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Solar energy is one of the best sources of renewable energy with minimal environmental impact. A numerical study has been conducted to investigate the natural convection inside a solar collector having a flat-plate cover and a sine-wave absorber. The water-alumina nanofluid is used as the working fluid inside the solar collector. The governing differential equations with boundary conditions are solved by the penalty finite element method using Galerkin's weighted residual scheme. The effects of physical parameters on the natural convection heat transfer are simulated. These parameters include the number of wave λ and non-dimensional amplitude A of the sinusoidal corrugated absorber. Comprehensive average Nusselt number, average temperature, and mean velocity field for both nanofluid and base fluid within the collector are presented as functions of the parameters mentioned above. Comparison with previously published work is made and found to be in excellent agreement. The numerical results show that the highest heat transfer rate is observed for both the largest λ and A. In addition, the design for enhancing the performance of the collector is determined by examining the above-mentioned results.

The present work describes the effect of magnetohydrodynamic (MHD) natural convection flow along a vertical flat plate with Joule heating and heat conduction. The governing boundary layer equations are first transformed into a non-dimensional form and resulting nonlinear system of partial differential equations are then solved numerically by using the implicit finite difference method with Keller box scheme. The results of the skin friction co-efficient, the surface temperature distribution, the velocity and the temperature profiles over the whole boundary layer are shown graphically for different values of the Prandtl number Pr (Pr = 1.74, 1.00, 0.72, 0.50, 0.10), the magnetic parameter M (M = 1.40, 0.90, 0.50, 0.10) and the Joule heating parameter J (J = 0.90, 0.70, 0.40, 0.20). Numerical values of the skin friction coefficients and surface temperature distributions for different values of Joule heating parameter have been presented in tabular form.

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In the present paper, a study of magnetohydrodynamic (MHD) mixed convection around a heat conducting horizontal circular cylinder placed at the center of a rectangular cavity along with joule heating has been carried out. Steady state heat transfer by laminar mixed convection has been studied numerically by solving the equations of mass, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Richardson number, Hartmann number and the cavity aspect ratio. The results are presented in the form of average Nusselt number at the heated surface; average fluid temperature in the cavity and temperature at the cylinder center for the range of Richardson number, Hartmann number and aspect ratio. The streamlines and isotherms are also presented. It is found that the streamlines, isotherms, average Nusselt number, average fluid temperature and dimensionless temperature at the cylinder center strongly depend on the Richardson number, Hartmann number and the cavity aspect ratio.

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MHD natural convection flow of an electrically conducting fluid along a vertical flat plate with temperature dependent thermal conductivity and conduction effects is analyzed. The governing equations with associated boundary conditions for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method with Keller-box scheme. Numerical results of the velocity, temperature, skin friction coefficient and surface temperature for different values of the magnetic parameter, thermal conductivity variation parameter, Prandtl number and conjugate conduction parameter are presented graphically. Detailed discussion is given for the effects of the aforementioned parameters.

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