Heat Transfer is part of a free web series, ChemPlugin Modeling with Python, by Aqueous Solutions LLC.
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A ChemPlugin instance can trace how temperature varies over the course of a simulation by keeping track of the net accumulation or loss of heat energy during the time marching procedure.
If Q, as before, is the flow rate in m3 s−1 across a link, the rate of advective heat transfer is given by
in units of J s−1. Here, ρw is the fluid density in kg m−3, Cw is fluid heat capacity in J kg−1 K−1, and T is temperature in K.
A client uses the “FlowRate()” member function to set the flow rate Q across a link, as described earlier. Once Q is specified, the instance computes the effects of advective heat transport whenever the client program calls the “AdvanceHeatTransport()”member function.
Fourier's law gives the rate of conductive heat transfer in J s−1 by
In this equation, A is the link's cross-sectional area in m2, KT is the thermal conductivity in W m−1 K−1, and dT/dx is the temperature gradient across the plane, in K m−1.
ChemPlugin calculates the conductive heat flux according to an approximate equation
where τT is the thermal transmissivity in W K−1 , and Tj and Tlinked are temperature of the originating and linked instances, respectively, in K. Calculation of the thermal transmissivity τT closely parallels determination of the transmissivities τ for mass transport, as described earlier.
The thermal transmissivity is set using the “HeatTrans()” member function. The default units are W K−1. In the time marching loop, use “AdvanceHeatTransport()” to transfer heat energy. For more information, see the Heat Transfer chapter in the ChemPlugin User's GuIde.
Craig M. Bethke and Brian Farrell. © Copyright 2016–2021 Aqueous Solutions LLC. This lesson may be reproduced and modified freely to support any licensed use of The Geochemist's Workbench® software, provided that any derived materials acknowledge original authorship.
Bethke, C.M., 2008, Geochemical and Biogeochemical Reaction Modeling. Cambridge University Press, New York, 547 pp.
Bethke, C.M., 2021, The Geochemist's Workbench®, Release 15: ChemPlugin™ User's Guide. Aqueous Solutions LLC, Champaign, IL, 332 pp.
Carslaw, H.S. and Jaeger, J.C., 1959, Conduction of Heat in Solids. Clarendon Press, Oxford, 510 pp.