Effect of uniform inclined magnetic field on natural convection and entropy generation in an open cavity having a horizontal porous layer saturated with a ferrofluid

Numerical analysis of natural convection combined with entropy generation in a square open cavity partially filled with a porous medium has been performed for a ferrofluid under the effect of inclined uniform magnetic field. Governing equations with corresponding boundary conditions formulated in dimensionless stream function and vorticity using Brinkman–extended Darcy model for porous layer have been solved numerically using finite difference method. An influence of key parameters on ferrofluid flow and heat transfer has been analyzed. It has been found that an inclusion of spherical ferric oxide nanoparticles can lead to a diminution of entropy generation in the case of similar flow and heat transfer structures.     

The cooling of a plate by combined thermal radiation and convection

The cooling of a plate by a combination of thermal radiation and free or forced convection is a commonly occurring process for which no analytical solution exists. Elaborate numerical solutions are possible but there is an obvious need for a more accessible solution which may be used for engineering calculations such as the estimation of thermal stresses. This paper describes the development of such a solution using the heat balance integral technique. The accuracy is demonstrated to be acceptable for engineering purposes and the solution requires only simple arithmetic operations.     

Mixed convection flow in an inclined enclosure under magnetic field with thermal radiation and heat generation

The influence of thermal radiation and heat generation on an unsteady two-dimensional natural convection flow in an inclined enclosure heated from one side and cooled from the adjacent side under the influence of a magnetic field using staggered grid finite-difference technique has been studied. The governing equations have been solved numerically for streamlines, isotherms, local Nusselt numbers and the average Nusselt number for various values of thermal radiation and heat generation parameters by considering three different inclination angles and magnetic field directions, keeping the aspect ratio fixed. The results indicate that the flow pattern and temperature fields are significantly dependent on the above mentioned parameters. It is found that magnetic field suppresses the convection flow and its direction influences the flow pattern which results in the appearance of inner loop and multiple eddies.     

Unsteady numerical computation of combined thermally and electromagnetically driven convection in a rectangular cavity

A series of numerical simulations of fluid flow and heat transfer based on two-dimensional unsteady model of MHD thermal convection have been performed. The computational domain is a rectangular cavity with an aspect ratio of 2, filled with electrically conductive fluids at different Prandtl numbers. The process medium is assumed to be subjected to DC heating by a pair of plate electrodes located at the cavity sidewalls. The top and bottom walls are assumed to be electrically insulated. The upper boundary of the cavity is cooled by the atmosphere and all the other walls are kept thermally insulated. For Pr = 1 and Pr = 0.1 fluid, the simulation results show that the fluid flow and heat transfer rate become time independent and reach steady-state conditions. On the contrary, for Pr = 0.01 fluid, it is found that physically realizable periodic oscillation flow evolves, significantly affecting the heat transfer. These transient characteristics of velocity and temperature fields are presented graphically.     

Turbulent free convection in a porous square cavity using the thermal equilibirum model

This work investigates the influence of porosity and thermal conductivity ratio on the Nusselt number of a cavity filed with a fluid saturated porous substrate. The flow regime considered intra-pore turbulence and a macroscopic k-ε model was applied. Heat transfer across the cavity assumed the hypothesis of thermal equilibrium between the solid and the fluid phases. Transport equations were discretized using the control-volume method and the system of algebraic equations was relaxed via the SIMPLE algorithm. Results showed that when using the one energy equation model under the turbulent regime, simulated with a High Reynolds turbulence model, the cavity Nusselt number is reduced for higher values of the ratio k_s/k_f as well as when the material porosity is increased. In both cases, conduction thorough the solid material becomes of a greater importance when compared with the overall transport that includes both convection and conduction mechanisms across the medium.     

