This study numerically investigates laminar forced convection in a porous channel with elliptic wavy cavities, a geometry relevant to compact heat exchangers and energy systems. The governing equations, expressed in vorticity–stream function form, are solved using a finite difference method on a boundary-fitted curvilinear grid generated through elliptic grid-generation techniques. Parametric analyses explore the influence of the Reynolds number ( Re), Darcy number ( Da), Prandtl number ( Pr), and cavity dimensions on fluid flow and heat transfer. Streamlines, isotherms, and local and average Nusselt numbers are used to characterize thermal performance. The results show that higher Re and Pr enhance convective heat transfer, while increased Da and cavity height reduce the Nusselt numbers due to weakened circulation. The elliptic wavy design improves mixing and localized heat transfer, offering guidance for optimizing porous thermal systems.
We formulate and solve a reduced electrostatic model of an open finite-length cylindrical conductor represented by two coaxial lateral surfaces of inner radius a, outer radius b = a + t, and common length L, maintained at the same prescribed potential V 0 . The annular end surfaces are omitted, and the regions adjacent to the inner and outer cylindrical surfaces are characterized by permittivities ε in and ε out , respectively. Exploiting axial symmetry, the surface-integral formulation is reduced analytically to a coupled 2 × 2 system of one-dimensional singular integral equations for the two surface-charge densities. The self- and mutual-interaction kernels are obtained in closed form in terms of complete elliptic integrals. The equations are solved using a Chebyshev-weighted Nyström discretization that incorporates the square-root endpoint behavior of the charge densities and treats the weak logarithmic self-interaction singularities through an explicit local diagonal prescription. Surface-charge profiles and capacitance are computed as functions of the aspect ratio α = a/ L, radial ratio δ = b/ a, and dielectric contrast κ = ε out /ε in . The zero-thickness limit δ → 1 + recovers the single-surface open-cylinder formulation, whereas increasing radial separation progressively shifts the charge toward the outer cylindrical surface. In the slender-cylinder regime, finite radial separation produces only subleading corrections to the dominant logarithmic behavior. In the opposite short-cylinder regime, the capacitance does not approach a finite plateau; instead, for fixed δ > 1, it retains a slow logarithmic decay described by a coupled-ring asymptotic expression derived from the large-α kernel structure. The numerical results are further validated against an independent graded-panel boundary-element discretization, providing benchmark data for coupled axisymmetric electrostatic solvers.
The scattering properties of pure gaseous methane and ethylene (CH4 and C2H4) are investigated in the temperature range 1–100 K. The s-wave scattering lengths (a0) for CH4 and C2H4 molecules are calculated for the first time. They are found to be 8.948 and 10.528 Å for CH4 and C2H4 molecules, respectively. Using these values of a0 together with the dispersion coefficient C6, the binding energy ε0s of the corresponding dimers is estimated. The binding energies between molecules are calculated using s-wave scattering lengths. It is found that CH4 and C2H4 can form weakly bound dimers. The binding energy ε0s for (CH4)2 falls within the range −0.002 to −0.40 kcal/mol, whereas for (C2H4)2 it ranges from −0.003 to −0.2 kcal/mol. The total and viscosity cross-sections are computed to provide insight into the interaction dynamics governing the molecular systems. The cross-sections showed a minimum and maximum structure. The shape resonances are produced by centrifugal barriers (when ℓ>0). The peak of the resonance portion of the cross-section is close to energy, ER (when δℓ(k)=π2). The resonances can be interpreted as an indication of a quasibound state. The lifetime τ of the quasibound states for ℓ-wave (ℓ=2,4,6, and 8) is also computed and found to be in the range ~10−11 s. The study of the molecular cross-sections of CH4 and C2H4 has provided valuable insights into the properties and behavior of these molecules. Also, the average cross-sections are obtained over 1–100 K. The present work establishes a unified framework linking long-range interactions to near-threshold bound states and scattering properties.
In the context of f(R, T) gravity, this work examines an anisotropic cosmological model taking into account a Bianchi Type-V space–time with a dynamical matter–geometry coupling α (t) = α0 a−m . We introduce a shear-dependent equation of state p = ωρ + ξσ2 and an anisotropy-evolving parameter ω=ω0+ω1σ2θ2, creating a feedback system between thermodynamic fluid characteristics and space–time geometry. The analysis of energy conditions and the deceleration parameter demonstrates a transition from early deceleration to late-time acceleration, with a transition redshift consistent with observations and close agreement with the ΛCDM model. The model naturally explains cosmic acceleration without invoking a cosmological constant, while capturing early-universe anisotropy and late-time isotropy. The thermodynamic analysis also confirms that the proposed model is physically viable.
This study investigates the influence of a magnetic field and couple stresses on the initiation of thermal convection in a viscoelastic fluid described by the Navier–Stokes–Voigt (NSV) model, subjected to heating from below. The study is motivated by applications in polymer processing, crystal growth, and magnetohydrodynamic heat transfer. The analysis examines three types of boundary conditions using both linear (normal mode) and nonlinear (energy method) techniques. The energy method incorporates an energy decay framework to evaluate the impact of viscoelasticity, while a variational principle is applied to formulate the eigenvalue problem. Critical Rayleigh numbers obtained from both methods consistently predict the onset of convection. It is observed that convection occurs solely through stationary modes, in agreement with the principle of exchange of stabilities. The findings indicate that the presence of a magnetic field and couple stresses stabilizes the fluid layer by postponing the onset of convection. These insights are valuable for enhancing thermal stability and optimizing heat-transfer processes in engineering applications involving viscoelastic and magnetized fluid systems.
