Purpose: The purpose of this paper is to highlight the advantages of a simplified algorithm to solve the problem of heat and mass transfer in porous medium by reducing the number of partial differential equations from four to three. Design/methodology/approach: The approach of the present paper is to develop a simplified algorithm to reduce the number of equations involved in conjugate heat transfer in porous medium. Findings: Developed algorithm/method has many advantages over conventional method of solution for conjugate heat transfer in porous medium. Research limitations/implications: The current work is applicable to conjugate heat transfer problem. Practical implications: The developed algorithm is useful in reducing the number of equations to be solved, thus reducing the computational resources required. Originality/value: Development of simplified algorithm and comparison with conventional method.

The present study examines the effect of silicon dioxide (SiO₂) nano-additives on the performance and emission characteristics of a diesel engine fuelled with soybean biodiesel. Soybean biofuel was prepared using the transesterification process. The morphology of nano-additives was studied using scanning electron microscopy (SEM), X-ray diffraction (XRD) and energy-dispersive X-ray spectroscopy (EDS). The Ultrasonication process was used for the homogeneous blending of nano-additives with biodiesel, while surfactant was used for the stabilisation of nano-additives. The physicochemical properties of pure and blended fuel samples were measured as per ASTM standards. The performance and emissions characteristics of different fuel samples were measured at different loading conditions. It was found that the brake thermal efficiency (BTE) and brake specific fuel consumption (BSFC) increased by 3.48–6.39% and 5.81–9.88%, respectively, with the addition of SiO₂ nano-additives. The carbon monoxide (CO), hydrocarbon (HC) and smoke emissions for nano-additive added blends were decreased by 1.9–17.5%, 20.56–27.5% and 10.16–23.54% compared to SBME25 fuel blends.