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Conduction

2 tools in the Fluids and Heat Transfer area.

Thermal Stress and Conduction

Four thermal analyses chosen by checkboxes. Thermal stress: a bar heated between rigid walls with an optional initial gap, two segments in series, members in parallel (a bolt in a sleeve, posts under a rigid cap, with an external load) by force equilibrium and strain compatibility, and the bimetallic strip by Timoshenko's 1925 curvature formula with the stresses through both layers. Steady conduction: a plane wall, cylinder or sphere of up to five layers with contact resistances and convection on both faces as a thermal-resistance network, the heat rate, every interface temperature, the temperature profile and the critical insulation radius. Fins: straight rectangular, pin and annular fins (Bessel functions) with adiabatic, convective, corrected-length and infinite-fin tip conditions, the fin parameter m, efficiency, effectiveness, heat rate and the temperature along the fin. Transient: lumped capacitance with the Biot check and the one-term and N-term series for the plane wall, long cylinder and sphere (eigenvalues solved, not read from a table), centre and surface temperatures, energy transferred and the time to reach a temperature. The default inputs are Hibbeler's bolt-and-sleeve Example 4.12 (20.3 kN), the single-pane window of Cengel's Example 3-2 (266 W), the copper rod of Incropera's Example 3.8 (8.3 W) and the thermocouple of Incropera's Example 5.1 (5.2 s to 199 °C).

1 worked example reproduced, listed on the tool page.

Fins and Extended Surfaces

Performance of a single fin and of a fin array by the classical one-dimensional theory: the fin parameter m = √(hP/(kA_c)), the temperature distribution, the heat rate, the fin efficiency and effectiveness for six profiles (straight fins of rectangular, triangular and parabolic profile, cylindrical and conical pin fins, and the annular fin of rectangular profile) with the four tip conditions of the uniform fin (adiabatic, convecting, prescribed temperature, infinitely long), using the closed forms in hyperbolic and modified Bessel functions of Gardner (1945) as tabulated by Incropera and DeWitt (Table 3.5); the Harper–Brown corrected length and the corrected-radius value are printed beside the exact tip solutions, the Biot number checks the one-dimensional assumption, and the overall surface efficiency gives the array's total heat rate. The default is an aluminium straight rectangular fin 3 × 50 × 100 mm at 100 °C in 20 °C air with h = 100 W/(m²·K), checked against scipy and the NACA Report 158 example.

1 worked example reproduced, listed on the tool page.

Other Fluids and Heat Transfer sections

Pipe Flow · Pumps and Fans · Compressible Flow · Convection · Radiation · Heat Exchangers · Thermodynamic Cycles · Fluid Properties