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The purpose of this paper is to determine the thermo-gravitational convective state of a non-Fourier fluid layer of the single-phase-lagging type, heated from below. Unlike existing methodologies, the spectral modes are not imposed arbitrarily. They are systematically identified by expanding the spectral coefficients in terms of the relative departure in the post-critical Rayleigh number (perturbation parameter). The number and type of modes is determined to each order in the expansion. Non-Fourier effects become important whenever the relaxation time (delay in the response of the heat flux with respect to the temperature gradient) is of the same order of magnitude as process time.

In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A perturbation approach is developed to solve the nonlinear spectral system in the post-critical range.

The Nusselt number increases with non-Fourier effect as suggested in experiments in microscale and nanofluid convection.

Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection.

This study presents a mathematical approach and model that can be useful to investigate the thermal performance of fluids with microstructures via hybrid nanoparticles in conventional fluid. It has been found from the extensive literature survey that no study has been conducted to investigate buoyancy effects on the flow of Maxwell fluid comprised of hybrid microstructures and heat generation aspects through the non-Fourier heat flux model.

Non-Fourier heat flux model and non-Newtonian stress–strain rheology with momentum and thermal relaxation phenomena are used to model the transport of heat and momentum in viscoelastic fluid over convectively heated surface. The role of suspension of mono and hybrid nanostructures on an increase in the thermal efficiency of fluid is being used as a medium for transportation of heat energy. The governing mathematical problems with thermo-physical correlations are solved via shooting method.

It is noted from the simulations that rate of heat transfer is much faster in hybrid nanofluid as compare to simple nanofluid with the increasing heat-generation coefficient. Additionally, an increment in the thermal relaxation time leads to decrement in the reduced skin friction coefficient; however, strong behavior of Nusselt number is shown when thermal relaxation time becomes larger for hybrid nanofluid as well as simple nanofluid.

According to the literature survey, no investigation has been made on buoyancy effects of Maxwell fluid flow with hybrid microstructures and heat generation aspects through non-Fourier heat flux model. The authors confirm that this work is original, and it has neither been published elsewhere nor is it currently under consideration for publication elsewhere.

To give a new method to calculate the thermal conductivity of thin films which thickness is less than micro‐nanometer when non‐Fourier effect will appear in heat conduction and Fourier law is not applicable for calculating the thermal conductivity.

The Cattaneo equation based on the heat flow relaxation time approximation is used to calculate the thermal conductivity.

The results show that the thermal conductivity is not the thermophysical properties of material, but is the non‐linear function of temperature and film thickness when the dimension of film is less than micro‐nanometer.

The application of this method is limited by little experimental data of heat flow relaxation time for materials other than Ar crystals.

The paper demonstrates how the thermal conductivity of Ar crystals film can be calculated by NEMD algorithm and considers the non‐Fourier effect in the simulation.

Sheet processing of magnetic nanomaterials is emerging as a new branch of smart materials’ manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve the understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, this study aims to develop a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet.

This study developed a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant-strength magnetic field is applied transversely to the stretching flow plane. The Buongiorno nanofluid model is used to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo–Christov) model is used to simulate thermal conduction effects, of which the Fourier model is a special case when thermal relaxation effects are neglected.

The governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth-order Runge–Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters, e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nanoparticle concentration distributions, is investigated.

A strong elevation in temperature accompanies an increase in Brownian motion parameter, whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nanoparticle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter, whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values, i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model.

Numerical instability such as spurious oscillation is an important problem in the simulation of heat wave propagation. The purpose of this study is to propose a time discontinuous Galerkin isogeometric analysis method to reduce numerical instability of heat wave propagation in the medium subjected to heat sources, particularly heat impulse.

The essential vectors of temperature and the temporal gradients are assumed to be discontinuous and interpolated individually in the discretized time domain. The isogeometric analysis method is applied to use its property of smooth description of the geometry and to eliminate the mesh-dependency. An artificial damping scheme with proportional stiffness matrix is brought into the final discretized form to reduce the numerical spurious oscillations.

