Heat and Mass Transfer Model Including Shrinkage Applied to Ellipsoidal Products: Case Study for Drying of Bananas

Abstract

This paper presents an investigation of the simultaneous heat and mass transfer in solidr with prolate spheroidal shape. A two-dimensional unsteady dflusion model applied to a prolate spheroid is presented assuming that liquid d@usion is IntroductionSince the last century the study and analysis of heat and mass transfer in porous media have been the subject of many investigations, due to the many applications in industrial processes. For the diffusion problem, with specified initial and boundary conditions, the goal is to obtain the solution of the diffusion equation. Based on a review of the technical literature, it can be noted that only the simple geometric bodies * Author for correspondence. The development of appropriate equations for heat and mass diffision in a prolate spheroid is of interest, because it represents a higher degree of precision compared to the usual treatment of simplifLing the shape as a sphere or cylinder. If the solid properties including the diffision coefficient are invariant, it is possible to treat both heat and mass transfer in a similar manner. This is important, since it is unnecessary to repeat the complex derivation for each process.As a complement to this research, a two-dimensional numerical analysis was performed for simultaneous heat and mass processes including shrinkage in ellipsoidal shaped bodies, with particular reference to bananas, using the finite-volume method to discretize the transient diffusion equations. Heat and Mass Transfer Model for Drying of Bananas Modelling DevelopmentsFor a non-steady-state process, the diffusion equation in any coordinate system is given in the short form by:The diffusion phenomenon in an ellipsoid of revolution was considered, in which the axis of revolution is greater than the other axis as shown in Figure 1. In this case it is said to be prolate, while, if the axis of revolution is smaller than the other, it is called oblate. The following assumptions are made:The shrinkage of the solid is equal to the volume of water evaporated.The shrinkage is two-dimensional and axi-symmetric around the z-axis.The solid is composed of water in the liquid phase and solid material.The only mechanism of drying is diffusion.The thermo-physical properties are variables during the drying process.The body is axially symmetric around the z-axis.The moisture content and temperature field is considered symmetric around the z-axis at any time and is constant at the beginning of the process.The phenomenon occurs under evaporative and convective boundary conditions including heating of vapor produced at the surface.No energy or mass generation occurs.The diffusion phenomenon occurs under falling rate conditions.In many physical problems, it is better to use a new orthogonal coordinate system instead of the Cartesian coordinates x, y, z. In the case of a body with ellipsoidal geometric shape, an adequate coordinate system is the prolate spheroidal. The relations between Cartesian and prolate spheroidal coordinate systems are given by The average moisture conten...

Heat and Mass Transfer, and Volume Variations in Banana Slices during Convective Hot Air Drying: An Experimental Analysis

“…This occurs regardless of the geometric shape of the banana and the dying condition (air temperature and relative humidity). Obviously, the air velocity has a major effect in the heating rates [9,[33][34][35], but, herein, drying was done in an air circulation oven where low air velocity was used (almost natural convection of heat).…”

“…This occurs regardless of the geometric shape of the banana and the dying condition (air temperature and relative humidity). Obviously, the air velocity has a major effect in the heating rates [9,[33][34][35], but, herein, drying was done in an air circulation oven where low air velocity was used (almost natural convection of heat). The heat transfer effect can be verified by the convective heat transfer coefficient; however, in practical applications, heat flux and temperature at the surface of a porous material are very difficult to measure without disturbing the heat transfer, especially in the drying process of materials with high moisture content, where simultaneous mass and heat transfer and dimensions variations have occurred.…”

“…This last characteristic provides an increase of the air flow turbulence level in the boundary layer around the fruit, increasing energy transfer between air and material. Thus, additional complications in the measurement of the heat transfer coefficient are evident [13,35].…”

Apparent thermal diffusivity estimation of the banana during drying using inverse method

“…Furthermore, few references concern about thermophysical properties during drying, as Lima (1999), Lima, Queiroz, and Nebra (2002), Pérez (1998) and Queiroz and Nebra (2001). However, the two first works use other methodology to obtain the apparent thermal diffusivity while the last work to solve the mass transfer determining diffusion and convective coefficients.…”

Mathematical modeling of drying process of unripe banana slices

“…Reduction in diameter and length of dried fruits reduces the volume itself. Normally, an empirical fitting through experimental test is used to find an equation for shrinkage (CHEMKHI; ZAGROUBA; BELLAGI, 2005;LIMA et al, 2002;QUIROZ;NEBRA, 2001;SIMAL 1998).…”