Weber-Type Integral Transform Connected with Robin-Type Boundary Conditions

Thanaa Elnaqeeb, Nehad Ali Shah and Dumitru Vieru
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Thanaa Elnaqeeb: Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif 888, Saudi Arabia
Nehad Ali Shah: Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 58307, Vietnam
Dumitru Vieru: Department of Theoretical Mechanics, Technical University, “Gheorghe Asachi” of Iasi, 6600 Iasi, Romania

Mathematics, 2020, vol. 8, issue 8, 1-10

Abstract: A new Weber-type integral transform and its inverse are defined for the representation of a function f ( r , t ) , ( r , t ) ∈ [ R , 1 ] × [ 0 , ∞ ) that satisfies the Dirichlet and Robin-type boundary conditions f ( R , t ) = f 1 ( t ) , f ( 1 , t ) − α ∂ f ( r , t ) ∂ r | r = 1 = f 2 ( t ) , respectively. The orthogonality relations of the transform kernel are derived by using the properties of Bessel functions. The new Weber integral transform of some particular functions is determined. The integral transform defined in the present paper is a suitable tool for determining analytical solutions of transport problems with sliding phenomena that often occur in flows through micro channels, pipes or blood vessels. The heat conduction in an annular domain with Robin-type boundary conditions is studied. The subroutine “ r o o t ( ⋅ ) ” of the Mathcad software is used to determine the positive roots of the transcendental equation involved in the definition of the new integral transform.

Keywords: integral transforms; Weber transform; Bessel functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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