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Sugat Kirti ¹, Deepak Kumar ¹, Navin Kumar Mogha ¹, Virender Singh ¹, Dhanraj T. Masram ¹

Affiliations
1 Department of Chemistry, University of Delhi, Delhi, IN

Abstract

Silica supported poly-phosphoric acid (PPA-SiO₂) has been utilized as an efficient and an environmentally friendly heterogeneous, reusable catalyst for the synthesis of bis(indolyl)methanes under solvent free condition. The significances of this protocol are mild reaction condition, excellent yield and simple work up procedure.

Keywords

Bis (Indolyl) Methanes, Polyphosphoric Acid, Silica, Solvent Free, Recyclable Catalyst.

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Jyoti Prakash ¹, Shweta Manan ¹, Virender Singh ¹, Kanu Vaid ²

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-5, IN
2 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-5

Abstract

Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation, which may be neutral or unstable for triply diffusive convection in porous medium (Darcy model) in the presence of a uniform vertical rotation, are obtained. It is further proved that the result obtained herein is uniformly valid for quite general nature of the bounding surfaces.

Keywords

Triply Diffusive Convection, Porous Medium, Taylor Number, Concentration Rayleigh Number, Darcy Model.

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Jyoti Prakash ¹, Virender Singh ¹, Shweta Manan ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN

Abstract

Condition for characterizing nonoscillatory motions, which may be neutral or unstable, for rotatory hydrodynamic triply diffusive convection in a porous medium is derived. It is analytically proved that the principle of the exchange of stabilities, in rotatory triply diffusive convection in a porous medium, is valid in the regime R₁E₁σ/2τ²₁π⁴ + R₂E₂σ/2τ²₂π⁴ + T_a/π²ΛD_a^-1 ≤ 1, where R₁ and R₂ are the concentration Raleigh numbers, and τ₁ and τ₂ are the Lewis numbers for the two concentration components respectively, T_a is the Taylor number, σ is the Prandtl number, D_a is the Darcy number, E₁ and E₂ are constants.

Keywords

Triply Diffusive Convection, Porous Medium, Darcy-Brinkman Model, the Principle of the Exchange of Stabilities, Taylor Number, Concentration Rayleigh Number.

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Jyoti Prakash ¹, Shweta Manan ¹, Virender Singh ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla – 171005, IN

Abstract

Condition for characterizing nonoscillatory motions, which may be neutral or unstable, for multicomponent convection is derived.

Keywords

Multicomponent Convection, The Principle of the Exchange of Stabilities, Oscillatory Motions, Complex Growth Rate, Concentration Rayleigh Number.

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Suresh Rana ¹, Virender Singh ²

Affiliations
1 Department of Mathematics, Government College, Shahpur (H.P) 176206, IN
2 Department of Mathematics, Government College, Jawalamukhi (H.P) 176031, IN

Abstract

A theoretical analysis of free convective flow of viscous incompressible fluid through a porous medium bounded by a flat porous plate subject to periodic suction and constant heat and mass flux has been presented. The flow becomes three dimensional due to variation of suction velocity in transverse direction. Analytical expression for velocity, temperature, concentration and skin friction are obtained using perturbation technique. Numerical solutions are obtained for different values Grash of number (G_r), mass Grashof number(Gc), Prandtl number (Pr), Schmidt number (Sc) and Radiation (R). It is found that non-dimensional velocity increases with increase of Gr, Gc and Sc and decreases with increase of R, non-dimensional temperature decreases with increasing of R, Concentration decreases with increase of Sc. and skin friction co-efficient increases with increase of Gr and R but effect of Gr is more than R.

Keywords

Free Convection, Oscillatory Flow, Sinusoidal Suction, Mass Transfer, Radiation.

