Unsteady Free Convection Flows Research Articles

Effects of fractional derivative and heat source/sink on MHD free convection flow of nanofluids in a vertical cylinder: A generalized Fourier's law model

This research looked at the unsteady free convection flows of an incompressible viscous fluid with heat/sink in a vertical cylinder containing a mixture of 47 nm alumina nanoparticles in water. The flow direction is subjected to a perpendicular magnetic field. The generalization entails taking into account a new version of the constitutive equation for thermal flux, known as the generalized Atangana-Baleanu derivative, which is based on the generalized time-fractional derivative with Mittag-Leffler kernel. Using the Laplace transform and the finite Hankel transform, closed forms of analytical solutions for temperature and velocity fields, represented with Bessel and generalized G–function of Lorenzo and Hartley functions, are determined. The generalized solutions are appropriate for particularizations to yield solutions corresponding to fractional derivatives with power-law kernel and exponential kernel. The Mittag-Leffler function is a one-parametric function. It is also possible to acquire the usual situation, which corresponds to classical Fourier's law. To compare models based on generalized Atangana-Baleanu, Atangana-Baleanu, Caputo, and Caputo-Fabrizio time fractional derivatives, numerical simulations produced with the program Mathcad are carried out and visually depicted.

Effects of Magnetohydrodynamics and Heat Transfer in Casson Fluid Through a Channel

Unsteady flow of Casson fluid past through a vertical channel has been studied by some researchers due to its importance of applications in science and technology. Therefore, the main purpose of this paper is to obtain exact solutions for unsteady free convection flows of Casson fluid with effects of magnetohydrodynamics (MHD) past through vertical channel. This paper is continued study from published article [18] with additional effects of magnetohydrodynamics (MHD). Dimensional governing equations are converted into dimensionless forms by using appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid, time, Prandtl number, Grashof number and magnetic field. Laplace transform method is used to solve the dimensionless equations with associated initial and boundary conditions. Solutions for velocity and temperature profiles are obtained. Skin friction and Nusselt number are also calculated. The obtained analytical results for velocity and temperature are plotted graphically to discuss the influence of dimensionless parameters on profiles. It is observed that fluid velocity increases with increases of Grashof number, Gr and time, t whereas it decreases with increases of Casson parameter, γ, magnetic field parameter, M and Prandtl number, Pr. Besides that, it is found that temperature profiles decrease with high value of Prandtl number, Pr while increases with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and it is found to be in a mutual agreement.

Heat transfer analysis in convective flows of fractional second grade fluids with Caputo–Fabrizio and Atangana–Baleanu derivative subject to Newtonion heating

Unsteady free convection flows of an incompressible differential type fluid over an infinite vertical plate with fractional thermal transport are studied. Modern definitions of the fractional derivatives in the sense of Atangana–Baleanu (ABC) and Caputo Fabrizio (CF) are used in the constitutive equations for the thermal flux. Exact solutions in both cases of the (ABC) and (CF) derivatives for the dimensionless temperature and velocity fields are established by using the Laplace transform technique. Solutions for the ordinary case and some well-known results from the literature are recovered as a limiting case. Expressions for Nusselt number and Skin friction coefficient are also determined. The influence of the pertinent parameters on temperature and velocity fields are discussed graphically. A comparison of ordinary model, and (ABC) and (CF) models are also depicted. It is found that memory of the physical aspects of the problem is well explained by fractional order (ABC) and (CF) models as compared to ordinary one. Further it is noted that the (ABC) model is the best fit to explain the memory effect of the temperature and velocity fields.

Unsteady Electromagnetic Free Convection Micropolar Fluid Flow through a Porous Medium along a Vertical Porous Plate

Unsteady electromagnetic free convection flows of two-dimensional micropolar fluid through in a porous medium parallel to a vertical porous plate have been investigated numerically. Similarity analysis has been used to transform the governing equations into its non-dimensional form by using the explicit finite difference method to obtain numerical solutions. Estimated results have been gained for various values of Prandtl number, Grashof number, material parameters, micropolar parameter, electric conductivity, electric permeability, thermal relaxation time and the permeability of the porous medium. The effects of pertinent parameters on the velocity, electric induction, magnetic induction, microrotation and temperature distributions have been investigated briefly and illustrated graphically.

