The mixed convection in a thin liquid film flow over a horizontal plate is investigated under finite Prandtl numbers. The gas–liquid interface is considered free, nondeformable and subject to surface tension gradients and convection, while gravity is assumed negligible. Therefore, thermocapillary instead of buoyancy effects appears due to the unstable temperature stratification induced by the internal heating generated by viscous dissipation. A linear and modal stability analysis of this model is then performed to identify its convective/absolute nature. This is achieved by solving the resulting differential eigenvalue problem with a shooting method. Longitudinal rolls are the most unstable at the onset of instability for most parametric conditions. Otherwise, transverse rolls are the first to become convectively unstable. Finally, longitudinal rolls are absolutely stable. A transition to absolute instability occurs through transverse rolls, but only within a limited region in parametric space.

In this paper, we incorporate a nonequilibrium thermodynamics perspective that is consistent with the Onsager reciprocity principle into the lattice Boltzmann framework to propose a novel regularized lattice Boltzmann formulation for modeling the Navier–Stokes–Fourier equations. The new method is applied to one-dimensional (1D) isothermal situations wherein the advantages of incorporating such a nonequilibrium perspective can be explicitly appreciated. In such situations, the nonequilibrium contribution of the lattice populations obtained by the new method completely vanishes, and the lattice update is entirely reduced to evaluating the equilibrium distribution function. Such a counterintuitive 1D mesoscopic description is not obtained in any other existing lattice Boltzmann scheme. We therefore numerically test the proposed formulation on two complex problems, namely, shockwave and nonlinear wave propagation, and compare results with analytical results along with six existing lattice Boltzmann schemes; it is found that the new method indeed yields results that are more stable and accurate. These results highlight the potency of the nonequilibrium thermodynamics-based approach for obtaining accurate and stable lattice Boltzmann computations, and provide new insights into established lattice Boltzmann simulation methods.

This paper investigates the propagation of thermoelastic waves in a homogeneous, linear, and isotropic porous solid. For physical and mathematical simplicity, one-dimensional wave propagation in a porous solid rod is considered to explain the concept of heat transfer caused by motion. The solutions of governing equations show that the transfer of heat in a porous rod is not only due to the conduction but also produced by the local particle displacement phenomenon. It is observed that the time-averaged transfer of heat depends on the circular frequency, porosity, thermal conductivity, thermal relaxation, specific heat, and other material coefficients.

A simple analytical calculation scheme to determine near field radiation through decomposing an emission domain into lots of thin thermal current sheets is presented. Through finding the orthogonal modes of thermal current of each thin layer, the thin current sheets can be treated as radiation sources of electromagnetic waves with determined analytical solutions. The outgoing electromagnetic waves from each thin current sheets can be either in transverse electric (TE) or transverse magnetic (TM) modes depending on the orientations of the current in the thin current sheets with respect to the directions of amplitude modulations of the orthogonal modes. Electromagnetic waves arriving to a collection domain are related to the electromagnetic waves leaving from each thin current thermal sheet with transfer coefficients. Transfer coefficient for TE and TM waves can be determined analytically with transfer matrix method or scattering matrix methods. Compared with existing dyadic Green's function method, the new calculation scheme allows material and temperature variations along one direction of the emission domain based on determined analytical expressions of TE and TM waves leaving from each thin current sheets. The simple calculation scheme is especially useful in near field radiation of layered structures with different material such as hyperbolic material with negative refractive indices. With this new approach, we recovered analytical solutions of near field radiation between two semi-infinite domains with uniform temperature and derived closed form solution of near field radiation between two semi-infinite domains with temperature profiles with/without laminated structures.

A series of rotating convection experiments have been conducted in a novel configuration, which comprises a cylindrical annulus with spot heating on the bottom outer edge and uniform cooling on the inner surface. Such a system provides bi-directional thermal gradients in both radial and vertical directions, thereby reenacting the thermal gradient patterns encountered in the atmosphere. Bulk heat transfer characteristics are studied by quantifying the overall Nusselt number, Nu, for a range of Taylor number, Ta, heating rate, Q, and Rayleigh number, Ra. Temperature measurements are carried out at different locations with the help of thermocouples. The Nusselt number is found to be quite sensitive to the buoyancy and relatively insensitive to the rotation rate. The correlation for Nu as a function of Ra revealed different power law exponents for low and high Ta values. The varying exponent is attributed to the presence of baroclinic eddies at high Ta, which in turn is verified with the help of flow visualization. The heat transfer characteristics in this new configuration are significantly different compared to other conventional rotational convection systems, where thermal gradients are present in only one direction.

