ConductionDirect_Pipe class

Contents

Description

This is a sub-class of the ConductionDirect class for the implementation of the Thermal Pipe direct heat conduction model.

This model assumes that heat is exchanged through a ficticious "thermal pipe" connecting both elements, and the discrete Fourier law governs the rate of heat transfer:

$$Q = \frac{k.A}{d}\Delta T$$

Where:

$$k = \left ( R_{i}+R_{j} \right ) \left ( \frac{R_{i}}{k_{i}} + \frac{R_{j}}{k_{j}} \right )^{-1}$$

$$A = \pi \left ( R_{c} \right )^{2}$$

Notation:

$k$: Thermal conductivity of particles i and j

$R$: Radius of particles i and j

$R_{c}$: Contact radius

$d$: Distance between the center of the particles

$\Delta T = T_{j}-T_{i}$: Temperature difference between elements i and j

References:

classdef ConductionDirect_Pipe < ConductionDirect

Constructor method

    methods
        function this = ConductionDirect_Pipe()
            this = this@ConductionDirect(ConductionDirect.PIPE);
            this = this.setDefaultProps();
        end
    end

Public methods: implementation of super-class declarations

    methods
        %------------------------------------------------------------------
        function this = setDefaultProps(this)

        end

        %------------------------------------------------------------------
        function this = setFixParams(this,~)

        end

        %------------------------------------------------------------------
        function this = setCteParams(this,~)

        end

        %------------------------------------------------------------------
        function this = evalHeatRate(this,int)
            % Assumption: pipe cross-section area is a circle for spherical
            % particles and a rectangle for cylindrical particles
            switch int.elem1.type
                case int.elem1.SPHERE
                    A = pi * int.kinemat.contact_radius^2;
                case int.elem1.CYLINDER
                    A = 2 * int.kinemat.contact_radius * int.elem1.len;
            end
            this.total_hrate = A * int.avg_conduct * (int.elem2.temperature-int.elem1.temperature) / int.kinemat.distc;
        end
    end

end


Published with MATLAB® R2019b