Integral transform method for laminar heat transfer convection of herschel-bulkley fluids within concentric annular ducts

ABSTRACT: Related momentum and energy equations describing the heat and fluid flow of Herschel-Bulkley fluids within concentric annular ducts are analytically solved using the classical integral transform technique, which permits accurate determination of parameters of practical interest in engineering such as friction factors and Nusselt numbers for the duct length. In analyzing the problem, thermally developing flow is assumed and the duct walls are subjected to boundary conditions of first kind. Results are computed for the velocity and temperature fields as well as for the parameters cited above with different power-law indices, yield numbers and aspect ratios. Comparisons are also made with previous work available in the literature, providing direct validation of the results and showing that they are consistent.

A mass transfer model applied to the supercritical extraction with CO2 of curcumins from turmeric rhizomes (Curcuma longa L)

ABSTRACT: Increasing restrictions on the use of artificial pigments in the food industry, imposed by the international market, have increased the importance of raw materials containing natural pigments. Of those natural substances with potential applications turmeric rhizomes (Curcuma longa L), are one of the most important natural sources of yellow coloring. Three different pigments (curcumin, desmetoxycurcumin, and bis-desmetoxycurcumin) constitute the curcuminoids. These pigments are largely used in the food industry as substitutes for synthetic dyes like tartrazin. Extraction of curcuminoids from tumeric rhizomes with supercritical CO2 can be applied as an alternative method to obtain curcuminoids, as natural pigments are in general unstable, and hence degrade when submitted to extraction with organic solvents at high temperatures. Extraction experiments were carried out in a supercritical extraction pilot plant at pressures between 25 and 30 MPa and a temperature of 318 K. The influence of drying pretreatment on extraction yield was evaluated by analyzing the mass transfer kinetics and the content of curcuminoids in the extracts during the course of extraction. The chemical identification of curcuminoids in both the extract and the residual solid was performed by spectrophotometry. Mass transfer within the solid matrix was described by a linear first-order desorption model, while that in the gas phase was described by a convective mass transfer model. Experimental results showed that the concentration profile for curcuminoids during the supercritical extraction process was higher when the turmeric rhizomes were submitted to a drying pretreatment at 343 K.