Presence Of Heat Flux Research Articles

Design of neural networks for Darcy–Forchheimer viscous fluid subjected to electro-magnetohydrodynamic and thermal impacts

In this article, the electro-hydrodynamic Darcy–Forchheimer viscous fluid model EHDF−VFM over an extending surface is observed by operating the algorithm based on supervised learning through Artificial Levenberg Marquardt with backpropagated neural networks ALM−BPNNs. Energy correspondence is given the assistance of the primary law of thermodynamics in the presence of heat flux, dissipation, and Joule heating. Irreversibility investigation is demonstrated through the second law of thermodynamic. Partial differential equations of EHDF−VFM were transformed to ordinary differential equations using appropriate factors. These acquired non-linear ODEs are solved using the ND-solve procedure to take dataset of ALM−BPNNs for scenarios of this proposed model by varying E1, λ, Fr, Rd, Br, M, Pr, Sc, γ parameters and were graphically represented applying nftool to get performance, regression, fitness, error histogram, and training state analysis. Computational results for surface drag power, temperature slope, and mass exchange rate are discussed. Bejan number and entropy age have comparative effects on the electric field. For bigger porosity boundary, the entropy rate is expanded. An augmentation in porosity parameter decreases the velocity. The velocity profile shows conflicting conduct for higher approximation of electric and magnetic field parameters. The temperature has similar features for magnetic and radiation parameters.

Numerical and experimental estimation of building wall heat flux in presence of moisture transfer

Insulating building envelope is an efficient way to increase building energy efficiency and minimize greenhouse gas emissions related to heating. After building refurbishment, on-site measurements are suitable for verifying the actual thermal transmission properties of plane building components. For instance, the standard ISO 9869-1 describes a HFM method based on the measurement of surface heat flux with heat flow sensor (HFS). This method has been extensively investigated in the literature and successfully applied on vapor tight building walls. Nevertheless, hygroscopic building insulation materials (like biobased materials) are increasingly used, and heat transfer are coupled to moisture transfer within the wall. In this case, the HFS acts as a vapor barrier: it modifies the local moisture transfer and the associated latent heat flux. In this view, this study aims to clarify what it is measured with HFS in presence of moisture transfer. The question is first treated by numerical simulation of heat and moisture transfer within hygroscopic building wall. Then, experiments are carried out on hygroscopic building insulation where the moisture effects are exaggerated.

Wave propagation in a non-local magneto-thermoelastic medium permeated by heat source

In this paper, we consider the new concept of non-local heat conduction equation to generalized magneto-thermoelastic problem of two dimensional isotropic and homogeneous half-space in presence of heat-flux at the boundary surface. By using the harmonic plane waves, the governing equations are transformed to the vector matrix differential equation which is then solved by eigenvalue method. The analytical closed form solutions for displacement component, temperature distribution and stress components have been made and comparisons are also illustrated graphically with the theory of non-local dual-phase-lag (NLDPL) and non-local Lord-Shulman (NLLS) theory for different values of physical parameters. The significant effects of non-local variables as well as phase lagging parameters on displacements, temperature distribution and stress components are studied by means of graphically and concluding remarks are drawn.

Realizability conditions for relativistic gases with a non-zero heat flux

This work introduces a limitation on the minimum value that can be assumed by the energy of a relativistic gas in the presence of a non-zero heat flux. Such a limitation arises from the non-negativity of the particle distribution function and is found by solving the Hamburger moment problem. The resulting limitation is seen to recover the Taub inequality in the case of a zero heat flux but is more strict if a non-zero heat flux is considered. These results imply that, in order for the distribution function to be non-negative, (i) the energy of a gas must be larger than a minimum threshold; (ii) the heat flux, on the other hand, has a maximum value determined by the energy and the pressure tensor; and (iii) there exists an upper limit for the adiabatic index Γ of the relativistic equation of state and that limit decreases in the presence of a heat flux and pressure anisotropy, asymptoting to a value Γ = 1. The latter point implies that the Synge equation of state is formally incompatible with a relativistic gas showing a heat flux, except in certain gas states.

