Time-dependent Free Convection Research Articles

MHD Free convection flows of Jeffrey fluid with Prabhakar-like fractional model subject to generalized thermal transport

This article examines the effects of magnetohydrodynamics and heat absorption on an incompressible Jeffrey fluid’ time-dependent free convection flow over an infinite, vertically heated plate with homogeneous heat flux. The constitutive equation for heat flow utilizes the Prabhakar-like fractional derivative. The Laplace transform technique obtains the precise solution for the momentum and thermal profiles. The typical case and well-known outcomes from the literature are retrieved as restraining cases. The graphical analysis of the impact of the flow and fractionalized parameters on the thermal and momentum profiles is presented. Additionally, a comparison is made between the ordinary model and the Prabhakar-like fractional model, which shows that the latter better captures the retention of the physical features of the problem. It is concluded that the Prabhakar-like fractional model is better suited for describing the memory effect of the thermal and momentum fields.

Unsteady Radiative Natural Convective MHD Nanofluid Flow Past a Porous Moving Vertical Plate with Heat Source/Sink.

In this research article, we investigated a comprehensive analysis of time-dependent free convection electrically and thermally conducted water-based nanofluid flow containing Copper and Titanium oxide (Cu and ) past a moving porous vertical plate. A uniform transverse magnetic field is imposed perpendicular to the flow direction. Thermal radiation and heat sink terms are included in the energy equation. The governing equations of this flow consist of partial differential equations along with some initial and boundary conditions. The solution method of these flow interpreting equations comprised of two parts. Firstly, principal equations of flow are symmetrically transformed to a set of nonlinear coupled dimensionless partial differential equations using convenient dimensionless parameters. Secondly, the Laplace transformation technique is applied to those non-dimensional equations to get the close form exact solutions. The control of momentum and heat profile with respect to different associated parameters is analyzed thoroughly with the help of graphs. Fluid accelerates with increasing Grashof number (Gr) and porosity parameter (K), while increasing values of heat sink parameter (Q) and Prandtl number (Pr) drop the thermal profile. Moreover, velocity and thermal profile comparison for Cu and -based nanofluids is graphed.

Time-dependent free convection motion and heat transfer in an infinite porous medium induced by a heated sphere

Buoyancy driven thermal convection due to the presence of a sphere of constant heat flux in an unbounded fluid-saturated porous medium is studied analytically. Transient and steady-state solutions have been obtained for the velocity and temperature fields in the form of series expansions in the Rayleigh number, which is based on the permeability of the porous medium and the heat flux from the sphere. All discussions are based on the assumptions that the flow is governed by Darcy's law and that the thermal Rayleigh number is small.

Transition to time-dependent free convection in an inclined air layer

The steadiness of free convection flow of air inside a rectangular tilted enclosure was investigated. The transition from a stationary to a non-stationary state was detected by measurement of the temperature within the air. The transition thresholds were plotted with respect to the Rayleigh number, the tilt angle and the aspect ratio. For the horizontal situation the results are in good agreement with previous data, but for tilted situation the lack of previous data makes valid comparisons difficult.

Time-Dependent Free Convection in Vertical Slots

Time-dependent free convective flow phenomena are investigated in slender vertical containers heated from below. Power-density spectra are calculated from time-dependent thermocouple signals. The range of oscillatory convective flow yields periodic, quasiperiodic, or stochastic structures. After stochastic flow, quasiperiodic and periodic oscillations reappear with increasing temperature difference. Finally, at even higher Rayleigh numbers, a stationary flow pattern develops.

Advanced numerical computation of two-dimensional time-dependent free convection in cavities

A two-dimensional time-dependent numerical computation method has been developed to determine laminar free convection in closed cavities and forced convection in ducts and open cavities. The transport equations for energy and vorticity are solved with the aid of the ADI-method, but the more recently established method of cyclic reduction is applied to the Poisson equation. The resulting implicit method remains stable up to a Rayleigh number of 10 12. Due to the acceptable large time step, the method is particularly qualified for transient problems with extremely slow changing properties. A transformation relation, q( x, ε), is proposed for sufficiently accurate determination of thermal and hydrodynamic boundary layers near the vertical side walls in cavities. The benefit of the present numerical computation technique has been demonstrated by solving two problems of free convection in a rectangular cavity, namely with differentially but uniformly heated side walls and with only one side wall non-uniformly heated.

Transient Free Convection From a Vertical Flat Plate

Abstract The method of characteristics is employed to obtain solutions to the time dependent free-convection equations of momentum and energy placed in integral form (Karman-Pohlhausen method). Two boundary conditions are considered for a vertical flat plate of infinite width and semi-infinite length which is initially at ambient temperature in quiescent fluid: (a) The plate is suddenly raised to a uniform higher temperature, and (b) the plate suddenly begins to produce a uniform heat flux at its surface. The results yield the time required for steady flow to be established as a function of position along the plate. Heat-transfer coefficients are obtained for the initial stage of motion during which the convective process is one dimensional. The approximate velocity and temperature profiles obtained from the analysis are compared with more precise solutions of the differential equations for the initial stage of motion and for steady state.