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Entropy generation in the human circulatory system represents the natural energy dissipation and transformation processes within the complex blood vessel network. This phenomenon has captivated the attention of biomedical engineers, clinicians, and medical scientists due to its potential to provide valuable insights into complex physiological and pathological conditions, such as cardiovascular diseases, thrombosis, and hemodynamic disorders. This present study illustrates the interplay between entropy generation, electro-magnetic field, and thermal radiation in bio-magnetic ternary hybrid nanofluid flow over non-linearly heated stretched sheet with porosity and Darcy-Forchheimer. The novelty of this research lies in introducing a comprehensive analysis of entropy generation in a bio-magnetic ternary hybrid nanofluid, incorporating the combined effects of multiple nanoparticles (Cu, Au, Ti) to enhance thermal conductivity and optimize biomedical applications. This study introduced a novel approach utilizing a multi-layer artificial neural network (ANN) with the MLP feed-forward backpropagation and Levenberg–Marquardt algorithm to effectively model entropy generation in bio-magnetic fluid flow. A comprehensive dataset was meticulously gathered and processed to ensure accurate testing, validation, and training of the ANN model. Furthermore, nonlinear mathematical equations governing variables like velocity, temperature, skin friction coefficient, and rate of heat transfer are rigorously resolved using the bvp4c solver in MATLAB. The impact of the active parameters in the flow dynamics of the bio-magnetic flow is effectively showcased through suitable tables and graphs, providing a visual representation of their influence. The variable of wall thickness influences the rise of the electric field, resulting in an observed intensification in the velocity profile. Increases in the volume fraction of nanoparticles result in higher levels of entropy generation and Bejan number. Skin friction coefficient decreases by approximately 0.49%, 0.99%, 1.50%, and 2.01% for E= 0.04, 0.06, 0.08, and 0.1, respectively. Rate of heat transfer increases by approximately 4.8%, 9.1%, 12.8%, and 16.1% for ϕ=0.01,0.02,0.03,and 0.04, respectively.

This work is concerned with the study of laminar, steady electro-magnetohydrodynamic flow and entropy generation of SWCNT-blood nanofluid with melting/non-melting heat transfer. A study is also underway to analyze the heat transfer phenomenon under factors such as viscous dissipation and joule heating. The homotopy perturbation method is employed to solve the coupled non-linear ordinary differential equations. The calculated results are plotted graphically through velocity, temperature, entropy generation, local skin friction coefficient, and rate of heat transfer. Melting/non-melting heat transfer is used in biomedical for example vanquish uses radio frequency to dangerously destroy fat cells. This model may use heat to melt away fat cells in the body. The entropy generation increases with increasing the electric field parameter. The heat transfer rate enhances with the higher values of the melting parameter.

Present research deals with the study of time-dependent pulsatile MHD (Magnetohydrodynamics) hybrid nanofluid with entropy optimization and electrokinetic force in a channel. The current mathematical model is formulated as the Cu−Au−blood (Casson fluid) hybrid nanofluids flow between the bottom and wavy top walls. The pulsatile flow is subjected to an inverse magnetic field of uniform force to study the effect of the resulting Lorenz force. Exact solutions for velocity, temperature, heat transfer rate, and streamlines are constructed by employing the perturbation approach to evaluate coupled nonlinear partial differential equations (PDEs). The velocity (us)of the blood-based Cu−Auhybrid nanofluid increases with increasing values of the electro-osmotic parameter. The higher values of copper-gold nanoparticle volume fraction increase the entropy generation (NG). This theoretical investigation helps estimate entropy in systems biology, which is used to treat cancer and improve the function of medical devices.