Generation of High-frequency Whistler Waves in the Earth’s Quasi-perpendicular Bow Shock

Abstract We use observations from the Magnetospheric Multiscale spacecraft to identify a free energy source for high-frequency whistler waves in the Earth’s quasi-perpendicular bow shock. In the considered measurements, whistlers propagate both parallel and antiparallel to the background magnetic field B 0 with frequencies around 100 Hz (0.15 f ce, where f ce is the electron cyclotron frequency) and amplitudes between 0.1 and 1 nT. Their growth can be attributed to localized pitch angle anisotropy in the electron velocity distribution function that cannot be precisely described by macroscopic parameters like heat flux or temperature anisotropy. However, the presence of heat flux along − B 0 does create preferential conditions for the high-frequency whistler waves that propagate in this direction. These waves are directed partially toward the shock, meaning they can scatter electrons that are streaming from the shock. This prolongs the time the electrons spend in the shock transition region and thereby promotes electron energization.

Temperature Fields and Thermal Stress in the Solidification of Cylindrical Continuous-Cast Steel Billet

Abstract—The influence of nonuniform boundary conditions on the cooling rate of stainless steel in continuous casting of cylindrical billet is investigated. Nonuniformity of the boundary conditions over the billet perimeter is assumed. The longitudinal cooling rate is assumed constant within the cooled sector of the billet. The presence of heat fluxes between cooling sectors is assumed. The gradients of the temperature and the thermal stress that develop in the solidifying billet are compared at different cooling rates in the secondary-cooling zone. The thermal stress is compared with the permissible value for each grade of steel, so as to determine cooling conditions corresponding to permissible thermal stress. The results indicate that the cooling rate affects the appearance of external and internal defects in the continuous-cast cylindrical billet. It is also found that the nonuniformity of the boundary conditions affects the temperature fields in the solidifying continuous-cast cylindrical billet. The results are presented in graphical form and analyzed in detail. A mathematical model is developed to calculate the temperature fields in the solidifying billet, on the basis of the nonsteady heat-conduction equation. The thermal stress is calculated by familiar methods that permit the determination of the stress that appears between cooling zones in the solidifying billet. The results may be used to develop cooling conditions that correspond to permissible thermal stress. By that means, the frequency of internal and external defects in the solidifying continuous-cast cylindrical billet may be decreased.

Pool boiling in deep and shallow vessels and the effect of surface nano-texture and self-rewetting

Pool boiling of ethanol and self-rewetting fluids on bare copper surface and copper surface with polymer nanofibers were studied experimentally. No significant effect of the depths of ethanol layer on the heat removal rate was found. That indicates that only the heat transfer in the liquid microlayer near the heater surface is a dominant factor. As a result, one can expect that self-rewetting fluids can significantly affect boiling performance. Accordingly, several alcohol solutions including the self-rewetting ones were investigated as working fluids in the boiling chamber. It was found that at the 0.1% (v/v) concentration, only the high carbon-alcohol, n-heptanol in aqueous solution, improved boiling heat transfer considerably. Furthermore, the experimental study of the effect of surface nano-texture on boiling characteristics was undertaken. For that aim, polyacrylonitrile (PAN) nanofibers were deposited onto the copper heater surface. Measurements of the boiling curve revealed a detrimental effect of such nano-texture in the case of such working fluids as ethanol and self-rewetting n-heptanol solutions. On the other hand, when polystyrene (PS) nanofibers were deposited onto the copper heater surface instead of PAN nanofibers, a significant improvement in boiling heat transfer was observed. The more hydrophobic nature of PS compared to copper is responsible for this effect, i.e. is the reason of the heat transfer enhancement on such a nano-textured surface compared to the pure copper one. In addition, the critical heat flux in the case of n-heptanol solution was found to be reduced considerably on the PS nano-textured surface compared to the pure copper one. This stems from the increased propensity of the heater surface to be covered by vapor, while the rewetting is insufficiently effective at high heat fluxes in presence of PS nanofibers.