The simultaneous effect of a time-dependent velocity term in the momentum equation and a maximum density property on the stability of natural convection in a vertical layer of Darcy porous medium is investigated. The density is assumed to vary quadratically with temperature and as a result, the basic velocity distribution becomes asymmetric. The problem has been analyzed separately with (case 1) and without (case 2) time-dependent velocity term. It is established that Gill's proof of linear stability effective for case 2 but found to be ineffective for case 1. Due to the lack of Gill's proof for case1, the stability eigenvalue problem is solved numerically and observed that the instability sets in always via traveling-wave mode when the Darcy–Prandtl number is not larger than 7.08. The neutral stability curves and isolines are presented for different governing parameters. The critical values of Darcy–Rayleigh number corresponding to quadratic density variation with respect to temperature, critical wave number, and the critical wave speed are computed for different values of governing parameters. It is found that the system becomes more stable with increasing Darcy–Rayleigh number corresponding to linear density variation with respect to temperature and the Darcy–Prandtl number.

The influence of partitions on natural convection in a differentially heated porous enclosure has been investigated for three different partition shapes, namely, sine-wave, corrugated and square-wave shape. The objective is to identify the best partition shape with regard to achieve maximum reduction in the rate of convection heat transfer. Darcy flow model has been used to describe flow in porous media. Coordinate transformation has been used to formulate the governing equations for sine-wave partition owing to its wavy nature. To assess the effectiveness of various partition shapes, the results are compared with porous enclosure without partition and with straight partition. The governing equations are solved using the successive accelerated replacement scheme for a wide range of parameters like partition amplitude, position, Rayleigh number, enclosure aspect ratio (AR), and inclination angle. One of the findings reveals that for the same amplitude and position, the square-wave partition yields the maximum suppression in the value of Nusselt number.

This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

Recently metamaterials made of periodic nanowire arrays, multilayers, and grating structures have been studied for near-field thermal radiation with enhanced coupling of evanescent waves due to surface plasmon/phonon polariton, hyperbolic mode, epsilon-near-zero and epsilon-near-pole (ENP) modes, guided mode, and wave interference. In this work, both effective uniaxial electric permittivity and magnetic permeability of a nanowire-based metamaterial are retrieved theoretically through the far-field radiative properties obtained by finite difference time-domain (FDTD) simulations. The artificial magnetic response of metamaterials, which cannot be obtained by traditional effective medium theory (EMT) based on electric permittivity of constitutes only, is successfully captured by the nonunity magnetic permeability, whose resonant frequency is verified by an inductor-capacitor model. By incorporating the retrieved electric permittivity and magnetic permeability into fluctuational electrodynamics with multilayer uniaxial wave optics, the near-field radiative heat transfer between the metallic nanowire arrays is theoretically studied and spectral near-field heat enhancements are found for both transverse electric and magnetic waves due to artificial magnetic resonances. The understanding and insights obtained here will facilitate the application of metamaterials in near-field radiative transfer.

In 2000, Kulish and Lage proposed an elegant method, which allows one to obtain analytical (closed-form) solutions to various energy transport problems. The solutions thus obtained are in the form of the Volterra-type integral equations, which relate the local values of an intensive property (e.g., temperature, mass concentration, and velocity) and the corresponding energy flux (e.g., heat flux, mass flux, and shear stress). The method does not require one to solve for the entire domain, and hence, is a nonfield analytical method. Over the past 19 years, the method was shown to be extremely effective when applied to solving numerous energy transport problems. In spite of all these developments, no general theoretical justification of the method was proposed until now. The present work proposes a justification of the procedure behind the method and provides a generalized technique of splitting the differential operators in the energy transport equations.

