Augmentation of heat transfer occurrence describing the complete structure of heat, energy (Energy flux vectors) and fluid flow in a trapezoidal enclosure in presence of the thermal radiation. The computational results are describing the various values of thermal radiation of the trapezoidal enclosure and their effect on heat transfer rate.

Modern magnetic nanomaterial processing operations are progressing rapidly and require increasingly sophisticated mathematical models for their optimization. Stimulated by such developments, in this paper, a theoretical and computational study of a steady magnetohydrodynamic nanofluid over an exponentially stretching/shrinking permeable sheet with melting (phase change) and radiative heat transfer is presented. Besides, wall transpiration, that is, suction and blowing (injection), is included. This study deploys Buongiorno's nanofluid model, which simulates the effects of the Brownian motion and thermophoresis. The transport equations and boundary conditions are normalized via similarity transformations and appropriate variables, and the similarity solutions are shown to depend on the transpiration parameter. The emerging dimensionless nonlinear coupled ordinary differential boundary value problem is solved numerically with the Newton-Fehlberg iteration technique. Validation with special cases from the literature is included.

A theoretical and computational study of MHD natural convection in an isotropic non-Darcian porous medium saturated with electrically conducting helium gas in an enclosure in the presence of heat generation is presented. A Brinkman extended Darcy-Forchheimer model is employed and the working fluid is assumed to be incompressible. The model is non-dimensionalised and converted into pressure-velocity form. The Harlow-Welch marker and cell (MAC) finite difference technique is employed to solve the nonlinear boundary value problem via pressure-vorticity coupling. A parametric investigation of the influence of Grashof number ( Gr), Hartmann magnetic number ( Ha), Darcy number ( Da), and the internal heat generation parameter ( Γ) on streamline and isotherm distributions with Prandtl number ( Pr) is 0.71 (Helium) is conducted. The variation in local Nusselt number along the left and right walls of the computational 2 D enclosure is also studied. Validation house-computational numerical MATLAB code is tests are included. Local Nusselt number is elevated at both left and right walls with greater Darcy number (higher medium permeability) and Grashof number. However, with greater internal heat generation, local Nusselt number magnitudes are enhanced at the left (cold) wall only but suppressed at the right (hot) wall. Increasing magnetic field reduces local Nusselt number at both left and right walls. With increasing magnetic field, the single vortex is strongly distorted and skewed towards the top left and lower right corners of the enclosure. Temperature contours at the left and right wall are however less intense with greater magnetic field effect. The simulations are of relevance to hybrid electromagnetic gaseous fuel cells, magnetic field control of filtration processes and porous media materials processing systems.

A detailed theoretical examination laminar natural convection heat flow in a triangular porous cavity with significant radiative heat transfer and porosity variation is presented. Twodimensional laminar incompressible flow is considered with the left slant and right walls are low and high temperature respectively, and the remaining (top) wall prescribed as adiabatic. The Darcy-Brinkman isotropic model is utilized, and the coupled governing equations are solved by a numerical method utilizing finite differences. Visualization of isotherms and streamlines is achieved with the method of Energy Flux Vectors (EFVs). The impacts of the different model parameters (Rayleigh number Ra, Darcy number-Da, porosity-𝜀 and radiation parameter-Rd) on the thermo fluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with greater Darcy parameter (permeability) which also leads to intensification in the density of energy flux vector patterns. The flow is accelerated with increasing buoyancy effect (Rayleigh number) and temperatures are also increased with greater radiative flux. Average Nusselt number is decreased with higher porosity. The simulations are relevant to hybrid porous media solar collectors.

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