Search

The present work investigates the magnetohydrodynamic (MHD) convective heat transport of hybrid nanofluids in a chamber with multiple heaters (such as hot microchips). The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) and graphics processing unit (GPU) computing are used here. The present study is important due to its relevance to real-world applications, the use of advanced simulation techniques, the consideration of hybrid nanofluids, the inclusion of magnetohydrodynamics, and the identification of critical parameters influencing heat transfer. Thermally homogeneous blocks are set at the bottom of a rectangular enclosure filled with ethylene glycol Cu-Al2O3 hybrid nanofluids with temperature-dependent viscosity. The cold temperature of the enclosure's left and right walls and the bottom and top surfaces is kept at adiabatic conditions. The numerical outcomes for the various parameters Rayleigh number (1 0 4 ≤ Ra ≤ 1 0 6 ), volume fraction (0.00 ≤ ϕ ≤ 0.04), Hartmann number (0 ≤ Ha ≤ 60), and viscosity variation parameter (0 ≤ ε ∗ ≤ 5) are presented in terms of streamlines, isotherms, and the peripheral local and average Nusselt numbers for the heated chips. The results demonstrated that inside the chamber, the Rayleigh number (Ra), the Hartmann number (Ha), and the volume fraction of nanoparticles (ϕ) have the highest impact on the heat transfer rate for hybrid nanofluid. For increased Ha from 0 to 20, while ϕ = 0.0 and Ra = 1 0 6 , average Nusselt number decreased with 13.65%. For the same case, if the volume fraction was increased to ϕ = 0.04 , then the average Nusselt number decreased 14%. Finally, a sensitivity analysis was done to analyze the system's correctness and effectiveness to determine the significance of the specified parameters. [ABSTRACT FROM AUTHOR]

The phenomena of unsteady magnetohydrodynamics (MHD) natural convection flow in an inclined square cavity filled with nanofluid and containing a heated circular obstacle at its center with heat generation/absorption impact are examined numerically. The cavity's right and left walls are maintained at low temperatures, while the remaining walls are adiabatic. The volumetric external force, MHD, is applied across the inclined cavity. A penalty formulation-based finite element method is used to solve the nonlinear set of governing equations iteratively. The numerical scheme and results are validated through a comparison with the benchmark results, and it shows that our solutions are in good agreement with them. The results are shown in terms of contours of streamlines, isotherms, and average Nusselt number. It is observed that MHD alters the streamlines, isotherms, and average Nusselt number and dominates the flow as compared to any other physical parameter. The average Nusselt number is found sensitive to the central obstacle's size, and it reduces sufficiently when the radius of the inner cylinder increases. For all the parameters, the streamlines' symmetric pattern holds, such that the anti-clockwise cells on the left side of the cavity have their symmetric clockwise cells on the right side. [ABSTRACT FROM AUTHOR]

Natural convective flow and heat transfer around a locally heated circular cylinder kept in a rectangular enclosure are investigated. At first, a problem valid for a rectangular domain is formulated and then an analytical coordinate transformation is introduced to map the rectangular domain to the physical domain considered here. Based on the coordinate transformation, a set of governing equations is obtained which is further simulated by imposing appropriate conditions on the walls of the cavity and the inner solid bodies. Numerical solutions are validated through comparison of the present results with the available published data. It is found that streamlines and isotherms are greatly influenced by the width (w) and breadth (b) of the heat source and the Rayleigh number (Ra). The Nusselt number (Nu) is computed at the surface of the inner and outer cylinders, revealing that it grows considerably when controlling parameters w, b, and Ra are increased. The strength and number of the vortices generated within the velocity field heavily depend on the size and location of the outer cylinder. The span-wise local Nusselt number variation shows some sharp rises compared to the neighboring values in Nui and Nuo, which is due to the large temperature gradient at those points. [ABSTRACT FROM AUTHOR]

A mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of Ri = 1.0 \mathrm{Ri}=1.0 , the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic. [ABSTRACT FROM AUTHOR]

In this paper biomagnetic fluid flow in a rectangular enclosure is studied under the influence of applied magnetic field and temperature-dependent viscosity. An electrically conducting magnetic fluid (blood) is considered here which also exhibits magnetization. It is assumed that the magnetization M ¯ of the fluid is varying linearly with temperature T ¯ and magnetic field intensity H ¯ . The viscosity μ ¯ of biofluid is taken to be an exponential function of temperature. The mathematical model for the present problem results in a nonlinear and coupled system of equations and is given in stream function-vorticity-temperature formulation for the purpose of numerical treatment. Solutions are obtained iteratively by employing upwind scheme together with successive over relaxation method. Numerical results are presented in terms of average Nusselt number, streamlines, isotherms and vorticity function contours indicating that presence of magnetic source and viscosity variations influences the flow field considerably. It is found that the strength of the vortices and the temperature increases by magnifying the magnetic intensity and circular contours are generated extensively for the blood having variable viscosity. [ABSTRACT FROM AUTHOR]

The problem considered in this paper deal with the transient behavior of heat transfer by natural convection flow of fluid along an infinite vertical heated wavy surface. The governing equations are transformed into dimensionless form and solutions are obtained for the two dimensional flow for both pure (α = 0) and uneven surface (α ≠ 0). For pure vertical surface boundary layer equations are solved in the (i) upstream (small τ) (ii) downstream (large τ) and (iii) entire (0<τ<∞) regimes using analytical and numerical techniques. A very good agreement is found when results of above mentioned regimes are compared. Further, for wavy surface solutions are obtained for the entire time regime and results are discussed in terms of average Nusselt number coefficient and isotherms. Numerical results are served to reveal the influence of the physical parameters such as the Prandtl number, Pr, and wavy geometry, α, for the surface conditions. [ABSTRACT FROM AUTHOR]

