Unsteady Natural Convection Flow within a Thermally Stratified Air-Filled Rectangular Cavity

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.

We consider the optimal control of unsteady natural convective flow of reactive viscous fluid with heat transfer. It is assumed that Newton's law governs the heat transfer within an exothermic reaction under Arrhenius kinetics and Navier slip condition on the lower surface of the channel. The flow is examined in a vertical channel formed by two infinite vertical parallel plates, with a distance (H) between them. Time-dependent natural convective slip flow of reactive viscous fluid and heat transfer equations are solved in a unit interval using the Galerkin-Finite Element Method (FEM) with quadratic finite elements in space and the implicit Euler method in time. The direct solutions are obtained for testing various values of the problem parameters: the Biot number, the Frank Kamenetskii parameter, the Navier slip parameter, and the computation of the skin friction and the Nusselt number $(Nu)$. The optimal control problem is designed for the momentum and energy equations to derive the fluid-prescribed velocity and temperature profiles by defining controls on the boundary of the domain in two ways: (a) controls are formulated as parameters in the boundary conditions, such as slip length and Biot number; (b) controls are assigned as time-dependent functions in the boundary conditions, representing the slip velocity and the heat transfer rate. Following a discretize-then-optimize approach to the control problem, optimization is performed by the SLSQP (Sequential Least Squares Programming) algorithm, a subroutine of SciPy. Numerically simulated results show that the proposed approach successfully drives the flow to prescribed velocity and temperature profiles.

Unsteady natural convection from a horizontal annulus filled with a porous medium

The unsteady MHD free convective boundary-layer flow along an impulsively started semi-infinite vertical plate with variable heat flux and mass transfer have been investigated numerically. The effects of chemical reaction, thermal radiation and Joule heating are incorporated in the governing equations. Crank-Nicolson finite-difference method is used to solve the governing coupled non-linear partial differential equations. The influence of thermal radiation, chemical reaction and Joule heating on flow characteristics are presented graphically and discussed in detailed. To validate the present numerical results, a comparison study has been performed with the previously published results and found that the results are in excellent agreement. It is found that the local Nusselt and Sherwood numbers decreases with the intensification of magnetic field and the local Sherwood number slightly decreases with the increase of radiation parameter.

Based on a particular property of some liquid crystal to reflect a specific wavelength for a specific temperature, Particle Image Velocimetry and Thermometry (PIVT) is a method allowing to measure simultaneously velocity and temperature fields. In a first part, this study discusses PIVT calibration methods and especially the effect of liquid crystal particle deposition on hue and intensity response. An experimental set-up is designed and the results confirm the high variations of intensity response with time and the need to use a simple relationship between hue and temperature. In a second place, these results are used to apply PIVT to an unsteady natural convection flow in a cavity containing an internal heat source.

Unsteady natural convection flow due to fractional thermal transport and symmetric heat source/sink

Unsteady natural convection flow and heat transfer utilizing magnetic nanoparticles in the presence of a sloping magnetic field inside a square enclosure are simulated numerically following nonhomogeneous dynamic model. Four different thermal boundary conditions: constant, parabolic in space, sinusoidally in space, and time for the bottom hot wall are considered. The top wall of the enclosure is cold while the vertical walls are thermally insulated. Galerkin weighted residual finite element method is used to solve the governing nondimensional partial differential equations. For simulations, 12 types of nanofluids consisting magnetite (Fe3O4), cobalt ferrite (CoFe2O4), Mn–Zn ferrite (Mn–ZnFe2O4), and silicon dioxide (SiO2) nanoparticles along with water, engine oil, and kerosene as base fluids are used. The effects of the important model parameters such as Hartmann number, magnetic field sloping angle, and thermal Rayleigh number on the flow fields are investigated. The results show that the average Nusselt number, shear rate, as well as the nanofluid velocity decreases as the Hartmann number intensifies. Moreover, the rate of heat transfer in nanofluid exaggerates with the increase of the thermal Rayleigh number and the magnetic field sloping angle. Sinusoidally varied in space thermal boundary condition at the bottom wall provides the highest average Nusselt number and the shear rate compared to the other types of thermal boundary conditions studied here. For this case, the highest average Nusselt number is obtained for the Mn–ZnFe2O4–Ke nanofluid. On the other hand, Fe3O4–H2O nanofluid delivers the highest shear rate compared to the other premeditated nanofluids.

The fundamental study of the phenomenon of natural convective heat and mass transfer near a vertical plate in the presence of porous medium is investigated. The fluids considered in the discussion are air and water. The unsteady, coupled, non-linear partial differential equations are solved numerically by Crank Nicolson scheme. The influence of various parameters like velocity, temperature and concentration are analyzed. The skin friction, the Nusselt number, the Sherwood number, average skin friction, average Nusselt number and average Sherwood number are also presented graphically for both air and water. It has been observed that velocity components increase with permeability parameter where as temperature and concentration decreases with it. An analysis is performed to check the stability and the convergence of the finite difference scheme which converges faster and unconditionally stable.