Effects of double stratification and heat flux damping on convective flows over a vertical cylinder

Unsteady free convection flows of viscous fluids over a vertical circular cylinder are investigated by taking in consideration thermal and mass stratification and the thermal memory effects. The mathematical model of thermal transport is based on the fractional generalized Fourier's law for thermal flux with the kernel of power-law kind. In this model the histories of the temperature gradient influence the thermal and mass transport process and the fluid motion. On the cylinder's surface the temperature (or the thermal flux) and solute concentration are constant. Solutions in the transformed domain for the perturbation temperature and concentration and fluid velocity are determined using the Laplace transform coupled with the classical method for the ordinary non-homogeneous differential equations. The inverse Laplace transforms are obtained numerically by employing the Stehfest's algorithm. Solutions for the case corresponding to classical Fourier's law are obtained as particular case of general solutions by taking the memory parameter equal to zero. The influence of the thermal memory and of thermal and mass stratifications is numerically and graphically analyzed by using the software Mathcad 15.

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

We consider two unsteady free convection flows of a Bingham fluid when it saturates a porous medium contained within a vertical circular cylinder. The cylinder is initially at a uniform temperature, and such flows are then induced by suddenly applying either a new constant temperature or a nonzero heat flux to the exterior surface. As time progresses, heat conducts inwards and this may or may not overcome the yield threshold for flow. For the constant temperature case, flow begins immediately should the parameter, Rb, which is a nondimensional yield parameter, be sufficiently large. The ultimate fate, though, is full immobility as the cylinder eventually tends towards a new constant temperature. For the constant heat flux case, the fluid remains immobile but will begin to flow eventually should Rb be sufficiently large. The two cases have different critical values for Rb.

MHD free convection flow of a viscous fluid in a rotating system with damped thermal transport, Hall current and slip effects

Unsteady hydromagnetic free convection flows of a rotating incompressible viscous fluid over an infinite moving plate with fractional thermal transport are studied in the presence of heat source, Hall current and slip velocity effects. The modern definition of the fractional integral Caputo-Fabrizio operator with non-singular kernel is used in the constitutive equation for the thermal flux and closed form solutions for the dimensionless temperature and velocity components are established by using the Laplace transform technique. For comparison, the solutions for the ordinary fluid as well as those corresponding to the no-slip condition on the boundary are also determined. The influence of fractional, magnetic, Hall and rotation parameters as well as that of heat generation/absorption coefficient on the fluid motion and the heat transfer is graphically underlined and discussed. It is found that the damping of the thermal transport has significant influence on the fluid temperature and motion. The Hall current mainly affects the secondary flow.

Time-dependent hydromagnetic free convection nanofluid flows within a wavy trapezoidal enclosure

This paper considers unsteady MHD free convection flows of alumina (Al2O3)-water and single-walled carbon nanotube (SWCNT)-water nanofluids within a symmetrical wavy trapezoidal enclosure. Initially, the fluid within the enclosure has a constant cold temperature and is at rest. The temperature of the wavy bottom wall is suddenly raised to a constant hot temperature, while the top wall is thermally insulated. The temperature of the side walls is maintained at the initial cold temperature. The dimensionless governing equations with the corresponding initial and boundary conditions are solved using the mixed finite element method with polynomial pressure projection stabilization. The effects of Rayleigh number Ra and Hartmann number Ha on the nanofluid flow and heat transfer are investigated.

Unsteady MHD free convection nanofluid flows within a wavy trapezoidal enclosure with viscous and Joule dissipation effects

ABSTRACTThis article examines the unsteady magnetohydrodynamic free convection flows of Al2O3 (alumina)-water and single-walled carbon nanotube (SWCNT)-water nanofluids within a symmetrical wavy trapezoidal enclosure with viscous and Joule dissipation effects. The governing equations and the corresponding initial and boundary conditions are nondimensionalized and the resulting initial boundary value problem is solved using the mixed finite-element method with polynomial pressure projection stabilization. Streamline and isotherm plots are used to represent the numerical results for the velocity and temperature, respectively. The effects of time t, Hartmann number Ha, wall amplitude a, and solid volume fraction ϕ on the fluid flow and heat transfer are studied.

