Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

This paper numerically investigates radiative magnetohydrodynamic mixed convection boundary layer flow of nanofluids over a nonlinear inclined stretching/shrinking sheet in the presence of heat source/sink and viscous dissipation. The Rosseland approximation is adopted for thermal radiation effects and the Maxwell-Garnetts and Brinkman models are used for the effective thermal conductivity and dynamic viscosity of the nanofluids respectively. The governing coupled nonlinear momentum and thermal boundary layer equations are rendered into a system of ordinary differential equations via local similarity transformations with appropriate boundary conditions. The non-dimensional, nonlinear, well-posed boundary value problem is then solved with the Keller box implicit finite difference scheme. The emerging thermo-physical dimensionless parameters governing the flow are the magnetic field parameter, volume fraction parameter, power-law stretching parameter, Richardson number, suction/injection parameter, Eckert number and heat source/sink parameter. A detailed study of the influence of these parameters on velocity and temperature distributions is conducted. Additionally the evolution of skin friction coefficient and Nusselt number values with selected parameters is presented. Verification of numerical solutions is achieved via benchmarking with some limiting cases documented in previously reported results, and generally very good correlation is demonstrated. This investigation is relevant to fabrication of magnetic nanomaterials and high temperature treatment of magnetic nano-polymers

Mathematical modelling of entropy generation in magnetized micropolar flow between co-rotating cylinders with internal heat generation

The present study investigates analytically the entropy generation in magnetized micropolar fluid flow in between two vertical concentric rotating cylinders of infinite length. The surface of the inner cylinder is heated while the surface of the outer cylinder is cooled. Internal heat generation (which arises in energy systems) is incorporated. The Eringen thermo-micropolar fluid model is used to simulate the micro-structural rheological flow characteristics in the annulus region. The flow is subjected to a constant, static, axial magnetic field. The surface of the inner cylinder is prescribed to be isothermal (constant temperature wall condition), whereas the surface of the outer cylinder was exposed to convection cooling. The conservation equations are normalized and closed-form solutions are obtained for the velocity, microrotation and temperature. These are thereafter utilized to derive the expressions for entropy generation number, Bejan number and total entropy generation rate. The effects of relevant thermo-physical parameters on the flow, heat and entropy generation rate are displayed graphically and interpreted at length. It is observed that the external magnetic force enhances the entropy production rate is minimum at the center point of the channel and maximum in the proximity of the inner cylinder. This causes more wear and tear at the surface of the inner cylinder. Greater Hartmann number also elevates microrotation values in the entire annulus region. The study is relevant to optimization of chemical engineering processes, nuclear engineering cooling systems and propulsion systems utilizing non-Newtonian fluids and magnetohydrodynamics

Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders

The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the cylinders are assumed to be of infinite length or periodic in the axial direction, in which cases heat transfer occurs only through conduction as in a solid. We here investigate numerically heat transfer and the onset of turbulence in such flows by using both periodic and no-slip boundary conditions in the axial direction. We obtain a simple linear criterion that determines whether the infinite-cylinder assumption can be employed. The curvature of the cylinders enters this linear relationship through the slope and additive constant. For a given length-to-gap aspect ratio there is a critical Rayleigh number beyond which the laminar flow in the finite system is convective and so the behaviour is entirely different from the periodic case. The criterion does not depend on the Prandtl number and appears quite robust with respect to the Reynolds number. In particular, it continues to work reasonably in the turbulent regime.Comment: 25 pages, 9 figure

