M. Spiga

A symmetric solution for velocity profile in laminar flow through rectangular ducts

Abstract The present analysis is concerned with the velocity distribution in steady state, hydrodynamically fully developed, laminar flow for Newtonian fluids in rectangular ducts. The solutions describing velocity profiles and friction factors are derived by using the finite Fourier transform. The solution giving the two-dimensional velocity distribution is formally symmetric with respect to the rectangular Cartesian coordinates x and y, and provides more accurate numerical results, with shorter computational times, in comparison to the well known velocity distributions usually quoted in literature.

A rigorous solution to a heat transfer two phase model in porous media and packed beds

Abstract The dynamic response of porous media and packed beds systems to an arbitrary time varying inlet temperature is investigated analytically. A two phase model is developed taking rigorously into account the fluid to solid heat capacity ratio. At first the initial value problem is solved, including initially non-uniform spatial temperature distributions. Then a general solution, relevant to operational modes in which the initial conditions are forgotten, is proposed. Some graphs are shown for simple situations such as delta, step, ramp response (for the initial value problem) and periodic sinusoidal inlet temperature.

Nusselt numbers in laminar flow for H2 boundary conditions

Abstract The present analysis deals with the velocity and temperature distribution in steady state, hydro dynamically and thermally fully developed, laminar forced flow for Newtonian fluids in rectangular ducts. The analytical solutions are presented for all the eight modified H2 thermal boundary conditions around the periphery of the duct cross-section. The velocity profile represents the rigorous solution to the Navier Stokes equation; the temperature profile is obtained resorting to series solutions of trigonometric functions. The temperatures and the Nusselt numbers are predicted as functions of the aspect ratio and compared with the results available in literature. Finally, very simple polynomial representations are given for the Nusselt numbers.

Step response of the crossflow heat exchanger with finite wall capacitance

Abstract The step response of a single-pass crossflow heat exchanger is investigated. The two-dimensional transient temperature distributions in the core wall and in both the unmixed fluids are analytically determined, considering finite wall heat capacity (i.e. finite propagation speed of disturbances). The solutions are deduced by the local energy balance equations, resorting to the Green functions and to a threefold Laplace transform. The dimensionless temperatures are presented in terms of the governing parameters (number of transfer units, capacity ratios, heat transfer resistance ratio). Assuming constant initial conditions and entrance temperature of the hot fluid subjected to a sudden step increase, the transient temperature field is computed with extremely low computational time; the results are plotted for a wide range of the governing parameters.

Energy analysis of a passive solar system

Abstract This work aims at presenting the numerical solution to a natural convection problem concerning the use of a passive solar system for building heating purpose. The system consists of a modification of the well-known Trombe-Michel passive system. The main differences consist of thermal insulation on the southern wall surface, the presence of two solar ducts separated by a thin metallic plate with collector function, and a thermal storage over the ceiling of the heated rooms. The numerical solution to the simple mathematical model — based on energy and mass conservation equations — is achieved by a finite difference method, which allows to determine both the time-dependent temperature profile on each component of the system and the air flow pattern in the solar ducts. A comparison between the numerical results and some experimental data is reported: it shows a very satisfactory agreement. At last, the hour by hour energy fluxes are shown in some graphs.

Laminar viscous dissipation in rectangular ducts

Abstract In this paper, a theoretical study is conducted, calculating the temperature distribution in the cross-section of a rectangular duct, under the conditions of newtonian and incompressible fluid, fully developed laminar flow and steady-state regime. The governing equations are solved resorting to the finite Fourier transform The temperature distributions are obtained. The results concerning the temperature distribution in a square duct are shown by tables and figures, and a comparison between the present solution and some literature contributions is also presented. The viscous dissipation is responsible for a power generation that, for a particular Brinkman number ( Br q = 1/gF ∗ or Br w = ±∞ ), allows the wall heat flux to vanish. At last, the effects of viscous dissipation and wall heat flux are presented in some graphs, as a function of the duct aspect ratio.

Laminar heat transfer between parallel plates as the limiting solution for the rectangular duct

Abstract This paper is aimed at demonstrating that the velocity and the temperature distributions of a Newtonian fluid in fully developed laminar flow between infinite parallel plates with uniform wall heat flux, can be derived from the rectangular duct analysis, in H2 boundary conditions, in the limit of the aspect ratio β tending to infinity. Hence the 2-D analytical distributions of fluid velocity and temperature for the rectangular duct are elaborated to obtain the well known 1-D distributions for the slab geometry. The main outcome regards the Nusselt number; it is calculated for the rectangular duct, in the limit of β → ∞, and coincides with the Nusselt number of the infinite parallel plates.

Temperature in heat generating solids with memory

The present paper is concerned with time dependent heat transport by wave propagation in an homogeneous isotropic elastic solid with memory. The energy generated in the material for electrical heating or chemical or nuclear reactions is propagated with a finite speed.The effect of this thermal wave speed is noticeable in many practical applications involving short time and high heat flux situations. The one dimensional, time dependent temperature distribution in a heat generating solid is analytically determined resorting to the Maxwell-Cattaneo-Vernotte equation, following the theory of complex functions of complex variables. Some results are reported and shortly discussed; a comparison with the classical Fourier theory is made.ZusammenfassungDie Arbeit behandelt den zeitabhängigen Wärmetransport durch eine fortschreitende Welle in einem homogenen isotropen elastischen Festkörper mit Gedächtnis. Die im Material durch elektrische Heizung oder durch chemische oder nukleare Reaktionen erzeugte Wärme wird mit endlicher Geschwindigkeit fortgeleitet. Die Wirkung dieser thermischen Wellengeschwindigkeit ist für manche praktische Anwendungen von Bedeutung, soweit kurze Zeiten und hohe Wärmeflüsse eine Rolle spielen. Die eindimensionale zeitabhängige Temperaturverteilung in einem wärmeerzeugenden Körper ist analytisch bestimmt unter Benutzung der Maxwell-Cattaneo-Vernotte-Gleichung nach der Theorie komplexer Funktionen komplexer Variablen. Einige Ergebnisse werden mitgeteilt, kurz diskutiert und mit der klassischen Fourier-Theorie verglichen.

Radiant heat transfer in participating media bounded by reflecting surfaces

Abstract Transport of thermal radiation within an emitting, absorbing and scattering plane grey medium bounded by specularly- or diffusely-reflecting plates is investigated. The physical situation can simulate steady-state and accident conditions in nuclear reactor components, such as the gap in a fuel rod or the Ar cover gas blanket in LMFBRs. The integral transfer equation is solved in semi-analytical form by a collocation method, using Chebyshev polynomials as basis functions. Numerical results are presented and briefly discussed; the predictions for radiative heat flux and temperature are shown to be accurate over a large range of optical depths.

Radiative heat transfer in plane participating media

Abstract The problem of radiative heat transfer through a nonisothermal scattering, absorbing and emitting grey medium between reflecting, absorbing and emitting plates is analytically investigated. The solution technique is based on a projectional procedure, equivalent to a variational approach. The results concern the most meaningful physical quantities, and get an improved accuracy with respect to the data available in literature, with extremely low computational time.