Abstract
Both a numerical and an analytical models were developed to simulate temperature profiles in continuous laminar pipe flow during microwave heating. Fully developed velocity and thermally developing conditions were assumed. The numerical solution was obtained by first solving Maxwell equations and then by coupling them with the energy balance for the flowing fluid. On the other hand, the same problem was solved analytically under the simplifying assumption foreseeing uniform heat generation inside the pipe. With the aim of reducing computational efforts, numerical and analytical results were compared in order to investigate conditions for which the two models allowed to recover the same temperature patterns. Thus, it has been shown that suitable conditions can be found for which the simplified analytical model can lead to an easy way to predict the heat transfer through the pipe.
Highlights
Nowadays, it is widely accepted that using microwaves (MWs) as a source of energy turns out into a viable alternative for high-temperature/short-time processing featuring several industrial food treatments
(1) since available energy densities are typically smaller than the ones achievable by conventional techniques, laminar flow conditions are often realized in order to realize acceptable temperature increases [5, 6]; (2) wishing to enhance heat transfer rates, laminar flow is not disadvantageous since heat transfer is no more driven by wall conditions; reduced heat transfer coefficients could even be helpful, the walls being warmer than the external air
The Maxwell’s equations are solved by means of the finite element method (FEM) [26] using unstructured tetrahedral grid cells; the electric field distribution E in the microwave cavity, both for air and for the applicator pipe carrying the fluid under process, is determined by imposing where E is the electric field intensity, εr is the relative permittivity, ω is the angular wave frequency, μr is the relative permeability of the material, k0 is the wavenumber in vacuum, and σ is the electric conductivity
Summary
It is widely accepted that using microwaves (MWs) as a source of energy turns out into a viable alternative for high-temperature/short-time processing featuring several industrial food treatments. Alternative procedures based on approximate methods can be found; the latter are essentially based on attempting a suitable simplified modelling for the generation term in the energy equation The latter procedure is acceptable by considering that in the field of food engineering it is often desired to control the thermal effect of microwave heating, while detailed knowledge of EM field behaviour is unnecessary. The momentum and the energy equations turn out to be one way coupled with Maxwell’s equations and are solved both numerically and analytically; the developing temperature field for an incompressible laminar duct flow subjected to heat generation is considered The latter is sought as the effective one arising from the solution of the electromagnetic problem at hand, whereas its average value over the water volume is assumed with reference to the analytical solution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
