Maxwell Cattaneo Law Research Articles

Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh–Bénard–Magnetoconvection in Micropolar Fluid with Maxwell–Cattaneo Law

The effect of non-uniform temperature gradient on the onset of Rayleigh-Bénard magnetoconvection in a Micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal condition on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset of convection is discussed. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (Second Sound) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed.

Rayleigh-Bѐnard Convection in a Second-Order Fluid with Maxwell-Cattaneo Law

The objective of the paper is to study the Rayleigh-Bѐnard convection in second order fluid by replacing the classical Fourier heat law by non-classical Maxwell-Cattaneo law using Galerkin technique. The eigen value of the problem is obtained using the general boundary conditions on velocity and third type of boundary conditions on temperature. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. The classical Fourier flux law over predicts the critical Rayleigh number compared to that predicted by the non-classical law. The present non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigen values are less than the classical ones. Over stability is the preferred mode of convection.

On a phase-field system based on the Cattaneo law

Our aim in this paper is to study a generalization of the Caginalp phase-field system based on the Maxwell–Cattaneo law for heat conduction and endowed with Neumann boundary conditions. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. We also prove, when the enthalpy is conserved, the existence of the global attractor. We finally study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist and have a proper (spatial) decay at infinity.

The influence of thermal relaxation on the oscillatory properties of two-gradient convection in a vertical slot

We study the effects of the Maxwell–Cattaneo (MC) law of heat conduction on the flow of a Newtonian fluid in a vertical slot subject to both vertical and horizontal temperature gradients. Working in one spatial dimension (1D), we employ a spectral expansion involving Rayleigh’s beam functions as the basis set, which are especially well-suited to the fourth order boundary value problem (b.v.p.) considered here, and the stability of the resulting dynamical system for the Galerkin coefficients is investigated. It is shown that the absolute value of the (negative) real parts of the eigenvalues are reduced, while the absolute values of the imaginary parts are somewhat increased, under the MC law. This means that the presence of the time derivative of the heat flux increases the order of the system, thus leading to more oscillatory regimes in comparison with the usual Fourier case. Moreover, no eigenvalues with positive real parts were found, which means that in this particular situation, the inclusion of thermal relaxation does not lead to destabilization of the motion.

Study of Rayleigh-Bénard Magneto Convection in a Micropolar Fluid with Maxwell-Cattaneo Law

The effects of result from the substitution of the classical Fourier law by the non-classical Maxwell-Cattaneo law on the Rayleigh-Benard Magneto-convection in an electrically conducting micropolar fluid is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal or adiabatic temperature on the spin-vanishing boundaries. The influences of various micropolar fluid parameters are analyzed on the onset of convection. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones.

A generalization of the Caginalp phase-field system based on the Cattaneo law

We consider in this article a generalization of the Caginalp model for phase transitions based on the Maxwell–Cattaneo law, instead of the classical Fourier law. In particular, we prove the existence and uniqueness of solutions. We finally study the spatial behavior of the solutions in a semi-infinite cylinder.

On frame indifferent formulation of the Maxwell–Cattaneo model of finite-speed heat conduction

A material-invariant (frame indifferent) version of the Maxwell–Cattaneo law is proposed in which the relaxation rate of the heat flux is given by Oldroyd’s upper-convected derivative. It is shown that the new formulation allows for the elimination of the heat flux, thus yielding a single equation for the temperature field. This feature is to be expected from a truly frame indifferent description.

Nonlinear acoustic phenomena in viscous thermally relaxing fluids: Shock bifurcation and the emergence of diffusive solitons.

In this talk, we will consider the propagation of finite-amplitude acoustic waves in fluids that exhibit both viscosity and thermal relaxation. Under the assumption that the thermal flux vector is given by the Maxwell–Cattaneo law, which is a well known generalization of Fourier's law that includes the effects of thermal inertia, we derive the weakly nonlinear equation of motion in terms of the acoustic potential. We then use singular surface theory to determine how an input signal in the form of a shock wave evolves over time and for different values of the Mach number. Then, numerical methods are used to illustrate our analytical findings. In particular, it is shown that the shock amplitude exhibits a transcritical bifurcation; that a stable nonzero equilibrium solution is possible, and that a Taylor shock (i.e., a diffusive soliton), in the form of a “tanh” profile, can emerge from behind the input shock wave. Finally, an application related to the kinematic-wave theory of traffic flow is noted. [Work supported by ONR/NRL funding (PE 061153N)].

Effect of Second Sound on the Onset of Rayleigh- Benard Convection in a Micropolar Fluid

The effects resulting from the substitution of the classical Fourier law by the non-classical Maxwell-Cattaneo law in Rayleigh-Benard convention in micropolar fluid is studied. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical sign values are less than the classical ones.

From Boltzmann transport equation to single-phase-lagging heat conduction

In the present work the single-phase-lagging heat conduction model is re-derived analytically from the Boltzmann transport equation. In contrast to the Maxwell–Cattaneo law (CV model), it is Galilean invariant in the moving media. Based on this model, the governing equation of the microscale heat conduction is established, which is formulated into a delay partial differential equation. The corresponding initial and boundary conditions are prescribed. The thermal oscillation of the single-phase-lagging heat conduction is investigated.

Heat Conduction Paradox Involving Second-Sound Propagation in Moving Media

In this Letter, we revisit the Maxwell-Cattaneo law of finite-speed heat conduction. We point out that the usual form of this law, which involves a partial time derivative, leads to a paradoxical result if the body is in motion. We then show that by using the material derivative of the thermal flux, in lieu of the local one, the paradox is completely resolved. Specifically, that using the material derivative yields a constitutive relation that is Galilean invariant. Finally, we show that under this invariant reformulation, the system of governing equations, while still hyperbolic, cannot be reduced to a single transport equation in the multidimensional case.

Benard-Marangoni instability in a Maxwell-Cattaneo fluid

The effects resulting from the substitution of the classical Fourier law of heat conduction by the Maxwell-Cattaneo law in Bénard's and Marangoni's problems are examined.

Benard-Marangoni instability in a Maxwell-Cattaneo fluid

The effects resulting from the substitution of the classical Fourier law of heat conduction by the Maxwell-Cattaneo law in Bénard's and Marangoni's problems are examined.