Papers by S.Nanda Kishore
The flow of a micropolar fluid in a channel bounded below by a permeable bed is investigated. The... more The flow of a micropolar fluid in a channel bounded below by a permeable bed is investigated. The flow is analyzed by four parameters; they are viscous cross-flow Reynolds number, micropolar Reynolds number, microinertia parameter and micropolar parameter. The governing equations are solved to determine the expressions for velocity and microrotation fields. The effects of various parameters on the velocity and microrotation fields are discussed. Several graphs of physical interest are displayed and discussed.
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The electrically conducting flow of couple stress fluid in a vertical porous layer is investigate... more The electrically conducting flow of couple stress fluid in a vertical porous layer is investigated. It is assumed that the fluid possesses constant properties except for density. We assume that the density variation due to temperature differences is used only to express the body force term as buoyancy term. The perturbation method of solution is obtained in terms of buoyancy parameter N valid for small values of N. The flow is analysed for three cases having the parameter l which gives the combined effect of magnetic field and permeability. The velocity and temperature fields are determined. The effects of couple stress parameter K and the parameter l of the velocity and temperature are discussed. It is observed that the velocity decreases with increasing Darcy Number Da and l .
Advances in Applied Science Research, 2011
The electrically conducting flow of couple stress fluid in a vertical porous layer is investigate... more The electrically conducting flow of couple stress fluid in a vertical porous layer is investigated. It is assumed that the fluid possesses constant properties except for density. We assume that the density variation due to temperature differences is used only to express the body force term as buoyancy term. The perturbation method of solution is obtained in terms of buoyancy parameter N valid for small values of N. The flow is analysed for three cases having the parameter l which gives the combined effect of magnetic field and permeability. The velocity and temperature fields are determined. The effects of couple stress parameter K and the parameter l of the velocity and temperature are discussed. It is observed that the velocity decreases with increasing Darcy Number Da and l.
Conference Presentations by S.Nanda Kishore
AIP, 2023
This research article explores on the summation of fixed positive integral powers of first m-posi... more This research article explores on the summation of fixed positive integral powers of first m-positive integers. Authors are strongly believing that the following discussion depicts a method fromwhich one can easily compute the summation of fixed positive integral powers of first m-natural numbers. Furthermore they have given answers to two interesting questions in the research field of analytical number theory namely: Is the sum of fixed positive integral powers of first m-positive integers coincide with a polynomial?and Is such polynomial unique?. Some principles of linear algebra have been incorporated in this article to extract very interesting results regarding this summation. The uniqueness of the polynomial has been proved using Crammer’s rule also. Moreover a system of linear non homogeneous equations proposed here which help us to derive the formulas for the summations Σ n, Σ n2 , Σ n3…….
AIP, 2023
This research article mainly focuses on Kaprekar constants named after Indian recreational mathem... more This research article mainly focuses on Kaprekar constants named after Indian recreational mathematician Dattatreya Ramchandra Kaprekar. Kaprekar invented a mysterious property of the number 6174 in 1949. He depicted that the number 6174 is reached in the limit as one continuously subtract the smallest number from the largest number where these numbers are taken from a set of four digited numbers in which all four digits are not identical. The main task of this paper is to propose an analytical method for searching Kaprekar constants. In this research the 3-digited Kaprekar constant 495 is traced. The mystery behind the magic of the numbers 495and 6174 respectively known as three and four digit Kaprekar constants has been chased here and the authors proposed a path by which one can hunt the Kaprekar constants of any order.
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Papers by S.Nanda Kishore
Conference Presentations by S.Nanda Kishore