Understanding the frosting mechanisms on solid surfaces is crucial to a broad range of industrial sectors such as aerospace, power transmission, and refrigeration. During the last few decades, extensive studies have been conducted on fundamental frosting phenomena, including ice nucleation, growth, bridging, and frost propagation, with few studies focusing on frost halo formation which has been shown to affect frosting dynamics on hydrophilic substrates. The role of frost halo dynamics formation on superhydrophobic surface remains unclear due to limited characterization in the past. Here, in order to study frost propagation dynamics, particularly freezing-induced vapor diffusion and frost halo formation, condensation frosting on highly-reflective nanostructured superhydrophobic surfaces (θ ≈170º) was visualized using high-speed top-view optical microscopy. Condensation frosting was initiated by cooling the surface to -20 ± 0.5°C in atmospheric conditions (relative humidity ≈50% and air temperature ≈25°C). We show that the wave front reaches neighboring supercooled droplets along the path of frost propagation, resulting in supercooled droplet freezing within ~100 ms and numerous microscale (~1 µm) condensing droplets forming around the primary freezing droplet. The microscale droplets form a condensate halo stretching two times the freezing droplet radius. The condensate halo was formed by the rapid evaporation of the supercooled recalescent freezing droplet due to the fast (~100 ms) release of latent heat, resulting in the heating of the freezing droplet and thus outwards diffusion of vapor. Further diffusion of vapor led to the subsequent evaporation of the halo condensate droplets within ~4 s. Interestingly, accompanied by the freezing of the primary droplet and condensate halo formation, the neighboring satellite droplets in the halo zone were observed to oscillate directionally and dramatically, indicative of the presence of a strong flow field disturbance due to rapid vapor diffusion. The visualizations presented here not only help to quantify the physics of condensate halo formation during frost wave propagation on superhydrophobic surfaces, but also provide insights into the role of freezing-induced vapor diffusion during frost dynamics.

Planck's law describes thermal radiation into vacuum from a black body in thermal equilibrium. This law can be easily adapted to describe radiation into a transparent medium with a constant refractive index, and it admits a less trivial extension to radiation into a transparent medium with a nonconstant refractive index. However, this law cannot be straightforwardly generalized to describe thermal radiation into absorbing media and, in particular, to describe thermally exited electromagnetic fields inside the radiating body itself. We first analyze Planck's law and show why it cannot be straightforwardly extended to radiation into an absorbing medium. The derivation of this law relies on the assumption that a radiated field admits decomposition into normal modes, which cannot exist in absorbing media that are characterized by a complex-valued refractive index n = n ′ + i n ″ , whose imaginary part describes the rate of energy dissipation. Correspondingly, the speed of electromagnetic waves in absorbing media c = c 0 / n , where c 0 is the speed of light in vacuum, is also complex-valued, which suggests that the conventional concept of a complex valued wave speed is not suitable for modeling thermal radiation. We demonstrate that complex-valued wave speeds adequately describe waves that carry signals, such as radio waves and laser beams. Such waves decay because they pass some of their energy to the medium. The energy absorbed by the medium is eventually reradiated, but in studies focused on the transmission of signals, the reradiated fields are ignored as noise. In order to study thermal radiation in an absorbing material, one must treat the material and the radiation together as a closed system. The energy in such a system is conserved, and its distribution between the material and radiation does not change in time. This radiation admits decomposition into normal modes, which makes it possible to extend Planck's law to radiation into absorbing materials. This paper proposes a model of thermal radiation in an absorbing medium as a closed, energy conserving system. The radiation field has normal modes that correspond to an effective speed of wave propagation. Assuming that an absorbing material and the radiation in it are in thermal equilibrium, we show that deep inside the material, the average speed of photons is given by a frequency and temperature-dependent expression c ∗ = c 0 / ( 1 + e − ℏ ω / κ T ) . While this result is independent of the material, we further show that close to the boundary of the medium, the speed of thermal radiation depends in a complex way on the refractive index and the extinction coefficient of the material, as well as the direction of propagation and the distance from the material's surface.

This paper examines the effect of transfer of heat and mass on the capillary instability between a viscoelastic liquid and a viscous gas. The viscoelastic liquid obeys the Oldroyd B-model. These two fluid layers considered in coaxial cylinders and viscoelastic–viscous potential flow theory are used for investigation. To study the stability of the interface, the normal-mode procedure is employed and a cubic dispersion equation in terms of growth rate has been obtained. We observe that the viscoelastic liquid–viscous gas interface is more unstable than the viscous liquid–viscous gas interface. Additionally, we show that the unstable axisymmetric wave modes are stabilized by allowing heat transfer at the interface.