Velocity fluctuations and boundary layer structure in a rough Rayleigh-Bénard cell filled with water

We report Particle Image Velocimetry of the Large Scale Circulation and the viscous boundary layer in turbulent thermal convection. We use two parallelepipedic Rayleigh-B{\'e}nard cells with a top smooth plate. The first one has a rough bottom plate and the second one has a smooth one so we compare the rough-smooth and the smooth-smooth configurations. The dimensions of the cell allow to consider a bi-dimensional mean flow. Lots of previous heat flux measurements have shown a Nusselt--Rayleigh regime transition corresponding to an increase of the heat flux in presence of roughness which is higher than the surface increase. Our velocity measurements show that if the mean velocity field is not clearly affected by the roughness, the velocity fluctuations rise dramatically. It is accompanied by a change of the longitudinal velocity structure functions scaling. Moreover, we show that the boundary layer becomes turbulent close to roughness, as it was observed recently in the air [Liot et al., JFM, vol. 786, pp. 275-293]. Finally we discuss the link between the change of the boundary layer structure and the ones observed on the Large Scale Circulation.

Joule Heating and Viscous Dissipation on Effects on MHD Flow over a Stretching Porous Sheet Subjected to Power Law Heat Flux in Presence of Heat Source

In the present work we investigate the effects of Joule heating and viscous dissipation on MHD fluid flow. The viscous incompressible fluid flows over a stretching porous horizontal sheet subjected to power law heat flux in presence of heat source. The equations of momentum and heat transfer governing the problem are transformed into a system of dimensionless differential equations, which in turn solved numerically using shooting technique. The effects of the Joule heating parameter, permeability parameter, heat source parameter, Eckert number and Prandtl number are discussed and tabulated.

Hamiltonian magnetic reconnection with parallel electron heat flux dynamics

We analyse, both analytically and numerically, a two-dimensional six-field fluid model for collisionless magnetic reconnection, accounting for temperature and heat flux fluctuations along the direction of the magnetic guide field. We show that the model possesses a Hamiltonian structure with a non-canonical Poisson bracket. This bracket is characterized by the presence of six infinite families of Casimirs, associated with Lagrangian invariants. This reveals that the model can be reformulated as a system of advection equations, thus generalizing previous results obtained for Hamiltonian isothermal fluid models for reconnection. Numerical simulations indicate that the presence of heat flux and temperature fluctuations yields slightly larger growth rates and similar saturated island amplitudes, with respect to the isothermal models. For values of the sonic Larmor radius much smaller than the electron skin depth, heat flux fluctuations tend to be suppressed and temperature fluctuations follow density fluctuations. Increasing the sonic Larmor radius results in an increasing fraction of magnetic energy converted into heat flux, at the expense of temperature fluctuations. In particular, heat flux fluctuations tend to become relevant along the magnetic island separatrices. The qualitative structures associated with the electron field variables are also reinterpreted in terms of the rotation of the Lagrangian invariants of the system.

Collapsing plane symmetric source with heat flux and conformal flatness

This paper deals with the study of collapsing plane symmetric source in the presence of heat flux. For this purpose, we have calculated the Einstein field equations as well as Weyl tensor components. The conditions for the conformal flatness have been determined. The interior source has been matched smoothly with the exterior geometry in single null coordinate. It has been found the pressure is balanced with the out going heat flux and the continuity of the masses in two regions has been noted. A simple new model of collapse has been proposed which satisfies flatness condition, also we have discussed the physical properties of the model. For our model, we have calculated the temperature profile by using the approximation scheme.

