Analysis of Time-Fractional Heat Transfer and its Thermal Deflection in a Circular Plate by a Moving Heat Source

Abstract

Mathematical modeling of a thin circular plate has been made by considering a nonlocal Caputo type time fractional heat conduction equation of order 0 < α ≤ 2, by the action of a moving heat source. Physically convective heat exchange boundary conditions are applied at lower, upper and outer curved surface of the plate. Temperature distribution and thermal deflection has been investigated by a quasi-static approach in the context of fractional order heat conduction. The integral transformation technique is used to analyze the analytical solution to the problem. Numerical computation including the effect of the fractional order parameter has been done for temperature and deflection and illustrated graphically for an aluminum material.

Study of Convective Heating in a Thermosensitive Functionally Graded Plate with Time-Fractional Heat Equation

“…x are expressed as SME, CLTE, and PR of material as s [6] By using Noda [1], we gave following exponential law: The Equations ( 63) , (64), (67) to (70) in (24) to (29) gives the plane stress and strain field along the rectangular plate. The values of corresponding stresses n B and n D may be found by using the traction-free ee conditions given by Eq.…”

“…The values of corresponding stresses n B and n D may be found by using the traction-free ee conditions given by Eq. ( 30) and (31) in the stresses (24) to (29). Here the resultant stresses and the constants n B and n D are found using computer er simulation.…”

“…Kamdi and Kumar [23] discussed behaviour of stress and temperature variation in a fin in theory of fractional thermoelasticity. Thakre and Warbhe [24][25] analyzed deflection and temperature distribution effect on material (functionally graded) with heat source using fractional order theory.…”

Fractional Thermal Analysis in a Generalized two Dimensional Infinite half Space with Heat Source

“…The thermoelastic theory which deals with concept of two relaxation times or having temperature dependency is known as second generalization. The thermoelastic theory with two relaxation times was developed by Green and Lindsay [3].From last few years, a lot of research work has developed in theory of fractional [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Thermosensitive Response of a Functionally Graded Cylinder with Fractional Order Derivative

“…Cheng and Batra [14,15] established an exact deflection relationship between different functionally graded plate theories and that of an equivalent homogenous Kirchhoff plate. Other related studies by assuming cylindrical bodies with different boundary conditions are described in [16,17,18,19,20,21,22].…”