The numerical spurious oscillations in the simulation of heat wave propagation are effectively eliminated. The smooth description of geometry with spline functions solves the mesh-dependency problem and improves the numerical precision.

The time discontinuous Galerkin method is applied within the isogeometric analysis framework. The proposed method is effective in the simulation of the wave propagation problems subjecting to impulse load with numerical stability and accuracy.

This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the context of non-Fourier heat conduction featuring thermal relaxation effects.

Flow field is permeated to uniform transverse magnetic field. The governing transport equations are changed to globally similar ordinary differential equations, which are tackled analytically by homotopy analysis technique. Homotopy analysis method-Padè approach is used to accelerate the convergence of homotopy solutions. Also, numerical approximations are made by means of shooting method coupled with fifth-order Runge-Kutta method.

The solutions predict that fluid relaxation time has a tendency to suppress the hydrodynamic boundary layer. Also, heat penetration depth reduces for increasing values of thermal relaxation time. The general trend of wall temperature gradient appears to be similar in Fourier and Cattaneo–Christov models.

An important implication of current research is that the thermal relaxation time considerably alters the temperature and surface heat flux.

Current problem even in case of Newtonian fluid has not been attempted previously.

Using a non‐Fourier heat conduction (NFHC) hypothesis, the governing equations of thermal wave propagation are established. The resulting differential equations are transformed to integral forms using the Galerkin weighted residual method and then are discretized by a finite element technique. The proposed finite element formulation is verified by comparing the results of analytical and numerical solutions to a number of selected 1‐D problems. A couple of 2‐D sample problems are solved and the responses of the system to various input signals are studied. The proposed mixed approach shows superiority to the conventional finite element solution of hyperbolic heat conduction equation, because of the simultaneous determination of heat fluxes and temperature at each nodal point. The mixed approach is also shown to be capable of capturing the sudden temperature jump due to heat pulses.

This paper presents an unstructured discontinuous Galerkin finite element method for the solution of hyperbolic heat conduction problems that have found a wide range of applications in the pulsating laser treatment of thin films for electronic and MEMS applications. The mathematical formulation is described in detail and computational procedures are given. The computational algorithm is validated using the analytical solution for 1D thermal wave equations. Numerical simulations are made for 2D and 3D thermal wave propagations in regular and complex geometric configurations exposed to ultra‐short laser pulses. The stability of the algorithm is also studied using the matrix eigenvalue method and appropriate time step is determined for simulations. The numerical solutions exhibit strong wave behavior and reflection and interactions of thermal waves at the boundaries in multi‐dimensions. Simulations also show that the thermal wave behavior disappears and the classical Fourier heat conduction resumes when there is an instantaneous response between the heat flux and temperature gradient.

The purpose of this paper is to present a numerical methodology for the solution of non-Fourier conduction in two-dimensional (2-D) heterogeneous materials with contact resistance.

Energy and heat flux equations with time lagging constant are combined to form a 2-D hyperbolic conduction equation in conservational form, and the resulting equation is solved by finite volume method.

The magnitude of contact resistance is inversely proportional to the temperature jump at the contact surface and phonon transmission coefficient between heterogeneous medium. Numerical results show that higher the contact resistance, lower the heat flux through the interface, lower the strength of transmitted wave and higher the strength of reflected wave at the interface. These results are in agreement with physical expectations. Temperature profiles show expected discontinuity at the interface while the heat fluxes are continuous, demonstrating the accuracy of the proposed methodology.

In most available numerical methods for hyperbolic conduction with contact resistance, contact resistances are treated as internal boundaries at which boundary conditions are specified. In the present formulation, contact resistance between two heterogeneous materials is treated as a part of interface transport properties not as an added boundary condition. This approach makes the formulation much simpler and straightforward for multidimensional applications. This approach is never used previously and is original.

The numerical solution of a two‐dimensional thermal problem governed by a third‐order partial differential equation derived from a non‐Fourier heat flux model which may account for thermal waves and/or microscopic effects is considered. A dual‐reciprocity boundary element method is proposed for solving the problem in the Laplace transformation domain. The solution in the physical domain is recovered by a numerical inverse Laplace transformation technique.