Flow and Heat Transfer of Powell–Eyring Fluid due to an Exponential Stretching Sheet with Heat Flux and Variable Thermal Conductivity

Abstract An analysis was carried out to describe the problem of flow and heat transfer of Powell–Eyring fluid in boundary layers on an exponentially stretching continuous permeable surface with an exponential temperature distribution in the presence of heat flux and variable thermal conductivity. The governing partial differential equations describing the problem were transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the shooting method over the entire range of physical parameters. The effects of various parameters like the thermal conductivity parameter, suction parameter, dimensionless Powell–Eyring parameters and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. In this work, special attention was given to investigate the effect of the thermal conductivity parameter on the velocity and temperature fields above the sheet in the presence of heat flux. The numerical results were also validated with results from a previously published work on various special cases of the problem, and good agreements were seen.

Similarity Solution of Heat and Mass Transfer Flow over an Inclined Stretching Sheet with Viscous Dissipation and Constant Heat Flux in Presence of Magnetic Field

The present analysis of this paper is to examine the similarity solution of magnetohydrodynamics (MHD) free convection heat and mass transfer flow of an incompressible, electrically conducting and viscous fluid over an inclined stretching sheet with viscous dissipation and constant heat flux. So the present work is focused of the impact of the flow parameters on the velocity, temperature, and concentration are computed, discussed and have been graphically represented in figures and also the shearing stress, and rate of concentration shown in table 1 for various values of different parameters. The results presented graphically illustrate that velocity field decrease due to increasing of magnetic parameter, Prandtl number, Grashof number, and Eckert number whereas negligible increasing effects for Soret number, Schmidt number and noticeable increasing effect for angle of inclination but there is no effect for modified Grashof number. The temperature field decreases up to certain interval then increases in the presence of Magnetic parameter and reverse trend arise for Prandtl number but the temperature field increases for the remaining entering parameters. It is interesting to note that in a certain interval of η, the concentration profile is decreased and then increased but reverse trend arises in the case of Prandtl number and angle of inclination. By considering the hot plate the numerical results for the skin friction and the local Sherwood number are compared with the results reported by the other author when the magnetic field and modified Grashof number are absent. The present results in this paper are in good agreement with the work of the previous author.

Heat Transfer Analysis in Annular Two Phase Flow Using Finite Difference Method

Heat transfer in two phase flow is widely encountered in oil and gas industry in which heat is transported between two phase the fluid and the pipe wall with a rate depending on the hydrodynamic conditions. In present work, theoretical study was carried out to predict the temperature distribution within the liquid layer in annular gas–liquid (air–water) of two phase flow in presence of heat flux under laminar flow conditions. The temperature distribution was evaluated at different values of liquid Reynolds number (ResL), gas Reynolds number (Resg), wall heat flux, and inlet liquid as well as gas temperatures. The finite differences technique was employed to solve the energy equation to obtain the temperature distribution in the liquid layer. Additionally, the effect of Resg and ResL on the liquid layer thickness was investigated and discussed. It was found that the presence of heat flux through the pipe wall leads to an increase in the liquid temperature asymptotically with the axial distance (z) depending on the radial distance (r). The maximum increase occurred in the liquid layers adjacent to the pipe surface layers and the minimum increase was at the interface. The fully developed temperature profile varied with radial distance (r) where the surface layers reached at Lt/d=5. However, the Lt/d for the layers nearest to the interface was less than 5. At a particular (r) and constant Resg, the higher the ResL is, the higher the temperature will be. At a particular ResL and Resg, the liquid layer temperature distribution depends largely on the values of applied heat flux and the gas temperature.

The Role of Pressure During Shearing, Dissipative Collapse

We analyse a new family of solutions to the Einstein field equations describing the collapse of a fluid sphere in the presence of heat flux and shear. These solutions ensure that the collapsing fluid is accelerating and provide a generalisation of the geodesic fluid models studied in earlier treatments. In particular, we demonstrate the role played by pressure in the dynamics of the collapse process.

