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Understanding how human skin reacts to heat is vital for effective burn prevention and treatment. This study uses a bioheat transfer model to develop a comparative analogy to differentiate burn intensity from hot dishes, hot fluids, radiation, and flash fires, aiming to differentiate the burn profiles of each incident type. The finite element metho...
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... Figure 1 illustrates the complete structure of the flow process, including the required coordinates. According to Reddy [23], Mezaache et al. [24,25], Hossain et al. [26], and Ragavi et al. [27], we can formulate the equations for continuity, momentum, energy, and concentration as follows: ...
Exploring flow stability in porous media, the consequence of magnetic fields on heat transfer (HT), the influence of inclination on flow, and optimizing industrial cooling systems are crucial. This study explores the stability of magneto‐convective flow in unsteady porous media, focusing on orientation effects and the impact of boundary layer (BL) conditions on flow behavior and heat transmission while developing regression models to predict these dynamics. We explore nonlinear, time‐varying partial differential equations (PDEs) that govern mass conservation, momentum, energy, and concentration, making relevant adjustments as required. A comprehensive numerical framework is developed to address these governing equations, employing a finite difference method (FDM) for spatial discretization and an implicit approach for time integration. Through stability analysis, we assess the flow behavior under diverse conditions, elucidating the critical parameters influencing flow stability and transitions. Furthermore, an extensive investigation is undertaken to establish a suitable steady‐state condition and to ensure uniform meshing throughout the process. Regression analysis is applied to elucidate the relationships between the key factors. This study examines the consequence of several physical factors on the distribution of velocity, temperature, and concentration within the system. The findings indicate that increasing the mass Grashof number significantly enhances buoyancy‐driven convection, while an inclined magnetic field profoundly modifies the flow dynamics and thermal profiles. The newly developed two linear regression models of multiple variables have 95.25% and 98.49% correlation coefficients for mean Nusselt number and shear stress, respectively. The study's originality lies in its detailed examination of how these parameters interact to impact inclined magnetic field convection flows. This comprehensive understanding may facilitate more accurate predictive models and enhancements in engineering design. It is significant for several industries, including petroleum and agricultural engineering, gas turbines, nuclear power facilities, heat exchangers, cooling systems, and chemical processing.
... If the elements are linear, the pressure is considered discontinuous; if not, the pressure stays the same across the domain. Using Galerkin's weighted residual technique (Zienkiewicz and Taylor [37], Hossain et al. [38]), the nonlinear governing partial differential equations are converted into a set of integral equations. Each term evaluates the integration using either the exact integration formula or the Gauss quadrature method. ...
Microelectronic technologies are progressing rapidly. As devices shrink in size, they produce a substantial heat flux that can adversely affect performance and shorten their lifespan. Conventional cooling methods, such as forced-air heat transfer and essential heat sinks, are inadequate for managing the elevated heat flux generated by these devices. Consequently, microchannel heat sinks have been developed to address this challenge. The present research is intended to study forced flow convection and heat transfer in a cone–column combined microchannel heat sink (MCHS). This study examines a regularly shaped MCHS to evaluate its heat transfer rate. The heat transfer medium employed is a graphene–water nanofluid, and the heat sink’s base is assumed to maintain a constant heat flux. The Galerkin weighted finite element method solves the nanofluid’s governing partial differential equations. This thesis investigates the impact of varying intake velocities on the Reynolds number (100 ≤ Re ≤ 900), externally applied heat flux (10⁴ ≤ q ≤ 10⁶), and the volumetric ratio of nanoparticles (0.001 ≤ φ ≤ 0.04). The study conducts a mathematical analysis to explore how these parameters affect pressure drop, friction factor, average Nusselt number, average substrate temperature, and heat transfer enhancement. The findings are compared with those of a conventional MCHS as the Re increases. The results are analyzed and visually represented through isothermal lines for temperature contours and streamlines for velocity. An increase in the inlet velocity of the water–graphene nanofluid significantly enhances heat transfer and thermal efficiency, achieving improvements of approximately 27.00% and 21.21%, respectively. The research demonstrates that utilizing water–G as a smart coolant with the cone–column combined MCHS enhances thermal efficiency by 4.05% compared to standard water. A comparison of the hydraulic performance index at the substrate reveals that the cone–column combined MCHS is significantly more effective at dissipating heat than the traditional MCHS.