Conjugate thermal and mass diffusion effect on natural convection flow in presence of strong cross magnetic field

Analysis of magnetohydrodynamic natural convection boundary layer flow of an electrically conducting incompressible fluid along a heated vertical flat plate in the presence of strong cross magnetic field has been discussed. The boundary layer equations governing the flow are transformed to a convenient dimensionless form by using stream function formulation (SFF) and the numerical solution of which is obtained by employing an efficient marching order implicit finite difference scheme over the entire range of local Hartmann parameter, ξ. The behavior of ξ is also studied near the leading edge of the plate by embracing series solution method. However, asymptotic solution for large values of ξ is established analytically, based on the inverse coordinate expansion method. Here, consideration has been given to those fluids which served as liquid metals, by taking Pr << 1. Discussion has been carried out over the results obtained for small, large and all ξ regimes, for different physical parameters in terms of shear stress, τ_w, rate of heat transfer, q_w, and rate of mass transfer, m_w, in the strong cross magnetic field. Influence of local Hartmann parameter ξ and Schmidt number, Sc, on velocity, temperature and concentration distributions are also shown graphically. In addition, comprehensive interpretation of energy and species distributions is also given in terms of heatlines and masslines, respectively.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Mechanical and thermal characteristics of a mixed convection boundary-layer flow in a saturated porous medium

The mixed convection over a vertical surface adjacent to a fluid saturated porous medium and having the temperature distribution T_w(x) = T_∞ + T₀ · (x/L)^λ is considered in the boundary-layer and Boussinesq approximation for the value λ = −1/3 of the power-law exponent. It is shown that in the whole range −∞ < ε < +∞ of the mixed convection parameter ε an infinite number of solutions exist which are associated with different values of the dimensionless wall temperature gradient θ′(0) ≡ h. These solutions are investigated analytically and numerically in detail. The effect of a thermodynamic requirement on the existence domain of the physical solutions is discussed in the context of results reported by other authors.     

Combined effect of magnetic field and thermal dispersion on a non-darcy mixed convection

This paper is devoted to investigate the influences of thermal dispersion and magnetic field on a hot semi-infinite vertical porous plate embedded in a saturated Darcy-Forchheimer-Brinkman porous medium. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The effects of transverse magnetic field parameter (Hartmann number Ha), Reynolds number Re (different velocities), Prandtl number Pr (different types of fluids) and dispersion parameter on the wall shear stress and the heat transfer rate are discussed.     

Hydro-magnetic combined convection in a lid-driven cavity with sinusoidal boundary conditions on both sidewalls

Mixed convection in a square cavity of sinusoidal boundary temperatures at the sidewalls in the presence of magnetic field is investigated numerically. The horizontal walls of the cavity are adiabatic. The governing equations are solved by finite-volume method. The results are obtained for various combinations of amplitude ratio, phase deviation, Richardson number, and Hartmann number. The heat transfer rate increases with the phase deviation up to ? = π/2 and then it decreases for further increase in the phase deviation. The heat transfer rate increases on increasing the amplitude ratio. The flow behavior and heat transfer rate inside the cavity are strongly affected by the presence of the magnetic field.     

Nusselt number for the natural convection and surface thermal radiation in a square tilted open cavity

In this communication, the numeric results of the heat transfer by natural convection and surface thermal radiation in a tilted 2D open cavity are presented. This study has importance in the thermal design of receivers for solar concentrators. The opposite wall to the aperture in the cavity holds a constant temperature of 500 K, while the temperature of the surrounding fluid interacting with the aperture is 300 K. The other walls are kept insulated. The results in the steady state are obtained for a Rayleigh range from 10⁴ to 10⁷ and for an inclination angles range of the cavity from 0° to 180°. The results show that the Nusselt numbers increase with the Rayleigh number except the convective Nusselt number for 180°, where it stays almost constant. The convective Nusselt number changes substantially with the inclination angle of the cavity, while the radiative Nusselt number is insensitive to the orientation change of the cavity.     

