The present article involves a dual-phase-lag nonlinear bioheat model for living spherical tissue during magnetic hyperthermia. In this study, we considered temperature-dependent blood perfusion to forecast accurate hyperthermia temperature for the treatment of tumor cells. Due to the nonlinearity, this problem is handled by a finite element Runge-Kutta (4,5) technique, which is a combination of Runge-Kutta (4,5) and finite difference approaches. In this technique, we discretize the partial derivatives of space variables by using the central difference scheme. After the discretization, the current problem turns out as a system of second-order ODEs with initial conditions. Again, we convert the system of second-order ODEs into the system of first-order coupled ODEs. Then, we employed the RK (4,5) scheme to resolve the problem completely for time interval. The result obtained by the present numerical scheme is validated through an exact analytical result in a special situation, and it is noticed that both results are very close to each other. After analyzing the results, we found that when tumor cells are treated by magnetic hyperthermia, temperature-dependent blood perfusion significantly affects the hyperthermia temperature. It is seen that the impact of quadratically temperature-dependent blood perfusion is more effective than the linearly temperature-dependent types of blood perfusion. The convection effect due to the quadratically temperature-dependent term in the blood perfusion is greater than the other terms. The magnetic heat source is crucial in regulating the temperature inside the living tissue for determining hyperthermia temperature. By rising the ratio of lagging time due to heat flux (tau q) and temperature gradient (tau t), the temperature profile drops, and these effects are observed initially for a few seconds.
Deterioration in efficiency caused by elevated temperatures of solar photovoltaic (PV) panels limits their utilization in hot environments and in concentrated irradiance applications. This article proposes cooling PV panels without introducing bulky or costly components. The cooling effect is achieved through a basin attached below the panel. The basin is equipped with elliptic enclosures (EE) containing phase change material (PCM). The EEs are set at a distance below the PV allowing for a small gap. The EEs can rotate around their axes inducing motion that boosts PV cooling. This motion is sought to enhance heat transfer from the hot lower surface of the PV to the fluid and from the fluid to the PCM. The EE also acts as a constant temperature heat sink storing heat rejected by the panel during the day and rejecting this stored heat to the ambient (through water and then through the basin's lower surface) during the night. The current article discusses the effect of the number of EEs, their distance below the panel surface and their rotational speed on the PV electrical output. System performance is assessed numerically for ambient conditions of Cairo, Egypt at noon of the summer solstice. The best design is identified based on the highest overall efficiency, considering the enhancement in output power due to cooling and the power consumed in overcoming friction between the EEs and the surrounding water. The results were used to generate an optimum case resulting in 13.5% enhancement over an uncooled PV panel.
This study investigates the unsteady flow and heat transfer characteristics of a nanofluid composed of Fe3O4 (iron oxide) nanoparticles suspended in a base fluid, flowing over an inclined stretching sheet within a porous medium. The effects of magnetic fields, radiation, velocity slip, and convective boundary conditions are analyzed, along with the influence of different nanoparticle shapes (lamina, tetrahedron, and hexahedron) on heat transfer. By applying similarity transformations, the governing partial differential equations are reduced to ordinary differential equations and solved numerically. MATLAB is used to visualize velocity and temperature profiles and to tabulate skin friction coefficients and heat transfer rates. The results show that an increase in the magnetic field strength leads to a reduction in velocity, while higher porosity levels further decelerate the flow by 15%. Furthermore, increasing the Biot number (which measures convective heat transfer at the boundary) from 1.0 to 1.5 enhances heat transfer rates for lamina, tetrahedron, and hexahedron-shaped nanoparticles by 7.2%, 6.32%, and 5.79%, respectively. These results highlight that lamina-shaped nanoparticles significantly boost heat transfer rate compared to other shapes. This research provides valuable insights into nanofluid transport in porous media, with implications for energy efficiency and materials science.
Under the influence of an external magnetic field, the interaction between liquid metal magnetofluid (LMM) and the magnetic field gives rise to induced current, Lorentz force, and Joule heat in LMM, thereby affecting its flow and heat transfer characteristics. In order to investigate LMM boiling heat transfer under a magnetic field, a computational method was developed by integrating the Volume of Fraction (VOF) interface capture method, phase change model, and electromagnetic field model for solving LMM boiling flow. The boiling thermodynamic characteristics of LMM on a horizontal plate and horizontal cylinder were calculated. Under the magnetic field, induced current generates Lorentz force. Because of this force, bubble growth and detachment are delayed significantly. Simultaneously, due to the suppression effect caused by Lorentz force, there is a slight reduction in heat transfer performance as the strength of the applied magnetic field increases. Our understanding of LMM boiling heat transfer under the control of magnetic field is furthermore enhanced.
This article presents an investigation into the impact of viscous dissipation on thermogravitational convection within a U-shaped enclosure. The enclosure is filled with a water-based TiO2-CoFe2O4 hybrid-nanofluid, with baffles positioned at two corners of the lower surface. Four geometrical arrangements (Case-I, Case-II, Case-III, and Case-IV) are examined. The aim is to elucidate the intricate interplay between several aspects, including fluid dynamics, heat transfer, and the presence of hybrid nanofluids. The governing equations are examined using a higher-order compact formulation. The formulation is a finite difference compact scheme which is fourth order accurate in space coordinate. This scheme can capture the flow physics in low grids which reduces the computational cost. The reliability of our in-house program is established through rigorous verification procedures, encompassing grid independence tests and comparisons with experimental and theoretical findings from researchers. The novel importance of the work encompasses six key elements: the unique properties of hybrid nanofluids, the geometric arrangement of baffles, the U-shaped enclosure design, the influence of viscous dissipation (0 <= Ec <= 0.03), interactions with magnetic fields, and the utilization of advanced compact computational techniques, across a spectrum of parameters. The findings unveil that viscous dissipation impedes the thermal diffusion, precipitating a decline of thermal performance up to 36.34% in Case-I, 17.83% in Case-II, 15.70% in Case-III, and 5.23% in Case-IV with the upsurge of Eckert value. The mean Nusselt number in variation of magnetic field compared to without magnetic field results discernible increase of 8.53% in Case-II and 9.97% in Case-III. Furthermore, the strategic placement of corner baffles emerges as a pivotal mediator in the interplay of magnetic effect and fluid transportation. Remarkably, across the cases (II, III and IV), a discernible upward trajectory in the Nusselt number ratio is discerned concomitant with the escalation of nanoparticle volume fraction, which augmenting thermal efficacy.
