Inter-phase Heat Transfer Parameter Research Articles

Numerical simulation of Darcy–Forchheimer flow of Casson ternary hybrid nanofluid with melting phenomena and local thermal non-equilibrium effects

The Casson fluid flow over a stretching sheet is studied in this work in the presence of porous media with melting heat transfer and chemical reaction, combining nanoparticles of Ti4Al6V,AA7072 and AA7075 with a base fluid of sodium alginate (NaAlg). The porous medium Darcy Forchheimer effect is included in the momentum equation. Through the effects of melting, the process of heat transfer is described. In order to explore the features of heat transmission in the absenteeism of LTECs (local thermal equilibrium conditions), the current study employs a mathematical model that has been simplified. For both the solid and liquid phases, the LTNE model yields two different fundamental thermal gradients. This proposed model compares the YOM (Yamada-Ota model) and XM (Xue model), two well-known trihybrid nanofluid models, in terms of performance. After applying the proper transformations, modulated non-linear PDEs (partial differential equations) are simplified in ODEs (ordinary differential equations) and the bvp4c method is used to solve them numerically. A graphic discussion of the relevant factors' significance on the pertinent fields has been presented. It is observed that the Casson ternary hybrid nanofluid temperature and velocity distributions predominate at higher melting parameter. The solid phase's heat transport rate rises with an upsurge in the interphase heat transfer parameter.

Influence of variable viscosity and local thermal non-equilibrium on nanofluid flow stability in an inclined porous channel

This study delves into the influence of local thermal non-equilibrium and changing viscosity on the stability of nanofluid flow in an inclined porous channel. The flow in the porous region governs Brinkman’s equation as well as a three-field model for temperature, with each field constitute the fluid, particle, and solid-matrix phases individually. Eigenvalue problem for a perturbed state is obtained using a normal mode analysis, and the problem is afterwards solved by the utilization of the Chebyshev spectral collocation method. Impact of various local thermal non-equilibrium parameters, critical Rayleigh number, and associated wavenumber are graphically displayed. Increasing values of the modified thermal capacity ratios, modified thermal diffusivity ratios, variable viscosity parameter, and channel inclination decrease the system’s stability for the interphase heat transfer parameter, which means these parameters destabilize the flow. Flow is most unstable when the channel is vertically oriented and the variable viscosity parameter ([Formula: see text]) = 0.5.

The role of local thermal non-equilibrium on the instability analysis in the presence of variable gravity field with throughflow

The influence of variable gravity on the stability analysis has been investigated in a horizontal porous region with throughflow under a local thermal non-equilibrium (LTNE) situation. Flow inside the porous region is considered to be followed by the Darcy model. Also, the linear varying gravity field with height and nonlinear (parabolic, cubic, and exponential) changing gravity field depth have been considered to address the investigation. The obtained eigenvalue problem for the perturbed state is solved via bvp4c technique in MATLAB. Finally, we investigated the convective boundaries of the system due to the governing parameters, such as gravity variation parameter (λ), porosity-modified conductivity ratio (γ), interphase heat transfer parameter (H), and throughflow parameter (Q). The outcomes assure that the interphase heat transfer parameter has a significant impact on the breakdown of the convection inside of its intermediate range, while the local thermal equilibrium (LTE) state occurred when H converges both the limiting cases, i.e. H→0 and H→∞. It has also been observed that the gravity variation parameter and throughflow parameter have a stabilizing effect, whereas the porosity-modified conductivity ratio destabilizes the flow. Further, it is distinguished that the instability boundaries are unchanged by H when γ≥10. In addition, the flow field is more delayed for exponential changing gravity field, whereas more advanced for cubic varying gravity field.

