In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense impor-tance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.There-fore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation) is performed in the present study.The impacts of the hydrodynamic flow and Newton\'s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method (SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.