Despite the abundant theoretical studies of magnetic polaritons (MPs) in tailoring the radiative properties of nanostructures, experimental investigation of MPs in deep metal gratings is still lacking. This work experimentally demonstrates the excitation of MP from several microfabricated aluminum gratings in the mid-infrared region by measuring the specular reflectance (zeroth-order diffraction) of the specimen using a Fourier-transform infrared (FTIR) spectrometer. The rigorous coupled-wave analysis (RCWA) and an LC-circuit model are employed to elucidate the mechanism of various resonant modes and their coupling effect. The influence of incidence angle, plane of incidence, polarization, and the trench depth on the spectral reflectance is also discussed. Moreover, the MP dispersion for off-plane layout has been investigated and demonstrated for the first time. The insight gained from this work may facilitate future design and applications of subwavelength periodic structures with desired radiative properties.

In this study, free convection in a cavity with differentially heated wavy walls is numerically investigated in the presence of a magnetic source. Polyharmonic spline radial basis function (RBF) is utilized to discretize the governing dimensionless equations formulated by stream function-vorticity. The effects of dimensionless Hartmann number, Rayleigh number, the number of undulations, amplitude of wave, and the location of magnetic source are visualized in streamlines and isotherms as well as calculating average Nusselt number through the heated wall. Results show that primary vortex in streamlines is altered with the impact of magnetic source. The augmentation of undulations and amplitude causes convective heat transfer to decrease if Ra = 10 5 . The impact of location of magnetic source is noted close to the top wall.

Forced convection heat transfer in fully developed laminar flow in transversely corrugated tubes is investigated for nonuniform but constant wall heat flux as well as for constant wall temperature. Epitrochoid conformal mapping is used to map the flow domain onto the unit circle in the computational domain. The governing equations are solved in the computational domain analytically. An exact analytical solution for the temperature field is derived together with closed form expressions for bulk temperature and Nusselt number for the case of the constant heat flux at the wall. A variable coefficient Helmholtz eigenvalue problem governs the case of the constant wall temperature. A novel semi-analytical solution based on the spectral Galerkin method is introduced to solve the Helmholtz equation. The solution in both constant wall heat flux and constant wall temperature case is shown to collapse onto the well-known results for the circular straight tube for zero waviness.

In this study, air jet impingement on flat, triangular-corrugated, and sinusoidal-corrugated surfaces was numerically investigated. Bottom surface was subjected to constant surface temperature. Air was the working fluid. The air exited from a rectangular shaped slot and impinged on the bottom surface. The Reynolds number was changed between 125 and 500. The continuity, momentum, and energy equations were solved using the finite volume method. The effect of the shape of bottom surface on heat and flow characteristics was investigated in detail. Average and local Nusselt number were calculated for each case. It was found out that Nusselt number increases by increasing the Reynolds number. The optimum conditions were established to get much more enhancement in terms of performance evaluation criterion (PEC). It was revealed that the shape of the cooling surface (bottom wall) influences the heat transfer substantially.

In this paper, a non-Fourier model of heat conduction and moisture diffusion coupling is proposed. We study a hygrothermal elastic problem within the framework of time-fractional calculus theory for a centrally symmetric sphere subjected to physical heat and moisture flux at its surface. Analytic expressions for transient response of temperature change, moisture distribution, displacement, and stress components in the sphere are obtained for heat/moisture flux pulse and constant heat/moisture flux at the sphere's surface, respectively, by using the integral transform method. Numerical results are calculated and the effects of fractional order on temperature field, moisture distribution, and hygrothermal stress components are illustrated graphically. Subdiffusive and super-diffusive transport coupling behavior as well as wave-like behavior are shown. When fractional-order derivative reduces to first-order derivative, the usual heat and moisture coupling is recovered, which obeys Fourier heat conduction and Fick's moisture diffusion.

The aim of this investigation is to estimate the theory of generalized magneto-thermoelasticity to solve the problems of two-dimensional (2D) half-space under thermal shock, initial stress, and two temperatures. The governing equations are solved by using Lame's potentials method in the context of classical dynamical (CD) and Lord-Şhulman (LS) theories. The boundary conditions are as follows (i) the total normal stresses in the boundary equivalent to the initial stress; (ii) the shear stresses are vanished at the boundary; and (iii) the incidence boundary is thermal insulated. The reflection coefficients have been obtained for two incident p - and SV-waves. The results obtained for the incident waves calculated numerically by using appropriate metal and presented graphically. Comparisons have been made with the results obtained from the presence and absence of magnetic field and initial stress.