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 2016–2024 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., 2022, Geochemical and Biogeochemical Reaction Modeling, 3rd ed. Cambridge University Press, New York, 520 pp.
Bethke, C.M., 2024, The Geochemist's Workbench®, Release 17: ChemPlugin™ User's Guide. Aqueous Solutions LLC, Champaign, IL, 303 pp.
Carslaw, H.S. and Jaeger, J.C., 1959, Conduction of Heat in Solids. Clarendon Press, Oxford, 510 pp.