Natural convection in a differentially heated cavity filled with a Brinkman bidisperse porous medium

PurposeThe purpose of this work is the study of the steady free convection in a square differentially heated cavity filled by a Brinkman bidisperse porous medium. An appropriate mathematical model considering the Brinkman, momentum and energy interphase terms is proposed. The dependence of the stream functions, isotherms and of the Nusselt numbers on the governing parameters is analysed.Design/methodology/approachThe both phases of flow and heat transfer are solved numerically using a modified finite difference technique. The algebraic system obtained after discretization is solved using the SOR method. The results are found to be in a significant agreement with the ones presented by the literature for a Darcy bidisperse porous medium and a Brinkman monodisperse porous medium.FindingsThe effects of the governing parameters on stream functions, isotherms and Nusselt numbers are discussed. It has been found that in the case of the Brinkman bidisperse model, the Nusselt numbers decrease compared to the Darcy model, and this behaviour is significant in comparison to the Brinkman monodisperse case.Originality/valueA mathematical model for the free convection inside a cavity filled by a non-Darcy bidisperse porous medium, based on the Brinkman equation, is used. The effect of Darcy number, Rayleigh number, modified inter-phase heat transfer parameter, modified thermal conductivity ratio and the inertial parameters is studied. To the best of the authors’ knowledge, this problem has not been studied before, and the results are new and original.

THE EFFECT OF LOCAL THERMAL NON-EQUILIBRIUM AND MAGNETIC FIELD ON THE STABILITY IN A VERTICAL CHANNEL FILLED WITH NANOFLUID

In this investigation, the influence of local thermal non-equilibrium (LTNE) on the onset of convection in a channel occupied with nanofluid was examined. The flow took place in the presence of a transverse magnetic field. The Buongiorno and two-field models (each independently signifying the fluid and particle phases) were used for the nanofluid and energy equation, respectively. A normal mode analysis was applied to obtain the eigenvalue problem for the disturbed state, which was solved using the Chebyshev spectral collocation technique. The effects of the governing parameters on the Rayleigh number and corresponding wavenumber are presented graphically. It was noticed that the concentration Rayleigh number, inter-phase heat transfer parameter, and modified diffusivity ratio had a destabilizing effect, while the modified thermal capacity ratio, thermal diffusivity ratio, Lewis number, and modified particle density increment had a stabilizing effect on the system.

LOCAL THERMAL NON-EQUILIBRIUM CONDITION FOR THE FLOW OF WALTERS-B FLUID OVER A SHEET SATURATED IN A POROUS MEDIUM

Local thermal non-equilibrium (LTNE) has garnered significant interest in engineering applications like electronic cooling, heat pipes, nuclear reactors, drying technology, and multiphase catalytic reactors. Owing to this, the study numerically emphases on the LTNE effects on the flow of Walters-B liquid over a stretching sheet with Dufour and Soret effects. The LTNE model, which creates distinct thermal profiles for both solid and liquid phases, is utilized to formulate the energy equations, which constitutes the novelty of the present study. The governing equations for the flow assumptions are transformed to ordinary differential equations using the apt similarity transformations. The Runge-Kutta approach and the shooting technique are then used to numerically solve these reduced equations. The significant results of the current analysis are that an upsurge in Dufour number diminutions the heat transport in liquid phase. The increase in Soret number advances the mass transport. The augmented values of viscoelastic parameter drop down the velocity, but advance the fluid phase heat transference. Finally, the heat transport of the liquid phase increases and solid phase drops as inter-phase heat transfer parameter rises.

LTNE Effects on Triple-Diffusive Convection in Nanofluids

Abstract Triple-diffusive convection for nanofluids in which differences in density are derived because of triple diffusion process, i.e., with three diffusing components: nanoparticles, solute, and heat, using more realistic two temperature model with separate thermal energy equations for the two phases of the considered nanofluid has been investigated by making use of the method of superposition and one term Galerkin technique. A complex system with local thermal non-equilibrium (LTNE) effects along with the Brownian motions and thermophoresis to account for nanoparticles has been considered. The problem is solved for top-heavy arrangement of nanoparticles leading to stationary mode of convection and numerical computations are carried out by using Mathematica software. An additional solute concentration equation supplements the conservation equations due to the existence of solute, which introduces two additional nondimensional parameters, whereas three additional parameters came into existence due to the consideration of LTNE effects. The critical Rayleigh number remains constant for smaller values of interphase heat transfer parameter, whereas it diminishes for the intermediate range and approaches to constant value for higher ranges of the parameters. What all this means is that only the intermediate range of Nield parameter shows stabilizing/destabilizing effects. Interestingly, the additional parameters Lewis number and solute Rayleigh number enhance the effect of destabilization of considered nanofluid layer.

