FRACTIONAL THERMAL RESPONSE IN A THERMOSENSITIVE RECTANGULAR PLATE DUE TO THE ACTION OF A MOVING SOURCE OF HEAT

V. R. Manthena; V. B. Srinivas; N. K. Lamba; G. D. Kedar

V. R. Manthena Department of Mathematics, Priyadarshini J.L. College of Engineering, Nagpur, India
V. B. Srinivas Department of Mathematics, Anurag University, Venkatapur, Ghatkesar, Medchal-Malkajgiri District, Telangana, India
N. K. Lamba Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Mandhal, Nagpur, India
G. D. Kedar Department of Mathematics, RTM Nagpur University, Nagpur, India

Article ID: 2445

Keywords: fractional heat conduction, moving heat source, thermal deflection, thermal stresses

Abstract

The fractional order theory explores over the field of mathematics and physical sciences as it provides the generalization of non-integer order for derivative and integration. Numerical methods are used to study temperature fields with heat transfer in homogeneous bodies whose thermophysical characteristics depend on the temperature. However, analytical solutions of such problems are needed for qualitative analysis to solve the corresponding problems of thermoelasticity. This study focuses on examining the thermoelastic behavior of a rectangular plate, incorporating time dependent fractional order derivative. Moving line heat source in x-direction is considered for heat conduction analysis. The nonlinearity of the heat conduction equation is dealt using Kirchhoff’s variable transformation. The solution of fractional heat conduction equation (FHCE) is obtained using finite Fourier cosine transform and Laplace transform methods. The obtained solution in transformed domain is expressed in terms of Mittag-Leffler function, trigonometric functions and hypergeometric functions. The effect of time fractional order parameter and velocity on temperature profile and thermal profile is analyzed graphically. During the analysis, it is observed that the inhomogeneous material properties cause the magnitude of profile of thermal characteristics to increase on comparison to that of homogeneous case. Smaller magnitudes of temperature, deflection and stresses are seen for larger values of velocity.

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