Several numerical and experimental studies of natural convective heat transfer from two-sided heated horizontal plates are available. In the numerical studies it has usually been assumed that the plate is thin, effectively having no thickness, whereas plates of finite thickness have been used in the experimental studies. To determine whether the plate thickness has a significant influence on the heat transfer rates from the upper and lower surfaces of the plate, results have here been numerically obtained for circular and square plates having various thicknesses. The upper and lower surfaces of the plate have been assumed to be isothermal and at the same temperature. Both the case where the vertical side edges of the plates are isothermal and at the same temperature as the upper and lower plate surfaces and the case where these side edges are adiabatic have been considered. The flow has been assumed to be steady and the Boussinesq approach has been adopted. Conditions under which laminar, transitional, and turbulent flows exist have been considered, the standard k-epsilon turbulence model being used. The solution has been obtained using ANSYS FLUENT^©. Only the case where the heat transfer from the plate is to air has been considered. Variations of the Nusselt number with Rayleigh number for various dimensionless plate thicknesses for the two edge conditions considered have been obtained for circular and square plates. The results indicate that the dimensionless plate thickness has only a modest effect on the heat transfer rates from the plate surfaces.

Numerical and experimental studies of natural convective heat transfer from two-sided heated horizontal plates of simple shape are available. In the numerical studies it has usually been assumed that the plates have no thickness, whereas in the experimental studies plates of finite thickness have been used. To determine whether the plate thickness has a significant influence on the heat transfer rates from the surfaces of horizontal plates of various thicknesses having complex shapes results have here been numerically obtained for plates of having an I-shape and a +-shape. The upper and lower surfaces of the plates are assumed to be isothermal and at the same temperature. Both the case where the vertical side edges of the plates are isothermal and at the same temperature as the upper and lower plate surfaces, and the case where these edges are adiabatic have been considered. Conditions under which laminar, transitional, and turbulent flows exist have been considered. The standard k-epsilon turbulence model was used and was applied under all conditions. The solutions have been obtained using the commercial solver ANSYS FLUENT^©. The case where the heat transfer from the plate is to air has been considered. Variations of mean Nusselt numbers for the upper and lower plate surfaces and for the entire surface of the plate with Rayleigh number for various plate thicknesses have been obtained. The results indicate that the dimensionless plate thickness has a modest effect on the heat transfer rate from the upper surface of the plates.

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Simultaneous natural convective heat transfer from the top, bottom and side surfaces of two-sided inclined square plates having various thicknesses has been numerically investigated. The aim of this work is to determine whether the plate thickness has a significant influence on the heat transfer rates from the plate surfaces when the plate is inclined to the horizontal and to determine how the heat transfer rate varies with this angle of inclination. The upper, lower and side surfaces of the plate have been assumed to be isothermal and at the same temperature which is higher than that of the surrounding fluid. The range of conditions considered is such that laminar, transitional, and turbulent flow occur over the plate. The numerical solution has been obtained using the commercial CFD solver ANSYS FLUENT^©. In this study, results have only been obtained for the case where the plate is exposed to air. Inclination angles of between 0 and 40 degrees from the horizontal and plate dimensionless thicknesses (thickness-to-side length ratios) of between 0 and 0.3 have been considered. Variations of the mean Nusselt number with Rayleigh number for the top surface, bottom surface, side surface and that averaged over all heated surfaces of the plate for various inclination angles and for various plate dimensionless thicknesses have been obtained.

Fretting hysteresis loops are multivalued in displacement because loading and unloading branches revisit the same displacement at different tangential forces. This study applies a normalized path coordinate, \( u=\frac{k-1}{N-1} \), to represent displacement and force as the single-valued mappings \( \delta \left(u\right) \)and \( T\left(u\right) \), and compares four first-order Takagi–Sugeno fuzzy models using a 600-point experimental IC25 loop. Ten leakage-c⁠ontrolled 70/30 train–test partition⁠s yielded mean test NRMSEs of 0.00528 for ANFIS–TS, 0.00616 for SC16–TS, 0.00817 for FCM–TS, and 0.01333 for SC9–TS, with no significant difference between ANFIS–T⁠S and SC16–TS after⁠ Holm correcti⁠on (p=0.084)⁠. Physical fidelity and robustness were assessed through dissipated loop energy, peak force, displacement span, closure behavior, cumulative energy evolution, measur⁠ement-nois⁠e sensitivity, residual diagno⁠stics, ru⁠le density, and cycle-origin sensitivity. A same-input RBF–SVR benchmark achieved a lower NRMSE of 0.000838, whereas the fuzzy models retained explicit local rule bases and adjustable complexity. The same nine-rule ANFIS–TS procedure was independently fitted to experimental loops at approximately 1, 14, and 24.5 µm peak-to-peak displacement, demonstrating low-error reconstruction across multiple amplitude conditions without implying zero-shot prediction by a fixed model. Overall, the results establish pat⁠h parameterization as an accurate and int⁠erpretable framework for reconstructing experimental fretting hysteresis rather than as a new friction constitutive law.