Experimental and numerical studies on periodic convection flow and heat transfer in a lid-driven arc-shape cavity

This paper presents experimental and numerical studies on periodic convection flow and heat transfer in a lid-driven arc-shape cavity with temperature differential. Three cases were considered: Gr = 2 × 10⁵, 5 × 10⁵ and 1.2 × 10⁶ at Re = 100 (Gr = Grashof number; Re = Reynolds number). The mathematical model was proposed in our previous study. The current study performs an experiment to validate this model, to corroborate the existence of the periodic flow, and to more deeply probe the internal flow and temperature characteristics. The experimental setup primarily comprised an arc-shape cavity, a moving lid, a thermo-system, a smoke generator and an image acquisition system. The periodic convection flow in the cavity was visualized using kerosene smoke. The numerical and experimental results consistently reveal that the periodic flow pattern was observed in the case with Gr = 5 × 10⁵, whereas the steady-state flow pattern took place in the other two cases (Gr = 2 × 10⁵ and Gr = 1.2 × 10⁶). The numerical simulation produced reasonable and satisfactory agreement with the experiment for the periodic flow pattern and period. The difference between the predicted and measured periods is less than 5%. The transport properties, such as average kinetic energy, overall Nusselt number, stream function, phase space trajectory, local kinetic energy, velocity history and temperature distribution, were further analyzed and discussed in this paper. The proposed numerical simulation not only confirms the experimental observation, but also enhances the understanding of periodic convection in an arc-shape cavity subjected to a moving lid and temperature differential.     

Convective heat transfer of ferrofluid in a lid-driven cavity with a heat-conducting solid backward step under the effect of a variable magnetic field

The effect of variable magnetic field on the mixed convective flow of a ferrofluid within a lid-driven cavity has been analyzed numerically. A heat-conducting solid block is located in the bottom part of the cavity. Governing partial differential equations have been formulated taking into account that the magnetic source is a point source located over the moving lid. Analysis has been performed for a wide range of Hartmann number, nanoparticles volume fraction, and magnetic number. It has been found that the growth of the magnetic number leads to the heat transfer enhancement.     

Projection- and characteristic-based operator-splitting simulation of mixed convection flow coupling heat transfer and fluid flow in a lid-driven square cavity

ABSTRACT

Mixed convection flow in a 2D rectangular cavity is simulated by a novel finite element method, namely the projection- and characteristic-based operator-splitting algorithm. In each time step, the Navier–Stokes equations are split as follows: the diffusion part, the convection part by applying operator-splitting method, and the Poisson’s equation by adopting projection method. The implicit diffusion part is solved by the preconditioned conjugate gradient (PCG) method, whereas characteristic method is applied for the convection part in a multistep explicit scheme. The characteristic Galerkin approach is used to solve the energy equation. To validate the model, lid-driven cavity flow and natural convection flow are simulated.     

Mixed convection of transient MHD stagnation point flow over a stretching sheet with quadratic convection and thermal radiation

This study investigates the influence of quadratic (nonlinear) convection in transient magnetohydrodynamic (MHD) combined convection over a two-dimensional stretching sheet. It explores the effects of thermal radiation, suction, and heat sources or sinks. The Crank–Nicholson implicit finite difference method is employed for numerical computations. The significance lies in considering secondary convection, which is crucial in understanding nonlinear convective effects affecting flow and heat transfer properties. The study aims to advance our comprehension of how secondary convection impacts the overall system behavior. Through numerical calculations validated against existing literature, strong agreement is demonstrated. The study evaluates secondary convection effects, magnetic, buoyancy, gravitational parameters, Prandtl number, and radiation parameters. Notably, strong quadratic convection alters flow patterns, affecting velocity and temperature profiles. Moreover, it is observed that when increasing the nonlinear (quadratic) convective factors, the temperature profile increases for $$ and decreases for $$. The prevalence of nonlinear or second-order convection highlights magnetic dominance. In essence, this research enhances our understanding of complex convection interactions in MHD flow, shedding light on the role of secondary convection in shaping system behavior.