Heat-transfer geometries that enhance heat transfer performance for slurries increase the net raw biogas production in the bio-methane process. In this study, the precise temperature-dependent rheologies of corn straw slurry with 6 and 8% total solid were determined, collected, and modeled to conduct a numerical simulation via CFD, the first instance of such research. Subsequently, the reliability of the numerical results was verified with heat-transfer experiments. The heat-transfer performances of the circular, twisted square and twisted hexagonal tubes were estimated numerically, ultimately showing that the twisted hexagonal tube performed optimally with an enhancement factor of up to 2.0 in the turbulent region, compared to the circular tube. Based on the numerical results, the mechanism of heat-transfer enhancement was revealed, showing balanced radial mixing and the near-wall shear effect that leads to a strong and continuous shear rate under a considerable radial-flow intensity. An engineering equation was obtained for the performance evaluation, and the waste-heat recovery from corn straw slurry was analyzed, showing the twisted hexagonal tube can increase the net raw biogas production by up to 17.0% compared to the circular tube.