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The present study addresses the problem of ignition of a single sodium droplet, which is an important issue for the nuclear facilities safety. The study follows the approach of previous works and extends the results of those papers to the case of radiative heat loss. The contribution of the thermal radiation is taken into account based on the P-1 approximation for thermal radiation transfer. An extension of solutions of the existing model is obtained in the presence of radiative heat loss for ignition time and critical temperature by exploiting the sensitivity of the process to large chemical activation energy. Different qualitative effects of varying the dimensionless convective heat loss parameter with ignition time and critical temperature are presented in the graphs. The results show that the inclusion of additional heat sink mechanism, that is, radiative heat loss, causes significant delays in the ignition time and reduces the critical temperature with respect to results of previous studies.

PurposeIn this paper, we studied the steady flow of a radiative magnetohydrodynamics viscoelastic fluid over an exponentially stretching sheet. This present work incorporated the effects of Soret, Dufour, thermal radiation and chemical reaction.Design/methodology/approachAn appropriate semi-analytical technique called homotopy analysis method (HAM) was used to solve the resulting nonlinear dimensionless boundary value problem, and the method was validated numerically using a finite difference scheme implemented on Maple software.FindingsIt was observed that apart from excellence agreement with the results in literature, the results obtained gave further insights into the behaviour of the system.Originality/valueThe purpose of this research is to investigate heat and mass transfer profiles of a MHD viscoelastic fluid flow over an exponentially stretching sheet in the influence of chemical reaction, thermal radiation and cross-diffusion which are hitherto neglected in previous studies.

In this article analytical solution of one-dimensional heat equation in relaxation mode of heat generation and conduction using Laplace transforms method is presented. The model adopted takes into account finite velocity of heat propagation, and relaxation of heat source capacity. The properties of heat source terms in four different cases are incorporated in the model and investigated. Temperature distributions and variations with conduction mode and relaxation time are analyzed. High relaxation time is observed to lowers the temperature profile, whereas enhanced temperature distribution changes at particular values of α, and for source capacity proportional to temperature. How the steady state solution is achieved for some selected values of coefficients is also discussed.

Dielectric mixing model has been successfully employed to characterize the presence of lead in water-logged porous media, contaminated by lead at different temperatures and concentrations. This work has demonstrated the influence of temperature and concentration of lead on the bulk relative permittivity (ԑb) of lead-water system in porous media. Generally, the bulk relative permittivity of the lead-water-soil system, ԑb, decreases with rising temperature and the least value of ԑb was obtained in this work at 30oC while the highest ԑb was obtained at 20oC. It is visible from the combined plot that the bulk permittivity, ԑb, of lead-water system decreases as the lead concentration increases. The ԑb is highest at lead volume fraction of 0.05. This is closely followed by that at 0.01 and so on, while the least ԑb occurs at lead volume fraction of 0.1. The reason for this is owing to the fact that as the fraction of lead increases, that of water decreases. This work is important in the monitoring of water quality and contamination by lead in the subsurface.