In this paper bioconvection flow with heat and mass transfer of a water-based nanofluid containing gyrotactic microorganisms over a vertical wavy surface is investigated. The coupled nonlinear set of equations comprised of velocity, temperature, nanoparticle concentration and density of microorganisms is solved numerically by using implicit finite difference method. Flow characteristics are obtained in terms of skin friction coefficient, Nusselt number, Sherwood number and density number of microorganisms coefficient and are presented graphically by varying several controlling parameters. Interesting observations are recorded for the parameters: a , Nr , Lb and Rb . It is observed that the amplitude of the wavy surface has pronounced influence on the rates of heat and mass transfer, skin friction coefficient and density number of the microorganisms coefficient and all these quantities get augmented as the amplitude increases. [ABSTRACT FROM AUTHOR]

Natural convection laminar flow from an isothermal sphere immersed in a viscous incompressible optically dense fluid in the presence of radiation effects has been investigated. The governing boundary layer equations are transformed into a non dimensional form and the resulting nonlinear systems of partial differential equations are reduced to local non-similarity boundary layer equations, which are solved numerically by two distinct, efficient methods, namely, (i) implicit finite difference method together with the Keller box scheme and (ii) local non-similarity method. Numerical results of the velocity and temperature profiles of the fluid are presented. The results of the shearing stress and the heat transfer rate in terms of skin-friction coefficient and Nusselt number respectively are also presented for a wide range of the radiation-conduction parameter or Planck number Rd (=0.0, 1.0, 2.0, 3.0), the surface heating parameter θw (=1.1, 1.2, 1.4), and Prandtl number Pr (=7.0, 10.0, 15.0, 20.0). [ABSTRACT FROM AUTHOR]

The flow and heat transfer of electrohydrodynamics (EHD) natural convection in the annulus between a rectangular and a circular cylinder is studied numerically. The Rosseland diffusion approximation is used to account for the influence of heat radiation. The inner circular cylinder is considered to be heated and charged with a constant direct current (DC) voltage producing the electric field in the closed cavity. The fundamental Navier-Stokes equations and energy equation are coupled with Maxwell's and Gauss's law to establish the interaction between the velocity, temperature, and electric field for the dielectric fluid. While formulation, we presume that the charged fluid is ideal so that the effect of magnetic induction is negligible. A couple of transformations are used to convert the governing equations into the most appropriate form suitable for implementing the iterative finite difference scheme. According to the findings, the electric field and thermal radiations have a considerable impact on the flow field within the cavity. For instance, an increment in the charge diffusivity number, and the radiation parameter, the intensity of the streamlines, enhances significantly. The isotherms and isolines of electric charge density provide credible information about the heat flow and influence of charge injection. Moreover, the locally distributed Nusselt number at the inner and outer cylinders confirms that thermal radiation is the dominant mode of heat transfer. [ABSTRACT FROM AUTHOR]

• MHD natural convection and entropy generation of non-Newtonian ferrofluid is investigated in a wavy cavity. • Hartmann number attenuates the rate of heat transfer and convective flow within the enclosure. • The addition of ferro-particle augments the heat transfer rate in shear-thickening cases. • Rayleigh number is directly proportional to the average Nusselt number and total entropy. • A new correlation for the average Nusselt number is proposed for the shear-thinning fluids. [Display omitted] Two-dimensional laminar magneto-hydrodynamic (MHD) natural convection flow of non-Newtonian ferrofluid has been investigated to understand the characteristics of heat transfer, streamlines, isotherms, and entropy generation in a wavy enclosure using the finite volume method (FVM). The horizontal boundaries of the cavity are assumed to be thermally adiabatic, while the temperatures of the left and right vertical walls are presumed to be T H and T C , respectively. The rheology of the nanofluid is represented through the power-law model, and the density variations due to thermal expansion lie within the framework of the Boussinesq approximation. Numerical simulations have been carried out for a range of dimensionless parameters such as Rayleigh number (R a = 10 3 , 10 4 , 10 5), Hartmann number (H a = 0 , 10 , 20), power-law index (n = 0.6 , 0.8 , 1.0 , 1.2 , 1.4), volume fraction (ϕ = 0 , 0.05 , 0.1), and Prandtl number P r = 6.8377. Results indicate that the isotherms of the shear-thinning fluid are dominated by thermal convection, whereas conduction is more pronounced for shear-thickening fluids. The average Nusselt number of the non-Newtonian ferrofluid increases with the attenuation of the Hartmann number and augmentation of the Rayleigh number, and in our entire simulation, the maximum value of N u ¯ , due to the addition of ferro-particles, is found to be 8.07. The power-law index has a remarkable influence on the streamlines, and ψ m a x tends to decrease when n is increased gradually from shear-thinning to shear-thickening fluid behavior. Moreover, it is revealed that the heat transfer rate of ferrofluid (ϕ =10%) increases up to 26% for the shear-thinning case and 25% for the shear-thickening case, under the influence of the magnetic field. Further, it is inferred that the irreversibility due to heat transfer, fluid friction, and magnetic field for the shear-thinning, Newtonian and shear-thickening ferrofluids, can be minimized based on the optimal parametric combination. The increment of Hartmann number results in 60% attenuation of total entropy for shear-thinning fluid and 9% diminution for the shear-thickening case. With the augmentation of the power-law index, the entropy generation is found to decrease by 80% in the absence of the magnetic field effect and by 54% in the presence of it. A new correlation for the average Nusselt number is proposed for the shear-thinning fluids and shows a good agreement between the computed and predicted results. [ABSTRACT FROM AUTHOR]