Penetrative convection in a fluid saturated Darcy-Brinkman porous media with LTNE via internal heat source

Abstract The present work involves the study of penetrative convection in an incompressible fluid-saturated porous media with local thermal non-equilibrium. The onset of convection evaluated linearly and nonlinearly for the system influenced by heat extraction and heat generation. Darcy-Brinkman law is employed to model the momentum equation and four type of internal heat generating function are considered which leads to thermo-convective instability within the fluid layer. Linear analysis carried out by using normal mode technique and nonlinear stability analysis has been done by energy method. Due to heat generation within the fluid layer and heat extraction through boundary, the subcritical instability may exist with higher possibility. Effects of various parameters as: inter-phase heat transfer parameter, Darcy-Brinkman number, porosity-modified conductivity ratio, and heat parameter are explored on Darcy-Rayleigh number by Chebyshev pseudospectral method as numerical form and graphical form.

Anisotropic porous penetrative convection for a local thermal non-equilibrium model with Brinkman effects

The intent of the present problem is to observe the effect of internal heat source on the onset of convection in a fluid saturated anisotropic porous medium. Brinkman model is employed to formulate the momentum equation and fluid and solid phases are considered to be at local thermal non-equilibrium. The linear and non-linear theories are implemented to analyze the stability by computing the critical Rayleigh number and corresponding wave number. Normal mode technique is used for linear analysis and energy method is used for non-linear stability analysis. The presence of heat generation leads to the possibility of the existence of a subcritical instability. Effects of increase of Darcy-Brinkman number, inter-phase heat transfer parameter, anisotropy parameter, porosity-modified conductivity ratio and internal heat parameter on critical Rayleigh number was analyzed numerically using Chebyshev pseudospectral method.

Finite amplitude convection and heat transfer in inclined porous layer using a thermal non-equilibrium model

Finite amplitude convection in a inclined porous layer heated from below is studied by using local thermal non-equilibrium (LTNE) as mathematical model which takes into account the heat transferred between the solid phase and the fluid phase. Consequently, in addition to Darcy-Rayleigh number Ra and the inclination angle ϕ, two further non dimensional numbers are introduced: the inter-phase heat transfer parameter H and the porosity modified conductivity ratio γ. In a recent paper (Barletta and Rees, 2015), the linear stability analysis of the basic monocellular flow indicated that the inclination angle promotes the appearance of longitudinal rolls as the preferred mode of convection. The current paper focuses on the nonlinear evolution of longitudinal rolls in a supercritical regime of convection. A weakly nonlinear analysis, using a derived amplitude equation, is adopted to determine the nonlinear effects of the parameters Ra,ϕ,H and γ. The results indicate that in inclined layers (i) the nonlinearity decelerates the mean flow; (ii) the heat transfer, determined by the evaluation of the Nusselt number (Nu) at the layer boundary, corresponds to the one obtained for horizontal layers by scaling Ra with cosϕ, i.e.Nu=Nu(Racosϕ,H,γ); (iii) in accordance with existing laboratory experiments, the slope of Nu is less than 2, where 2 is the value predicted by the local thermal equilibrium model, and the slope represents the derivative of Nu with respect to the distance of the critical parameter from the threshold value for the onset of instability; (iv) increasing values of both H and γ produce an enhancement of the heat transfer across the layer. Finally, the comparison between the LTNE theoretical predictions and existing experiments conducted with various combinations of solid matrix and fluids suggests a possible alternative way to determine the heat transfer coefficient H.

