Impact of internal heat generation/absorption on MHD conjugate flow of aqueous-MWCNT nanofluid in a porous annulus

Abstract

This study deals with a numerical investigation of conjugate heat transfer phenomena in a porous enclosure subjected to magnetic field with internal heat generation/absorption. The physical domain of the numerical model encompasses a vertical annulus with a thick inner cylinder wall, where the porous annular region is saturated with an aqueous-MWCNT nanofluid. In this model, the momentum equation includes the non-Darcy viscous terms and additional body term to accurately represent the influence of porous media and magnetic fields on the flow behavior. To estimate conjugate heat transfer phenomena, the energy conservation equations for the solid wall and the fluid-saturated porous region are solved simultaneously. The finite difference technique is used to solve the non-dimensionalized governing equations, and validated against existing studies. Using the proposed model, a series of numerical calculations is performed for various parameters including Hartmann number $({\text {Ha}}=0\sim 50)$, Darcy number $({\text {Da}}\,=\,10^{-5}\sim10^{-1})$, thermal conductivity ratio $({\text {Kr}}\,=\,0.1\sim 10)$, dimensionless solid wall thickness $(\varepsilon \,=\,0.1\sim 0.5)$, nanoparticle concentration $(\phi =0\sim 0.05)$, and dimensionless internal heat generation/absorption rate $(Q\,=\,-10\sim 10)$. The numerical results reveal that a significant improvement in thermal transport can be achieved by increasing either Da or Kr: An increment in Da from $10^{-5}$ to $10^{-1}$, for example, results in 95.6% increase in the flow circulation rate. Either a decrease in Q or an increase in $\phi$ also contributes to enhancing the heat dissipation rate. For instance, there is a 16.6% reduction in heat dissipation rate for internal heat generation $(Q=10)$ case compared to internal heat absorption $(Q=-10)$ case. On the other hand, an increase in either Ha or $\varepsilon$ results in a suppression in flow and heat transport. Among the considered range of parameters, greater heat dissipation could be obtained for Da = $10^{-1}$, Kr = 10, $\varepsilon =0.1$, and Ha $<10$. These findings can expand our understanding of natural circulation and heat transfer within the fluid-filled enclosures and serve as building block for efficient thermal design guidelines in diverse applications.

Appendix: Applications

Nanofluids: For better and durable performance of thermal systems, substantial heat transport enhancement is essential. Also, the role of heat transport fluid is of significant importance in thermal engineering applications. The traditional fluids namely engine oil, water, ethylene glycol, and many more were utilized in heat transfer equipment in earlier times. These conventional heat transfer fluids were not effective since they exhibit poor thermal conducting behavior. Due to the increasing demand to obtain effective good-performance thermal devices, various efficient methods for improvising thermal conductivity of the heat transfer fluids have come into existence. Dispersion of solid nanoparticles to base fluids is one such method and the obtained fluids are called “Nanofluids.” Due to the unique structural properties and improved heat conducting capability, the field of nanofluid research is still evolving, and ongoing studies are exploring new applications to optimize the properties of nanofluids for various thermal engineering purposes.

Magnetic field: The application of magnetic field during convection of nanofluids corresponds to the industrial applications wherein the system requires precise control of fluid flow in micro-scale environment. Also, the magnetic field can induce convection in a nanofluid circulating around the tumor, leading to localized heating and improved treatment efficacy. Varying the strength or magnetic field orientation controls the convective heat transfer and allows for instant adjustments in the temperature. This capability is advantageous for performing temperature cycling in DNA amplification techniques like polymerase chain reaction (PCR) or other thermal cycling protocols required for specific applications.

Porous media flows: An appropriate application of nanofluid-saturated porous enclosure is the desalination process. The porous media helps in filtration of impurities, whereas the nanofluid improves the heat dissipation during condensation/evaporation processes. This combination can improve the efficiency and effectiveness of desalination technologies, contributing to the production of fresh water from seawater or brackish water sources. Another application can be thermal management of electronic equipment for effective heat dissipation. The prime advantage of porous media is it helps in the uniform distribution of nanofluid and prevent hot-spots inside the cavity.

Internal heat generation/absorption: The improved thermal conductivity and heat transfer efficiency obtained by IHG/A enable the design of space-efficient and compact thermal systems. With enhanced heat transport capabilities, the size and complexity of radiators, heat exchangers or other cooling equipment can be reduced, resulting in cost-effective system designs. One possible ways of heat generation inside the enclosure is Joule heating which can be done by introducing electrodes within the enclosure. As voltage is passed across the electrode, the resistance generates heat and gets transferred to nanofluid, and resulting in IHG.