A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance

In a theoretical analysis, a lump-integral model for freezing and melting of the bath material onto a cylindrical additive having its thermal resistance negligible with respect to that of the bath is developed. It is regulated by independent nondimensional parameters, namely the Stefan number, St the heat capacity ratio, Cr and the modified conduction factor, Cofm. Series solutions associated with short times for time variant growth of the frozen layer and rise in interface temperature between the additive and the frozen layer are obtained. For all times, numerical solutions concerning the frozen layer growth with its melting and increase in the interface temperature are also found. Time for freezing and melting is estimated for different values of Cr, St and Cofm. It is predicted that for lower total time of freezing and melting Cofm<2 or Cr<1 needs to be maintained. When the bath temperature equals the freezing temperature of the bath material, the model is governed by only Cr and St and gives closed-form expressions for the growth of the frozen layer and the interface temperature. For the interface attaining the freezing temperature of the bath material the maximum thickness of the frozen layer becomes ξmax-√Cr(Cr+St). The model is validated once it is reduced to a problem of heating of the additive without freezing of the bath material onto the additive. Its closed-form solution is exactly the same as that reported in the literature

Freezing and melting of a bath material onto a cylindrical solid additive in an agitated bath

In melting and assimilation of a cylindrical shaped additive in an agitated hot melt bath during the process of preparation of cast iron and steel of different grades, an unavoidable step of transient conjugated conduction-controlled axisymmetric freezing and melting of the bath material onto the additive immediately after its dunking in bath occurs. Decreasing the time of completion of this step is of great significance for production cost reduction and increasing the productivity of such preparations. Its suitable mathematical model of lump-integral type is developed. Its nondimensional format indicates the dependence of this step upon independent nondimensional parameters- the bath temperature, θb the modified Biot number, Bim denoting the bath agitation, the property-ratio, B and the heat capacity-ratio, Cr of the melt bath-additive system, the Stefan number, St pertaining to the phase-change of the bath material. The model provides the closed-form expressions for both the growth of the frozen layer thickness, ξ onto the additive and the heat penetration depth, η in the additive. Both are functions of these parameters, but when they are transformed to the growth of the frozen layer thickness with respect to the heat capacity ratio per unit Stefan number; and the time per unit property-ratio, B, their expressions become only a function of single parameter, the conduction factor, Cof consisting of the parameters, B, Bim and θb. The closed-form expression for the growth of the maximum thickness of the frozen layer, its time of growth, the time of the freezing and melting; the heat penetration depth are also derived. When the heat penetration depth approaches the central axis of the cylindrical additive in case of the complete melting of the frozen layer developed Cof≤11/72. It is found that the decreasing Cof reduces both the time of this unavoidable step and the growth of the maximum frozen layer thickness and at Cof=0, the frozen layer does not form leading to zero time for this step. If the bath is kept at the freezing temperature of the bath material, only freezing occurs. To validate the model, it is cast to resemble the freezing and melting of the bath material onto the plate shaped additive. The results are exactly the same as those of the plate

Prospects of biodiesel production from microalgae in India

Energy is essential and vital for development, and the global economy literally runs on energy. The use of fossil fuels as energy is now widely accepted as unsustainable due to depleting resources and also due to the accumulation of greenhouse gases in the environment. Renewable and carbon neutral biodiesel are necessary for environmental and economic sustainability. Biodiesel demand is constantly increasing as the reservoir of fossil fuel are depleting. Unfortunately biodiesel produced from oil crop, waste cooking oil and animal fats are not able to replace fossil fuel. The viability of the first generation biofuels production is however questionable because of the conflict with food supply. Production of biodiesel using microalgae biomass appears to be a viable alternative. The oil productivity of many microalgae exceeds the best producing oil crops. Microalgae are photosynthetic microorganisms which convert sunlight, water and CO2 to sugars, from which macromolecules, such as lipids and triacylglycerols (TAGs) can be obtained. These TAGs are the promising and sustainable feedstock for biodiesel production. Microalgal biorefinery approach can be used to reduce the cost of making microalgal biodiesel. Microalgal-based carbon sequestration technologies cover the cost of carbon capture and sequestration. The present paper is an attempt to review the potential of microalgal biodiesel in comparison to the agricultural crops and its prospects in India.Biodiesel Microalgae Triacylglycerol Algal reactors Biorefinery