Mixed Convection of Hybrid Nanofluids in an Annulus

 In this study, mixed convection in an annulus formed by two horizontal isothermal cylinder surfaces and filled with hybrid nanofluids was examined with Galerkin weighted residual finite element method. The outer cylinder is rotating and inner cylinder is stationary. Influence of Rayleigh number, angular rotational speed of the outer cylinder, eccentricity of the inner cylinder, solid volume fractions of different nanoparticles (alumina, copper, hybrid particles between 0 and 0.02) on the fluid flow and heat transfer characteristics were analyzed. It was observed that average heat transfer enhances with Rayleigh number, solid volume fractions of nanoparticles and eccentricity ratio and reduces as the angular rotational speed of the outer cylinder increases. Adding nanoparticles was found to be advantageous for lower values of Rayleigh number and higher values of angular rotational speed. At the highest volume fraction of Cu nanoparticles, average Nusselt number increases by 31.75 % when the inner cylinder center moves in +y direction. Nanofluid with hybrid nanoparticles gives heat transfer rates which are higher than that of with alumina and lower than that of with copper nanoparticles for the same volume fraction

Effects of Arc-Shaped Partitions in Corners of a Shallow Cavity on Natural Convection

I n this study, a numerical analysis carried out to determine the effects of arc-shaped partitions in corners of a shallow cavity on heat transfer which is natural convection and fluid flow. Partitions are accepted as conductive and two different partitions materials are chosen as wood and aluminum. The finite volume approach is used to discretize the governing equations for Rayleigh numbers Ra and shape ratio of the arc-shaped partition. It is found that arc-shaped partitions have effect on characteristic parameters of fluid flow and heat transfer. Specially, aluminum arc-shaped partition affects the average heat transfer enhancement, because it has high heat transfer coefficient. Also, possibilities of occurring dead regions are examined and streamlines obtained for without partitions and high Rayleigh numbers which are Ra=105 and Ra=106 show that dead regions occur in corners of the shallow cavity. Results obtained from the analysis using partitions and considering different Rayleigh numbers and partition materials show that using partition which is arcshaped prevent occurring dead region

Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system

In this paper, of primary concern is a time-delayed thermoacoustic system, viz. a horizontal Rijke tube. A continuation approach is employed to capture the nonlinear behavior inherent to the system. Unlike the conventional approach by the Galerkin method, a dynamic system is naturally built up by discretizing the acoustic momentum and energy equations incorporating appropriate boundary conditions using a finite difference method. In addition, the interaction of Rijke tube velocity with oscillatory heat release is modeled using a modified form of King’s law. A comparison of the numerical results with experimental data and the calculations reported reveals that the current approach can yield very good predictions. Moreover, subcritical Hopf bifurcations and fold bifurcations are captured with the evolution of dimensionless heat release coefficient, generic damping coefficient and time delay. Linear stability boundary, nonlinear stability boundary, bistable region and limit cycles are thus determined to gain an understanding of the intrinsic nonlinear behaviors

Natural convection in a trapezoidal cavity with an inner conductive object of different shapes and filled with nanofluids of different nanoparticle shapes

Natural convection in a trapezoidal cavity having different conductive obstacles which are portions of a full circular object and filled with different shaped nanoparticles (spherical, blade and cylindrical) was numerically investigated. The side walls of the trapezoidal cavity are kept at constant hot and cold temperatures, while the top and bottom walls are assumed to be adiabatic. The governing equations are solved with finite element method. The effects of the Rayleigh number (between 104 and 106), inclination angle of the side walls (between 0° and 20°), thermal conductivity ratio (between 0.01 and 100), solid volume fraction of the nanoparticles (between 0 and 0.04) and nanoparticle shape (spherical, blade and cylindrical) on the fluid flow and heat transfer characteristics were studied in detail. It was observed that the shape of the obstacle is very effective to change the heat transfer characteristic for lower values of Rayleigh number. Thermal conductivity ratio influences the heat transfer characteristics slightly. Averaged Nusselt number increases linearly with nanoparticle volume fraction and the slope of the curves is highest for the cylindrical nanoparticle and it is not affected by the obstacle types. Averaged Nusselt number enhancements are in the range of 13 and 16% when cylindrical nanoparticles are used instead of spherical ones with different obstacle shapes for thermal conductivity ratio of 0.01 and 100. Shiraz University 2017