A Mathematical Model on Heat Mass Transfer Including Relaxation Time for Different Geometries During Drying of Foods

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Subrahamanyam Upadhyay ◽  
K. N. Rai
Keyword(s):  
Mass Transfer ◽  
Boundary Condition ◽  
Relaxation Time ◽  
Diffusion Model ◽  
Heat Mass Transfer ◽  
Present Model ◽  
Spherical Shape ◽  
Cylindrical Shape ◽  
Phase Lag ◽  
Moisture Potential

Abstract In this paper, a single phase lag model on heat mass transfer in application of food drying has been developed. The present model is a generalization of the diffusion model. The whole analysis is presented in nondimensional form. The effects of shape parameter, relaxation time parameters, Luikov number, Kirpichev number, Biot number, Kossovich number, and Predvoditelev number on heat and mass transfer are discussed in detail. For experimental validation, we have taken examples of banana, mango, and cassava. Our simulations show that the present model is more suitable than diffusion model. The present model is in good agreement with experimental data. The moisture potential of slab food is higher than cylindrical food and moisture potential of cylindrical food is higher than spherical food for boundary condition of first, second, and third kinds. It has been observed that the moisture potential is highest in boundary condition of second kind and lowest in boundary condition of the third kind while in between in boundary condition of the first kind. We conclude that for complete drying, the spherical shape foods takes lesser time than cylindrical shape and cylindrical shape takes lesser time than slab shape.

Hydrodynamic Force and Heat/Mass Transfer From Particles, Bubbles, and Drops—The Freeman Scholar Lecture

2003 ◽  
Vol 125 (2) ◽  
pp. 209-238 ◽  
Author(s):  
Efstathios E. Michaelides
Keyword(s):  
Mass Transfer ◽  
Heat Mass Transfer ◽  
Hydrodynamic Force ◽  
Spherical Shape ◽  
Analytical Form ◽  
Transport Processes ◽  
Temperature Fields ◽  
Momentum Exchange ◽  
Mass Transfer Processes ◽  
Finite Concentration

Recent advances on the analytical form of the hydrodynamic force and heat/mass transfer from a particle, bubble, or drop are examined critically. Also some of the recent computational studies, which help strengthen or clarify our knowledge of the complex velocity and temperature fields associated with the momentum and heat/mass transfer processes are also mentioned in a succinct way. Whenever possible, the processes of energy/mass exchange and of momentum exchange from spheres and spheroids are examined simultaneously and any common results and possible analogies between these processes are pointed out. This approach results in a better comprehension of the transport processes, which are very similar in nature, as well as in the better understanding of the theoretical expressions that are currently used to model these processes. Of the various terms that appear in the transient equations, emphasis is given to the history terms, which are lesser known and more difficult to calculate. The origin, form, and method of computation of the history terms are pointed out as well as the effects of various parameters on them. Among the other topics examined here are the differences in the governing and derived equations resulting by finite Reynolds and Peclet numbers; the origin, theoretical validity and accuracy of the semi-empirical expressions; the effects of finite internal viscosity and conductivity of the sphere; the effects of small departures from the spherical shape; the effects of the finite concentration; and the transverse, or lift, components of the force on the sphere.

scholarly journals Prediction of Heat and Mass Transfer in a Rotating Ribbed Coolant Passage With a 180 Degree Turn

1998 ◽  
Author(s):  
David L. Rigby
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Turbulence Model ◽  
Heat Mass Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Wall Boundary Condition ◽  
Wall Boundary

Numerical results are presented for flow in a rotating internal passage with a 180 degree turn and ribbed walls. Reynolds numbers ranging from 5200 to 7900, and Rotation numbers of 0.0 and 0.24 were considered. The straight sections of the channel have a square cross section, with square ribs spaced one hydraulic diameter (D) apart on two opposite sides. The ribs have a height of 0.1D and are not staggered from one side to the other. The full three dimensional Reynolds Averaged Navier-Stokes equations are solved combined with the Wilcox k-ω turbulence model. By solving an additional equation for mass transfer, it is possible to isolate the effect of buoyancy in the presence of rotation. That is, heat transfer induced buoyancy effects can be eliminated as in naphthalene sublimation experiments. Heat transfer, mass transfer and flow field results are presented with favorable agreement with available experimental data. It is shown that numerically predicting the reattachment between ribs is essential to achieving an accurate prediction of heat/mass transfer. For the low Reynolds numbers considered, the standard turbulence model did not produce reattachment between ribs. By modifying the wall boundary condition on ω, the turbulent specific dissipation rate, much better agreement with the flow structure and heat/mass transfer was achieved. It is beyond the scope of the present work to make a general recommendation on the ω wall boundary condition. However, the present results suggest that the ω boundary condition should take into account the proximity to abrupt changes in geometry.

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