Abstract
In the current article, we have performed computational analysis on convection heat transfer of a hybrid nanofluid in occurrences where porous media and the effect of magnetic force are involved. In order to assess the time-fractional derivatives, Caputo’s notion is utilized while the Darcy–Forchheimer model is applied due to the involvement of the porous medium. Moreover, the boundary conditions are assumed to be nonuniform through the equilibrium between the surface tension and shear stress over a semi-infinite permeable flat surface. Keeping in view the complexity of the fractional derivative model and nonuniform boundary conditions, the problem in question is a complicated one. Accordingly, the coupled momentum and energy equation is linearized and the finite difference scheme is then applied and implemented in MATLAB Code R2020b. Furthermore, we have also offered a comprehensive analysis regarding error and convergence of the proposed numerical method. The newly introduced numerical technique to determine the numerical solutions and some unique and interesting deductions are established. From the computational results, one can conclude that the fluid motion in both hybrid and single nanofluids slows down due to magnetic field, porosity, and inertia coefficient as the magnetic and electric fields are synchronized due to the formation of the Lorentz force and viscous interference. We believe that our proposed numerical technique regarding employment of the fractional model for heat transfer application to the hybrid nanofluid over a semi-infinite nonuniform permeable surface along with variable heat flux is not found in the literature so far. Furthermore, the obtained results will be a valuable addition to fractional calculus from an engineering point of view.
Highlights
It has always remained one of the foremost objectives of researchers to formulate innovative methods to enhance the heat transfer rate in thermal systems, which will resultantly improve the productivity of heating systems while cutting off the expense simultaneously
Based on scientific research findings, nanofluids enhance the thermal conductivity and conductive heat transfer in relation to the base liquids.One cannot deny the fact that this modern kind of fluids received a remarkable acceptance from industry as these are deemed to be a good alternative of many traditional fluids, heat exchangers, and heat transport liquids [10] since nanofluids possess good temperature efficiency over liquids so that they can be utilized in numerous heating and ventilation applications (Figure 2(a)). e issue of water consumption in huge quantities and the production of excessive industrial waste can be addressed by increasing the heat transfer and simultaneously reducing water consumption
We considered the boundary conditions for u and T and negligible effect for v since convergence analysis for the above model equations is as follows:
Summary
It has always remained one of the foremost objectives of researchers to formulate innovative methods to enhance the heat transfer rate in thermal systems, which will resultantly improve the productivity of heating systems while cutting off the expense simultaneously. From [7,8,9], it is evident that the addition of solid nanoparticles to conventional fluids results in a visible increase in thermal conductivity. Based on scientific research findings, nanofluids enhance the thermal conductivity and conductive heat transfer in relation to the base liquids.One cannot deny the fact that this modern kind of fluids received a remarkable acceptance from industry as these are deemed to be a good alternative of many traditional fluids, heat exchangers, and heat transport liquids [10] since nanofluids possess good temperature efficiency over liquids so that they can be utilized in numerous heating and ventilation applications (Figure 2(a)). E researchers and scientists have employed the technique of diffusing tiny solid particles in conventional fluids to maximize fluids’ thermal characteristics. From [20,21,22,23], it is evident that
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