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S. K. Kango ¹, Vikram Singh ², Virender Singh ²

Affiliations
1 Department of Mathematics, Govt. College, Haripur (Manali) (H,P.) – 175136, IN
2 Department of Mathematics, Jwalaji Degree College, Jwalamukhi (H,P.) – 176031, IN

Abstract

In this paper we consider theoretical investigation of the effect hall current and the suspended particle under varying gravity field on the thermal instability of ferromagnetic fluid heated from below. For a fluid layer between two free boundaries and exact solution is obtained using a linearized stability theory and normal mode analysis. A dispersion relation governing the effect of hall current and the suspended particle is obtained. For the case of stationary convection it is found that the magnetic field has a stabilizing the system when the gravity is increasing upward i.e. (λ>0), where as the hall current and suspended particle are found to have the destabilizing effect on the system when the gravity is increasing upward i.e. (λ>0). The critical Rayleigh numbers and wave numbers of the associated disturbances for the onset of stability as stationary convection are obtained. The principle of exchange of stabilities is not valid for the problem under consideration, whereas in the absence of Hall currents hence magnetic field, it is valid under certain conditions.

Keywords

Hall Currents, Suspended Particles, Ferromagnetic Fluid and Varying Gravity Field.

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Jyoti Prakash ¹, Virender Singh ¹, Shweta Manan ¹, Vinod Kumar ²

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
2 Department of Physics, MLSM College, Sundernagar, H.P., IN

Abstract

The paper mathematically establishes that the complex growth rate (p_r,p_i ) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer in porous medium (Darcy Model) with one of the components as heat with diffusivity , must lie inside a semicircle in the right- half of the (p_r,p_i)-plane whose centre is origin and radius equals √(R₁+<R₂)σ where R₁ and R₂ are the Raleigh numbers for the two concentration components with diffusivities k₁ and k₂ (with no loss of generality, k > k₁> k₂ ) and is the Prandtl number. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.

Keywords

Triply Diffusive Convection, Oscillatory Motions, Complex Growth Rate, Porous Medium.

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Jyoti Prakash ¹, Shweta Manan ¹, Virender Singh ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN

Abstract

The present paper mathematically establishes that 'the principle of the exchange of stabilities' for triply diffusive convection in porous medium (Darcy model) is valid in the regime (R_1 σ)/(2〖ι_1〗^2 π^4 )+(R_2 σ)/(2〖ι_2〗^2 π^4)≤1, where R_1 and R_2 are the Rayleigh numbers for the two concentration components, ι_1 and ι_2 are the Lewis numbers for the two concentration components and σ is the thermal Prandtl number. It is further proved that the above result is uniformly valid for any combination of rigid and free boundaries.

Keywords

Triply Diffusive Convection, Nonoscillatory Motions, Principle of the Exchange of Stabilities, Concentration Rayleigh Number, Porous Medium, Darcy Model.

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Virender Singh ¹, Ashok Kumar ¹, Krishan Yadav ¹, Rajinder Kumar ², Anil Malik ¹

Affiliations
1 Department of Extension Education, CCS Haryana Agricultural University Hisar, Haryana, IN
2 Department of Assistant Librarian, CCS Haryana Agricultural University, Hisar, Haryana, IN

Abstract

The present study was conducted inYamunanagar district of Haryana. This area was selected purposely because of maximum area under mango fruit crops. Further two blocks, Chhachhrauli and Jagadhari were selected purposively from Yamunanagar district and from each block two villages were selected randomly and thereby a total number of four villages was selected for data collection. Thirty mango grower farmers were selected randomly from each village for the study and thus, a total number of 120 farmers were interviewed. The specific objectives of the present study were socio-economic status, knowledge, adoption and the constraints in adoption of post-harvest management practices by mango growers. The data were collected with the help of well-structured interview schedule..Twelve important independent variables such as age, education, socio-economic status, caste, family size, occupation of respondents, annual income, land holdings, farm implements, mass media exposure, extension contacts, and irrigation facilities were selected for the study. The study revealed that majority o f the farmers were middle aged and belonged to general caste, more than half of the respondents were educated matric to graduate and one-third of respondents had family members up to 5. Most of them were engaged in farming and nearly two-third per cent of the respondents had annual income above Rs. 1 lakh. More than half of the farmers belonged to medium to high level of socio-economic status. Majority of the farmers belonged to low to medium level of mass media and extension contacts. More than half of the farmers used tube well as source of irrigation.

