This manuscript optimizes the conjugate heat transfer and thermal-stress analysis for hydromagnetic Brinkman fluid with chemical reaction in permeable media. The governing equations of non-Newtonian Brinkman fluid have been traced out and then fractional derivative approach, namely, Caputo–Fabrizio, is invoked, subject to the exponential boundary conditions. The Fourier Sine and Laplace transforms are applied on governing partial differential equations for generating the analytical results of temperature, concentration and velocity. A comparative study of velocity field is investigated for the sake of long memory and hereditary properties. The analytical investigation of temperature, concentration and velocity field have strong effects on chemical reaction. The graphical depiction of vibrant characteristics of hydromagnetic Brinkman fluid with chemical reaction in permeable media is exhibited for disclosing the sensitivities of different embedded rheological parameters of fluid flow. The results suggested that temperature distribution for smaller and larger Prandtl number has disclosed quick and thicker heat diffusivity.

Abstract Re-examination of the potential-step chronoamperometry (PSCA) method through numerical inversion of Laplace transforms is proposed in this work. First, a general expression is derived in the Laplace domain for the current transient following the application of a potential step of arbitrary amplitude. The formulation applies to first-order electrochemical–chemical reactions (E, EC and CE reactions) with one-dimensional mass-transport processes of implicated species in the electrolytic solution or the electrode. Next, numerical inversion of the relevant Laplace transform is performed by the Gaver–Stehfest (GS), Fourier–Euler (FE) and ‘fixed’ Talbot (FT) methods. The so-called GS-, FE- and FT-PSCA algorithms in this work make it possible to investigate a wide range of electrode geometry and chemical, electrochemical and one-dimensional mass-transport processes by the PSCA method. Each algorithm provides a full explicit formulation of Faradaic current with respect to time, applied potential and electrochemical parameters (initial concentrations, geometrical parameter(s), standard potential, electrochemical and chemical rate constants and diffusion coefficients), which greatly simplifies the computation of potentiostatic current transients. Some application examples relative to diffusion equations with spherical electrode geometry will be presented in the second part of this work.

In the present investigation, the constitutive relations and field equations for micropolar generalized thermodiffusive are derived and deduced for the Green and Lindsay (G—L) theory, in which thermodiffusion are governed by four different relaxation times. The general solution to the field equations in micropolar generalized thermodiffusive is investigated by applying the Laplace and Fourier transforms as a result of concentrated normal force, or thermal point source or potential point source. To get the solution in the physical form, a numerical inversion technique has been applied. The components of displacement, stress, temperature distribution, and chemical potential for the G—L theory and coupled thermoelasticity theory on these quantities have been depicted graphically to show the impact of micropolarity and diffusion. Some special cases are also deduced from the present investigation.

Abstract In the present work, we consider a two dimensional axisymmetric problem of micropolar porous circular plate with thermal and chemical potential sources in the context of the theory of dual phase lag generalized thermoelastic diffusion. The potential functions are used to analyze the problem. The Laplace and Hankel transforms techniques are used to find the expressions of displacements, microrotation, volume fraction field, temperature distribution, concentration and stresses in the transformed domain. The inversion of transforms based on Fourier expansion techniques is applied to obtain the results in the physical domain. The numerical results for resulting quantities are obtained and depicted graphically. Effect of porosity, LS theory and phase lag are presented on the resulting quantities. Some particular cases are also deduced.

A vertical plate experiences a dynamic flow of fractionalized Brinkman fluid governed by fluctuating magnetic forces. This study considers heat absorption and diffusion-thermo effects. The novelty of model is the fractionalized Fourier's and Fick's laws. The problem is solved using the constant proportional Caputo derivative and Laplace transform method. The resulting non-dimensional equations for temperature, mass, and velocity fields are solved and compared visually. We explore the influence of various parameters like the fractional order, heat absorption/generation (Q), chemical reaction rate (R), and magnetic field strength (M) through informative graphs. Additionally, we contrast the velocity fields of fractionalized and regular fluids. The visualizations reveal that diffusion-thermo and mass Grashof number enhance fluid velocity, while chemical reaction and magnetic field tend to suppress it. For the interest of engineering, physical quantities such as Sherwood number, skin friction, and Nusselt number are computed. The present study satisfying all initial and boundary condition can be reduced to to previous published work which shows the validity of present work.