Analytical Study of Heat Flux Splitting in Micro-channels Filled with Porous Media

The conditions of occurring heat flux splitting (bifurcation) phenomenon in a micro-channel filled with a porous medium including internal heat generations within both the solid and fluid phases under the local thermal non-equilibrium (LTNE) condition is analytically studied in the slip regime. The channel walls are subjected to a constant heat flux. Exact solutions for both the dimensionless temperatures of the two phases and the Nusselt number are obtained. Effects of the pertinent parameters such as heat generation parameter (\(\omega \)), the interphase heat transfer parameter (Vadasz in J Porous Media 15:249–258, 2012) or Biot number (\(\textit{Bi}\)), the fluid-to-solid effective conductivity ratio (k), and the temperature jump coefficient (\(\beta \)) on the dimensionless temperature profile (\(\theta \)) of the two phases as well as the Nusselt number are investigated. Moreover, the validity of one-equation model (the local thermal equilibrium assumption) is analyzed by comparing the Nusselt number obtained by one-equation model (LTE) with that obtained by the two-equation model (LTNE). Results reveal that the conditions at which the heat flux bifurcation (splitting) occurs in the slip regime is the same as those of the no-slip regime. In addition, a kind of heat flux bifurcation in which the solid and fluid phases have the same dimensionless temperature sign is observed in the slip regime, while it was not previously observe in the no-slip regime. It is discussed that the Nusselt number can increase or decrease with respect to \(\omega \) and may have either positive or negative values in both the no-slip and slip regimes. The presence of internal heat generation intensifies the role of \(\beta \) in the Nusselt number reduction. In addition, the accuracy of LTE model increases with increased \(\textit{Bi}\) and with decreased \(\beta \), while it is not a monotonic function of k in the presence of internal heat generation.

Thermoconvective instability and local thermal non-equilibrium in a porous layer with isoflux-isothermal boundary conditions

The effects of lack of local thermal equilibrium between the solid phase and the fluid phase are taken into account for the convective stability analysis of a horizontal porous layer. The layer is bounded by a pair of plane parallel walls which are impermeable and such that the lower wall is subject to a uniform flux heating, while the upper wall is isothermal. The local thermal non-equilibrium is modelled through a two-temperature formulation of the energy exchange between the phases, resulting in a pair of local energy balance equations: one for each phase. Small-amplitude disturbances of the basic rest state are envisaged to test the stability. Then, the standard normal mode procedure is adopted to detect the onset conditions of convective rolls. Beyond the Darcy-Rayleigh number, playing the role of order parameter for the transition to instability, the relevant dimensionless parameters are the inter-phase heat transfer parameter and the thermal conductivity ratio. The disturbance governing equations, formulated as an eigenvalue problem, are solved numerically by a shooting method. Results are reported for the neutral stability curves and for the critical values for the onset of instability.

Nonsimilar Boundary Layer Analysis of Free Convection Heat Transfer Over a Vertical Cylinder in Bidisperse Porous Media

This work presents a boundary layer analysis for the free convection heat transfer from a vertical cylinder in bidisperse porous media with constant wall temperature. A boundary layer analysis and the two-velocity two-temperature formulation are used to derive the nonsimilar governing equations. The transformed governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The effects of inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Results show that an increase in the modified thermal conductivity ratio and the permeability ratio can effectively enhance the free convection heat transfer of the vertical cylinder in a bidisperse porous medium. Moreover, the thermal nonequilibrium effects are strong for low values of the inter-phase heat transfer parameter.

Free Convection Heat Transfer From A Sphere In A Porous Medium Using A Thermal Non-equilibrium Model

This work studies the free convection heat transfer from a sphere with constant wall temperature embedded in a fluid-saturated porous medium using a thermal non-equilibrium model. The governing equations are transformed into boundary-layer partial differential equations by the coordinate transform, and the obtained governing equations are then solved by the cubic spline collocation method. The temperature distributions for fluid and solid phases are shown for different values of the porosity scaled thermal conductivity ratio, the interphase heat transfer parameter, and the streamwise coordinate. The effects of the porosity scaled thermal conductivity ratio and the interphase heat transfer parameter between solid and fluid phases on the local Nusselt numbers for fluid and solid phases are examined. Results show the local Nusset number for the porous medium can be increased by increasing the porosity scaled thermal conductivity ratio. Moreover, the thermal non-equilibrium effect is more significant for low values of the porosity scaled thermal conductivity ratio or the interphase heat transfer parameter.

