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Steady-State Conduction and Shape Factors

In previous sections of this chapter we discussed steady-state heat conduction in one direction. In many cases, however, steady-state heat conduction is occurring in two directions i.e., two-dimensional conduction is occurring. The two-dimensional solutions are more involved and in most cases analytical solutions are not available. One important approximate method to solve such problems is to use a numerical method discussed in detail in Section 4.15. Another important approximate method is the graphical method, which is a simple method that can provide reasonably accurate answers for the heat-transfer rate. This method is particularly applicable to systems having Isothermal boundaries. [Pg.233]

Draw a model to scale of the two-dimensional solid. Lable the isothermal boundaries. In Fig. 4.4-1, Ti and T2 are isothermal boundaries. [Pg.234]

Select a number N that is the number of equal temperature subdivisions between the isothermal boundaries. In Fig. 4.4-1, N = 4 subdivisions between T, and Tj. Sketch in the isotherm lines and the heat flow or-flux lines so that they are perpendicular to each other at the intersections. Note that isotherms are perpendicular to adiabatic (insulated) boundaries and also lines of symmetry. [Pg.234]

Keep adjusting the isotherm and flux lines until for each curvilinear square the condition Ax = Ay is satisfied. [Pg.234]

In order to calculate the heat flux using the results of the graphical plot, we first assume unit depth of the material The heat flow q through the curvilinear section shown in Fig. 4.4-1 is given by Fourier s law. [Pg.234]


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