Keywords

Mango, Cultivation, Orchards, Respondents, Mango Grower.

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Virender Singh ¹, Ashok Kumar ¹, Krishan Yadav ¹, Rajesh Kumar ², Anil Malik ¹, Rajinder Kumar ³

Affiliations
1 Department of Extension Education, CCSHAU, Hisar, Haryana, IN
2 ATP O/o ADP, CCSHAU, Hisar, Haryana, IN
3 CCSHAU, Hisar, Haryana, IN

Abstract

Mango (Mangifera Indica L.) is known as king of fruits. It belongs to the family Anacardiaceae and genus Mangifera. In Haryana, the maximum area under mango cultivation is in Yamunanagar district with 5419 hectare followed by Ambala, Panchkula, andKamal. The production of mango in Yamunanagar is 60.02 thousand MT. The present study was conducted in Yamunanagar district of Haryana. This area was selected purposely because of maximum area under mango fruit crops. Further two blocks, Chhachhrauli and Jagadhari were selected purposively from Yamunanagar district and from each block two villages were selected randomly and thereby a total number of four villages was selected for data collection. Thirty mango grower farmers were selected randomly from each village for the study and thus, a total number of 120 farmers were interviewed. The specific objectives ofthe present study were socio-economic status, knowledge, adoption and the constraints in adoption of post-harvest management practices by mango growers. The data were collected with the help of well-structured interview schedule..Twelve important independent variables such as age, education, socio-economic status, caste, family size, occupation of respondents, annual income, land holdings, farm implements, mass media exposure, extension contacts, and irrigation facilities were selected for the study. The study revealed that majority of the farmers were middle aged and belonged to general caste, more than ha lf of the respondents were educated matric to graduate and one-third of respondents had family members up to 5. Most of them were engaged in farming and nearly two-third per cent of the respondents had annual income above Rs. 1 lakh. More than h a lf of the farmers belonged to medium to high level of socio-economic status. Majority ofthe farmers belonged to low to medium level of mass media and extension contacts. More than half of the farmers used tube well as source of irrigation.

Keywords

Adoption, Constraints, Respondents, Mango Grower, Marketing, Production.

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Virender Singh ¹, Ashok Kumar ¹, Satyakaam Malik ², Rajesh Kumar ¹, Anil Kumar ³, K.K. Yadav ¹, Jasvinder Kaur ²

Affiliations
1 Directorate of Extension Education, CCS Haryana Agricultural University, Hisar, Haryana, IN
2 EEI Nelokheri, CCS Haryana Agricultural University, Nelokheri, Haryana, IN
3 KVK Yamunanagar, CCS Haryana Agricultural University, Yamunanagar, Haryana, IN

Abstract

Post-harvest management is crucial for maintaining the quality and quantity of agricultural commodities after harvest. This study focuses on mango farmers in Yamunanagar district, Haryana, to improve their efficiency and scientific approach to post-harvest management practices. The study examined the relationship between selected independent variables and farmers' knowledge and adoption levels of post-harvest management practices. Results showed that education, mass media exposure, and extension contact positively correlated with farmers' knowledge and adoption levels at a 0.01 level of probability. Caste, family size, annual income, landholding, farm implements, and irrigation facilities were positively but non-significantly correlated with farmers' knowledge and adoption levels. Regression analysis revealed that the selected independent variables collectively accounted for 63.33% and 52.47% of the variation in farmers' knowledge and adoption levels, respectively.

Keywords

mango, technology, harvesting, adoption, economic, correlation, regression

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