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.

Local thermal non-equilibrium flow with viscous dissipation in a plane horizontal porous layer

Darcy’s flow in a horizontal porous layer with impermeable boundaries is studied. The viscous dissipation effect is taken into account and the local thermal non-equilibrium (LTNE) model for the energy balance is adopted. The upper boundary is assumed to be perfectly isothermal and the lower boundary is taken to be thermally insulated. The basic solution is expressed analytically. The case of a perfectly conducting solid phase is considered. The onset of convective roll instability is investigated by a linear analysis, with different values of the inter-phase heat transfer parameter. The eigenvalue problem is solved numerically by a Runge–Kutta method.

Free convection in a square cavity filled with a bidisperse porous medium

The classical problem of steady Darcy free convection in a square cavity filled with a porous medium has been extended to the case of a bidisperse porous medium (BDPM) by following the recent model proposed by Nield and Kuznetsov [D.A. Nield, A.V. Kuznetsov, Natural convection about a vertical plate embedded in a bidisperse porous medium, Int. J. Heat Mass Transfer 51 (2008) 1658–1664] and Rees et al. [D.A.S. Rees, D.A. Nield, A.V. Kuznetsov, Vertical free convective boundary-layer flow in a bidisperse porous medium, ASME J. Heat Transfer 130 (2008) 1–9]. The transformed partial differential equations in terms of the dimensionless stream function and temperature are solved numerically using a finite-difference method for some values of the governing parameters when the Rayleigh number Ra is equal to 10 2 and 10 3. Results are presented for the flow field with streamlines, temperature field by isotherms and heat transfer by local and mean Nusselt numbers are presented for both the f- and p-phases. It is found that the most important parameters that influence the fluid flow and heat transfer are the inter-phase heat transfer parameter H and the modified thermal conductivity ratio parameter γ .

Natural convection about a vertical plate embedded in a bidisperse porous medium

The classical Cheng–Minkowycz study of convection past a vertical plate embedded in a porous medium has been extended to the case of a bidisperse porous medium (BDPM). The boundary layer analysis leads to expressions for the velocity and temperature fields in terms of a geometrical parameter, an inter-phase momentum transfer parameter, a thermal diffusivity ratio, a permeability ratio, a thermal conductivity ratio, and an inter-phase heat transfer parameter. For the leading edge region, and for an inner layer, a similarity solution is obtained numerically. This involves the first four parameters, each of which is a characteristic of the BDPM.

The onset of convection in a bidisperse porous medium

The classical Rayleigh–Bénard theory, for the onset of convection in a horizontal layer uniformly heated from below, has been applied to a bidisperse porous medium. The linear stability analysis leads to an expression for the critical Rayleigh number as a function of a Darcy number, two volume fractions, a permeability ratio, a thermal capacity ratio, a thermal conductivity ratio, an inter-phase heat transfer parameter and an inter-phase momentum transfer parameter.

Stability of homogeneous-solid deflagration with two-phase flow in the reaction zone

An asymptotic model is derived for the nonsteady, nonplanar deflagration of energetic solids, such as nitramines, that experience exothermic reactions in liquid layers at their surfaces. The analysis takes into account the role of interphase heat transfer and the relative motion of gas and liquid in the resulting two-phase region at the surface. A basic solution corresponding to steady, planar burning is obtained, and a linear stability yields a neutral stability boundary beyond which the basic solution is unstable to pulsating disturbances. In particular, it is found that stability of the basic solution is lost for sufficiently large values of the activation energy and/or sufficiently small values of the interphase heat transfer parameter. In the combined limit that the latter approaches infinity and a velocity-perturbation parameter, which accounts for two-phase viscous and Marangoni effects, approaches zero, the neutral stability boundary is the same as that encountered for separate-phase solid propellants with an intrusive gas flame.