Browsing by Subject "heat transfer"

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    Physics and Dynamics of Density-Compensated Temperature and Salinity Anomalies. Part I: Theory
    (2005) Tailleux, Rémi; Lazar, Alban; Reason, C J C
    Subducted temperature anomalies have been invoked as a possible way for midlatitudes to alter the climate variability of equatorial regions through the so-called thermocline bridge, both in the Pacific and Atlantic Oceans. To have a significant impact on the equatorial heat balance, however, temperature anomalies must reach the equatorial regions sufficiently undamped. In the oceans, the amplitude of propagating temperature (and salinity) anomalies can be altered both by diabatic (nonconservative) and adiabatic (conservative) effects. The importance of adiabatic alterations depends on whether the anomalies are controlled by wave dynamics or by passive advection associated with density compensation. Waves being relatively well understood, this paper seeks to understand the amplitude variations of density-compensated temperature and salinity anomalies caused by adiabatic effects, for which no general methodology is available. The main assumption is that these can be computed independent of amplitude variations caused by diabatic effects. Because density compensation requires the equality T'/S' = βs/α to hold along mean trajectories, the ratio T'/S' may potentially undergo large amplitude variations if the ratio βs/α does, where a and βsare the thermal expansion and haline contraction coefficients, respectively. In the oceans, the ratio βs/α may decrease by an order-1 factor between the extratropical and tropical latitudes, hut such large variations are in general associated with diapycnal rather than isopycnal motion and hence are likely to be superimposed in practice with diabatically induced variations. To understand the individual variations of T' and S' along the mean streamlines, two distinct theories are constructed that respectively use density/salinity and density/spiciness as prognostic variables. If the coupling between the prognostic variables is neglected, as is usually done, both theories predict at leading order that temperature (salinity) anomalies should be systematically and significantly attenuated (conserved or amplified), on average, when propagating from extratropical to tropical latitudes. Along particular trajectories following isopycnals, however, both attenuation and amplification appear to be locally possible. Assuming that the density/spiciness formulation is the most accurate, which is supported by a theoretical assessment of higher-order effects, the present results provide an amplification mechanism for subducted salinity anomalies propagating equalorward, by which the latter could potentially affect decadal equatorial climate variability through their slow modulation of the equatorial mixed layer, perhaps more easily than their attenuated temperature counterparts. This could be by affecting, for instance, barrier layers by which salinity is known to strongly affect local heat fluxes and heat content.
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    Transient nonlinear heat transfer using finite elements
    (1986) Korvink, Jan Gerrit; Martin, JB
    This thesis is concerned with the numerical modelling of the transient nonlinear heat conduction problem in solid continua. The hyperbolic governing equation is specialised to a parabolic equation which is sufficient for most engineering applications. The theoretical development includes the effects of conduction, specific heat, internal heat generation and the boundary conditions of convection, radiation, specified temperatures and flux, as well as point sources in the domain. The finite element spatial semidiscretisation of the equations is formally derived from the weak form of the governing equations. Temporal discretisation is obtained through an implicit/explicit difference scheme. The material properties are allowed to be temperature dependent, and consequently a modified Newton-Raphson iterative scheme is employed to solve the equations. The fully discretised equations are solved by implementing the algorithm in an existing finite element stress analysis code. Modelling is possible using four or eight-noded isoparametric elements, and solution control is possible through choice of time step size and choice of time integration method. Five examples are employed to demonstrate the ability of the program. The results compare well with published analytical solutions.