Unsteady thermal boundary layer flows of a Bingham fluid in a porous medium

In this paper we consider some unsteady free convection flows of a Bingham fluid when it saturates a porous medium. These flows are induced by suddenly raising the constant temperature of a vertical bounding surface from that of the uniform ambient value to a new constant level. As time progresses heat conducts inwards and this induces flow. We consider both a semi-infinite domain and a vertical channel of finite width. Of interest here are (i) how the presence of yield surfaces alters the classical results for Newtonian flows and (ii) the manner in which the locations of the yield surfaces change as time progresses.

Closed Form Solutions for Unsteady Free Convection Flow of a Second Grade Fluid over an Oscillating Vertical Plate

Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions.

Similarity models for unsteady free convection flows along a differentially cooled horizontal surface

AbstractA class of unsteady free convection flows over a differentially cooled horizontal surface is considered. The cooling, specified in terms of an imposed negative buoyancy or buoyancy flux, varies laterally as a step function with a single step change. As thermal boundary layers develop on either side of the step change, an intrinsically unsteady, boundary-layer-like flow arises in the transition zone between them. Self-similarity model solutions of the Boussinesq equations of motion, thermal energy, and mass conservation, within a boundary-layer approximation, are obtained for flows of unstratified fluids driven by a surface buoyancy or buoyancy flux, and flows of stably stratified fluids driven by a surface buoyancy flux. The motion is characterized by a shallow, primarily horizontal flow capped by a weak return flow. Stratification weakens the primary flow and strengthens the return flow. The flows intensify as the step change in surface forcing increases or as the Prandtl number decreases. Simple formulas are obtained for the propagation speeds, trajectories and the evolution of velocity maxima and other local extrema. Similarity-model predictions are verified through numerical simulations in which no boundary-layer approximations are made.

Unsteady Free-Convection Flow on a Vertical Oscillating Porous Plate With Constant Heating

In this paper, we consider the unsteady free-convection flows of a viscous and incompressible fluid near an oscillating porous infinite vertical plate (or wall) during the heating of the plate. The governing equations are solved in closed form by the Laplace transform technique, when the Prandtl number (Pr) of the fluid is arbitrary and the suction (or injection) is constant. This solution is applied for a special case of the constant heating effects from the harmonically oscillating plate. The resulting velocity and temperature are shown graphically and are also discussed for the case of air (Pr=0.71) or water (Pr=7.0) flows.

Exact solutions for the unsteady free convection flows on a porous plate with time‐dependent heating

AbstractThe unsteady free‐convection flows of a viscous and incompressible fluid near a porous infinite vertical plate (or wall) are investigated under an arbitrary time‐dependent heating of the plate. Exact solutions of this problem are obtained with the help of Laplace transform technique, when the plate is moving with an arbitrary time‐dependent velocity and for special cases of the impulsive and the accelerated heating effects. These solutions are given in closed form for arbitrary Prandtl number of the fluid and for the thermal porous wall with or without suction or injection. The particular cases of the thermal plumes which are responsible for atmospheric pollution are also discussed.

Unsteady MHD free-convection flows on a porous plate with time-dependent heating in a rotating medium

The three-dimensional unsteady free-convection flows of a viscous fluid near a porous infinite vertical plate in a rotating medium in the presence of a constant transverse magnetic field are investigated under an arbitrary time-dependent heating of the plate. By using the Laplace transform technique, the Green function of the problem is determined and exact solutions are obtained for special cases of the impulsive and the accelerated heating effect for an arbitrary Prandtl number. The thermal influence on skin friction at the plate and the displacement thickness of the boundary layers are discussed.

Unsteady MHD free-convection flows with time-dependent heating in a rotating medium

Unsteady free-convection flows near an infinite vertical plate in a rotating medium in the presence of a constant transverse magnetic field are investigated under an arbitrary time-dependent heating of the plate. By using the Laplace transform technique, the Green's function of the problem is determined and exact solutions are obtained for special cases of the time-dependent heating effect. The thermal influence on skin friction at the plate and the displacement thickness of the boundary layer are determined, and the structure of the thermal wave trains is discussed.

Transient free convection flow around two-dimensional or axisymmetric bodies

A general analysis of the effects of curvature and displacement in unsteady free convection flows around two dimensional or axi-symmetric bodies is considered by taking the surface temperature as a power function of time. The full Navier-Stokes equations including the buoyancy term are solved using the method of matched asymptotic expansions and complete analytical solutions are obtained for velocity and temperature distributions. The application of the present theory to particular body shapes is shown by considering the free convection flow past a horizontal circular cylinder and a sphere.