Solvability and asymptotics of the heat equation with mixed variable lateral conditions and applications in the opening of the exocytotic fusion pore in cells

We investigate a mixed problem with variable lateral conditions for the heat equation that arises in modelling exocytosis, i.e. the opening of a cell boundary in specific biological species for the release of certain molecules to the exterior of the cell. The Dirichlet condition is imposed on a surface patch of the boundary and this patch is occupying a larger part of the boundary as time increases modelling where the cell is opening (the fusion pore), and on the remaining part, a zero Neumann condition is imposed (no molecules can cross this boundary). Uniform concentration is assumed at the initial time. We introduce a weak formulation of this problem and show that there is a unique weak solution. Moreover, we give an asymptotic expansion for the behaviour of the solution near the opening point and for small values in time. We also give an integral equation for the numerical construction of the leading term in this expansion.

An interdisciplinary approach to designing and evaluating a hybrid solar-biomass power plant

Purpose: Energy security is a major concern for India and many rural areas remain un-electrified. Thus, innovations in sustainable technologies to provide energy services are required. Biomass and solar energy in particular are resources that are widely available and underutilised in India. This paper aims to provide an overview of a methodology that was developed for designing and assessing the feasibility of a hybrid solar-biomass power plant in Gujarat. Design/methodology/approach: The methodology described is a combination of engineering and business management studies used to evaluate and design solar thermal collectors for specific applications and locations. For the scenario of a hybrid plant, the methodology involved: the analytical hierarchy process, for solar thermal technology selection; a cost-exergy approach, for design optimisation; quality function deployment, for designing and evaluating a novel collector - termed the elevation linear Fresnel reflector (ELFR); and case study simulations, for analysing alternative hybrid plant configurations. Findings: The paper recommended that for a hybrid plant in Gujarat, a linear Fresnel reflector of 14,000 m2 aperture is integrated with a 3 tonne per hour biomass boiler, generating 815 MWh per annum of electricity for nearby villages and 12,450 tonnes of ice per annum for local fisheries and food industries. However, at the expense of a 0.3 ¢/kWh increase in levelised energy costs, the ELFR can increase savings of biomass (100 t/a) and land (9 ha/a). Research limitations/implications: The research reviewed in this paper is primarily theoretical and further work will need to be undertaken to specify plant details such as piping layout, pump sizing and structure, and assess plant performance during real operational conditions. Originality/value: The paper considers the methodology adopted proved to be a powerful tool for integrating technology selection, optimisation, design and evaluation and promotes interdisciplinary methods for improving sustainable engineering design and energy management. © Emerald Group Publishing Limited.