This paper investigates the steady, two dimensional, and magnetohydrodynamic flow of copper and alumina/water hybrid nanofluid on a permeable exponentially shrinking surface in the presence of Joule heating, velocity slip, and thermal slip parameters. Adopting the model of Tiwari and Das, the mathematical formulation of governing partial differential equations was constructed, which was then transformed into the equivalent system of non-linear ordinary differential equations by employing exponential similarity transformation variables. The resultant system was solved numerically using the BVP4C solver in the MATLAB software. For validation purposes, the obtained numerical results were compared graphically with those in previous studies, and found to be in good agreement, as the critical points are the same up to three decimal points. Based on the numerical results, it was revealed that dual solutions exist within specific ranges of the suction and magnetic parameters. Stability analysis was performed on both solutions in order to determine which solution(s) is/are stable. The analysis indicated that only the first solution is stable. Furthermore, it was also found that the temperature increases in both solutions when the magnetic parameter and Eckert number are increased, while it reduces as the thermal slip parameter rises. Furthermore, the coefficient of skin friction and the heat transfer rate increase for the first solution when the magnetic and the suction parameters are increased. Meanwhile, no change is noticed in the boundary layer separation for the various values of the Eckert number in the heat transfer rate.

In this study, first-order slip effect with viscous dissipation and thermal radiation in micropolar fluid on a linear shrinking sheet is considered. Mathematical formulations of the governing equations of the problem have been derived by employing the fundamental laws of conservations which then converted into highly non-linear coupled partial differential equations (PDEs) of boundary layers. Linear transformations are employed to change PDEs into non-dimensional ordinary differential equations (ODEs). The solutions of the resultant ODEs have been obtained by using of numerical method which is presented in the form of shootlib package in MAPLE 2018. The results reveal that there is more than one solution depending upon the values of suction and material parameters. The ranges of dual solutions are S ≥ S c i , i = 0 , 1 , 2 and no solution is S < S c i where S c i is the critical values of S . Critical values have been obtained in the presence of dual solutions and the stability analysis is carried out to identify more stable solutions. Variations of numerous parameters have been also examined by giving tables and graphs. The numerical values have been obtained for the skin friction and local Nusselt number and presented graphically. Further, it is observed that the temperature and thickness of the thermal boundary layer increase when thermal radiation parameter is increased in both solutions. In addition, it is also noticed that the fluid velocity increases in the case of strong magnetic field effect in the second solution.

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Mechanical shear resistance of wheat grain is a significant concern for the designers and researchers related to the design of threshing, handling and processing machinery of the field crops. The grain mechanical properties directly affect the machine geometry and its operational parameters. The present study was carried out to determine the shear resistance of five wheat varieties (Locally names; TD-02, Sindhu-1105, Benazir, China and SKD-118) influenced by moisture content (16.7%, 18.7% and 19.5%) and loading rate (3 mm/s, 6 mm/s and 9 mm/s). However, some physio-dimensional properties (length, width, thickness, slenderness ratio, surface area and sphericity) were obtained at different moisture contents. The results showed that the shear resistance reduced by increasing the moisture content and loading rate. The average shear resistance decreased from 10.45 N to 3.74 N for 3-9 mm/s loading rate at moisture content of 16.7% to 19.5%. Thus, the maximum correlation (r = 0.905) of shear resistance obtained at 16.7%, whereas minimum correlation (r = 0.692) obtained at 19.5%. The shear resistance of wheat grain was highly significant (p<0.05) at 9 mm/s for 19.5%. Shear resistance decreased with an increase in the moisture content in the grain whereas deformation is increasing with the increase of moisture content. However, the maximum bulk density of wheat grain obtained at 19.5% for SKD-118, while the minimum obtained at 16.7% for TD-02. It is recommended that the design and modification of wheat grain processing equipment should be executed on the physio-mechanical properties of grain varieties.

Three common pretreatments (mechanical, steam explosion and chemical) used to enhance the biodegradability of rice straw were compared on the basis of bio-hydrogen production potential while co-digesting rice straw with sludge under mesophilic (37˝C) and thermophilic (55˝C) temperatures. The results showed that the solid state NaOH pretreatment returned the highest experimental reduction of LCH (lignin, cellulose and hemi-cellulose) content and bio-hydrogen production from rice straw. The increase in incubation temperature from 37˝C to 55˝C increased the bio-hydrogen yield, and the highest experimental yield of 60.6 mL/g VS removed was obtained under chemical pretreatment at 55˝C. The time required for maximum bio-hydrogen production was found on the basis of kinetic parameters as 36 h-47 h of incubation, which can be used as a hydraulic retention time for continuous bio-hydrogen production from rice straw. The optimum pH range of bio-hydrogen production was observed to be 6.7˘0.1-5.8˘0.1 and 7.1˘0.1-5.8˘0.1 under mesophilic and thermophilic conditions, respectively. The increase in temperature was found useful for controlling the volatile fatty acids (VFA) under mechanical and steam explosion pretreatments. The comparison of pretreatment methods under the same set of experimental conditions in the present study provided a baseline for future research in order to select an appropriate pretreatment method.