Heat transfer over a stretching porous sheet subjected to power law heat flux in presence of heat source

In the present investigation the boundary layer steady flow and heat transfer of a viscous incompressible fluid due to a stretching porous sheet in presence of heat source are studied. The equations of motion and heat transfer are reduced to non-linear ordinary differential equations and the exact solutions are obtained in the form of confluent hypergeometric function (Kummer?s Function) for prescribed heat flux, when the wall is at prescribed second order power law heat flux or the prescribed heat flux at the stretching porous wall varies as the square of the distance from the origin. The effects of the various parameters entering into the problem on the temperature distribution and recovery temperature are discussed.

Nonlinear vibrations of a vapor film in the presence of intense heat fluxes

Waves propagating along the interface between a thin vapor film and a liquid layer in the presence of a heat flux are investigated. The boundary conditions on the vapor-liquid phase surface take into account the temperature dependence of the pressure and the possibilities of formation of the metastable state of the superheated liquid and mass flow. Variations in the saturation pressure as functions of the temperature and mass flux lead to generation of weakly damped periodic waves of low amplitude whose velocity can be much higher than the velocity of the gravity waves. The waves ensure stability of the vapor film beneath the liquid layer in the gravity field. The finite-amplitude waves on the surface of the vapor film differ from the Stokes surface waves on the free surface of isothermal fluid. Instability regimes related with superheating of the liquid ant its explosive boiling when the amplitude of an initially small wave increases to infinity in a finite time can develop in a certain working-parameter regime.

Vibration Analysis of Sudden Enlargement Pipe Conveying Fluid with Presence of Heat Flux

Vibration Analysis of Sudden Enlargement Pipe Conveying Fluid with Presence of Heat Flux

Natural convection flow from a horizontal circular cylinder with uniform heat flux in presence of heat generation

Natural convection boundary layer laminar flow from a horizontal circular cylinder with uniform heat flux in presence of heat generation has been investigated. The governing boundary layer equations are transformed into a non-dimensional form and the resulting non-linear systems of partial differential equations, which are solved numerically by two distinct methods namely: (i) implicit finite difference method together with the Keller-box scheme and (ii) perturbation solution technique. The results of the surface shear stress in terms of local skin-friction and the rate of heat transfer in terms of local Nusselt number, velocity distribution, velocity vectors, temperature distribution as well as streamlines, isotherms and isolines of pressure are shown by graphically for a selection of parameter set consisting of heat generation parameter.

Stability of Taylor–Couette Magnetoconvection With Radial Temperature Gradient and Constant Heat Flux at the Outer Cylinder

An analysis is made of the linear stability of wide-gap hydromagnetic (MHD) dissipative Couette flow of an incompressible electrically conducting fluid between two rotating concentric circular cylinders in the presence of a uniform axial magnetic field. A constant heat flux is applied at the outer cylinder and the inner cylinder is kept at a constant temperature. Both types of boundary conditions viz; perfectly electrically conducting and electrically nonconducting walls are examined. The three cases of μ<0 (counter-rotating), μ>0 (co-rotating), and μ=0 (stationary outer cylinder) are considered. Assuming very small magnetic Prandtl number Pm, the wide-gap perturbation equations are derived and solved by a direct numerical procedure. It is found that for given values of the radius ratio η and the heat flux parameter N, the critical Taylor number Tc at the onset of instability increases with increase in Hartmann number Q for both conducting and nonconducting walls thus establishing the stabilizing influence of the magnetic field. Further it is found that insulating walls are more destabilizing than the conducting walls. It is observed that for given values of η and Q, the critical Taylor number Tc decreases with increase in N. The analysis further reveals that for μ=0 and perfectly conducting walls, the critical wave number ac is not a monotonic function of Q but first increases, reaches a maximum and then decreases with further increase in Q. It is also observed that while ac is a monotonic decreasing function of μ for N=0, in the presence of heat flux (N=1), ac has a maximum at a negative value of μ (counter-rotating cylinders).