The performance of fins, commonly used as heat enhancement devices are greatly affected by both the geometry and material properties. These consideration in fin design has stimulated an extensive research interest in the recent time. In this study, investigation on the thermal responses of moving irregular porous fins with trapezoidal, concave and convex profiles of copper, aluminium, silicon nitrides and stainless steel materials is examined. The developed thermal model is solved using differential transform method (DTM). On the verification of result obtained with numerical method using Runge-Kutta, a good agreement with the solution of approximate method is achieved. In the parametric studies carried out, the effect of physical parameters such as convective-conductive, convective-radiative term, internal heat generation, porosity, surface emissivity, power index of heat transfer coefficient, Peclet number and Darcy number on the thermal behaviour of fins are examined and discussed. The comparative analysis carried out on the effect of materials on non-dimensional temperature distribution reveals that copper obtains the highest temperature while the stainless steel gets the lowest. More-so, the fins with concave geometry gives the highest volume adjusted efficiency with increase in Peclet number while that with convex profile has the least. These result output are essential and would be useful in the future design of fins with optimum size reduction and high efficiency.

The article investigates the behaviour of the multiplication table of the ring \(\mathbb{Z}_n\). To count the number of 1s appear on the main diagonal of the multiplication table of \(\mathbb{Z}_n\), conclusively an explicit formula is induced for any \(n \geq 2\).

By using some mixed techniques of the Mawhin coincidence degree theory and the Krasnoselskii fixed point theorem, we obtained the existence of positive periodic solutions of the neutral nonlinear differential system. Also, sufficient conditions for the existence of positive periodic solutions to the system with feedback control are given. Our results substantially extend and improve existing results.

Generating homotopy-based approaches (HBAs) in thermal-fluid sciences is an efficient manner for finding absolutely convergent series expansions. The main objective of this paper is to analyze the viscoelastic Walter’s B fluid past a stretching wall. To answer this, the governing differential equation is derived by substituting similarity variables into the partial differential equations (PDEs) and associated boundary conditions. The present HBA is also developed by minimizing the averaged square residual error included in the quadratic resistance law (QRL). By comparing the present findings with those available in the literature, it is seen that the 9th-order HBA can provide an incredible degree of accuracy and reliability. Furthermore, it is found that the central processing unit (CPU) time is greatly reduced when the auxiliary parameter is selected as \(\hbar\)=-0.122.

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard-Fejér type inequality for generalized convex functions whose derivatives absolute values are generalized convex via local fractional integrals.

This work is concerned with a comparative study of performances of meshfree (radial basis functions) and mesh-based (finite difference) schemes in terms of their accuracy and computational efficiency while solving multi-dimensional initial-boundary value problems governed by a nonlinear time-dependent reaction-diffusion Brusselator system. For computing the approximate solution of the Brusselator system, we use linearly implicit Crank-Nicolson (LICN) scheme, Peaceman-Rachford alternating direction implicit (ADI) scheme and exponential time differencing locally one dimensional (ETD-LOD) scheme as mesh-based schemes and multiquadric radial basis function (MQRBF) as a meshfree scheme. A few numerical results are reported.

In ring \(\mathbb{R}=\mathbb{Z}_{2}+u\mathbb{Z}_{2}+u^2\mathbb{Z}_{2}\) where \(u^3=0,\) using Lee weight and generalized Lee weight, some lower bound and upper bound on the covering radius of codes is given and also to find the covering radius for various repetition codes with respect to same and different length in \(\mathbb{R}.\)

There has been much debate about the role Vitamin C plays in the innate immune response, and if it has the potential to be used as a drug to combat conditions in which the immune system is compromised, from the common cold to cystic fibrosis. Here, the author creates a basic model of the innate response, capturing the dynamics among phagocytic cells, host cells, foreign virus/bacteria, and Vitamin C. Through mathematical simulations, the author concludes that Vitamin C can be used as a stand-alone drug to eradicate a viral/bacterial infection if given constant infusions. If this is not possible due to other side effects that may harm the patient, Vitamin C may be used in quick succession with another anti-bacterial/anti-viral medication to aid the patient. This, moreover, could help minimize the amount of side effects of the anti-bacterial/anti-viral drug and slow down bacterial evolution. Finally, the author modifies the system to simulate cases of renal failure, acute lung injury, liver damage, chronic granulomatous disease, and the Chédiak-Higashi syndrome, showing how Vitamin C can help individuals with these diseases.

In this paper, we study a new distribution called the exponentiated transmuted Lindley distribution. The proposed distribution has three special cases namely Lindley, exponentiated Lindley and transmuted Lindley distributions. Along with the basic properties of the distribution, the maximum likelihood technique of estimating the parameters of the distribution are discussed. Two applications of the distribution are also part of this article.

In this note, we first show that the general Zagreb index can be obtained from the \(M-\)polynomial of a graph by giving a suitable operator. Next, we obtain \(M-\)polynomial of some cactus chains. Furthermore, we derive some degree based topological indices of cactus chains from their \(M-\)polynomial.