Unsteady time fractional natural convection flow of incompressible viscous fluid due to arbitrary velocity with radiation and Newtonian heating is investigated. By introducing dimensionless variables and functions, the resulting equations are solved by the Laplace transform technique. Exact solutions for temperature and velocity fields are obtained by Caputo time fractional derivatives in dimensionless form, and they are expressed in terms of Robotnov–Hartley function and Wright’s function. The rate of heat transfer on plate is obtained in terms of Nusselt number. Some known solutions from the existing literature are obtained as limiting case when \(\alpha = 1\). At the end, we have seen the significant influence of fractional parameter \(\alpha\) on the temperature and velocity graphically and observed that it has shown an opposite behavior on temperature and velocity for small and large values of time t, respectively. This shows that how fractional parameter \(\alpha\) affects the fluid flow.

A numerical investigation of unsteady hydromagnetic natural convection flow of a viscous, incompressible, electrically conducting and heat absorbing fluid past an impulsively moving vertical plate with ramped temperature embedded a porous medium in the presence of thermal diffusion is carried out. The governing equations are solved numerically by Crank-Nicolson implicit finite difference scheme. The numerical solution for fluid velocity and fluid temperature are depicted graphically whereas the numerical values of skin friction and Nusselt number are presented in tabular form for various values of pertinent flow parameters. Natural convection flow near a ramped temperature plate is also compared with the flow near an isothermal plate.

This paper introduces an innovative approach for modelling unsteady incompressible natural convection flow over an inclined oscillating plate with an inclined magnetic effect that employs the Atangana-Baleanu time-fractional derivative (having a non-singular and non-local kernel) and the Mittag-Leffler function. The fractional model, which includes Fourier and Fick's equations, investigates memory effects and is solved using the Laplace transform. The Mittag-Leffler function captures power-law relaxation dynamics, which improves our understanding of thermal and fluid behaviour. Graphical examination shows the influence of fractional and physically involved parameters, leading to the conclusion that concentration, temperature, and velocity profiles initially grow and then decrease asymptotically with time. Moreover, the study emphasizes the impact of effective Prandtl and Schmidt numbers on temperature, concentration, and velocity levels in the fluid.

This study analyzes time‐dependent magnetohydrodynamics natural convective flow of a viscous incompressible fluid in an annulus with ramped motion of the boundaries. The governing momentum and energy equations are solved analytically, in terms of the modified Bessel function of the first and second kinds. The influence of governing parameters such as the Hartman number, radius ratio, Grashof number, heat absorption parameter, and Prandtl number are discussed with the help of line graphs. It is found that the Hartmann number has a retarding effect on fluid velocity when K = 0.0 and K = 0.5, while the reverse effect is noticed when K = 1.0. The Hartman number also decreases the mass flow rate for all cases of while it enhances the skin friction at the inner surface of the outer cylinder. It increases the skin friction at the outer surface of the inner cylinder when K = 1.0 and K = 0.0, but decreases the skin friction at the outer surface of the inner cylinder when K = 0.5.

Numerical analysis is carried out on an unsteady MHD natural convective boundary layer flow of a nanofluid past an isothermal vertical plate in the presence of thermal radiation. The governing partial differential equations are solved numerically by an efficient, iterative, tri-diagonal, semi-implicit finite-difference method. In particular, we investigate the effects of radiation, magnetic field and nanoparticle volume fraction on the flow and heat transfer characteristics. The nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. The numerical results indicate that in the presence of radiation and magnetic field, an increase in the nanoparticle volume fraction will decrease the velocity boundary layer thickness while increasing the thickness of the thermal boundary layer. Meanwhile, an increase in the magnetic field or nanoparticle volume fraction decreases the average skin-friction at the plate. Excellent validation of the present results has been achieved with the published results in the literature in the absence of the nanoparticle volume fraction.

An analysis of unsteady MHD natural convective flow, transfer of mass, and radiation past linearly accelerated slanted plate inserted in an immersed permeable medium with uniform permeability, variable temperature, and concentration within the sight of a slanted magnetic field has been done. The novelty of the current examination is to analyze the effect of a slanted magnetic field on the flow phenomena with heat source/sink and destructive reaction for linearly accelerated slanted plate. The governing equations have been solved by using Laplace transform strategy. The estimations of flow velocity, concentration, and temperature are exhibited graphically, while local skin friction, mass, and heat transfer rates are put on view in tabular form for different values of relevant stream parameters. It is fascinating to observe that the raise of inclination angle of an applied magnetic field diminishes both velocity profiles and local skin friction.

Natural convection in square enclosure induced by inner circular cylinder with time-periodic pulsating temperature