linewidth clock transition has been shown, true continuous operation, without Fourier limitation, has turned out to be extremely challenging. The trade-off between maintaining a high atomic flux while minimizing decoherence effects presents a significant obstacle. Here, we discuss the design of a machine that could overcome this problem by combining a high-flux continuous beam of ultracold strontium atoms with a bowtie cavity for the generation of superradiant lasing. To evaluate the feasibility of our design, we present simulation results for continuous high-efficiency cooling, loading, and pumping to the upper lasing state inside the bowtie cavity. We then present two different models for simulating the generated superradiant field by taking into account position-dependent shifts, collisional decoherence, light shifts, and atom loss. Finally, we estimate a laser linewidth of less than <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>100</b:mn><b:mspace width="3.33333pt"/><b:mi>mHz</b:mi></b:mrow></b:math>, limited by atom number fluctuations, resulting in an output power of hundreds of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>fW</d:mi></d:math>.