Department of Mathematics,
Imo State University, Owerri, Nigeria.
Email: [email protected]
Page Number: 400-411
In this present paper, approximate analytical study of natural convection flow of non-Newtonian fluid
through Parallel-plates with heat generation is considered. The coupled non-linear momentum and energy
equations was solved using perturbation technique. The cases of constant viscosity and temperaturedependent viscosity
are treated with the case of temperature-dependent viscosity considered in two
models: Reynold’s model and Vogel’s model. Within the constant viscosity case, results show that
increase in the non-Newtonian parameters
β
, M, decreases the velocity of the fluid flow and increase in
these parameters enhances the temperature of the plates. The effects of non-Newtonian and viscosity
indices of both Reynold’s and Vogel’s models on velocity and temperature profiles are presented.
During COVID-19 pandemic crisis, ICT guided E-learning had played an important part in
educational forum. It had helped the students and teachers to carry out their studies through online
modes. There were plenty of advantages and disadvantages of E-learning. Observing this, we had
conducted an online survey to know the impact of ICT based E-learning. Web app was designed by us
and shared amongst targeted students of COVID-19 period. Some of the questions designed inside our
Google form are as follows. How attentive students were in online classes? How were online classes
helped to solve their own problems? i.e. Analysing on the data collection (69 responses received
through survey), we have found the following observations. Regarding the first question, we found
that 37.7% of the students took it as a medium to have half-half attention. 31.9% of the students
agreed a little more, 12.4% of the student paid attention at all and 4.3% were of the opinion that they
could not pay attention at all. E-learning had served the teaching-learning community a lot during
COVID-19.
keywords: Online Learning, ICT, COVID-19, Google Form
1,*Nkpordee Lekia,2Ogolo Ibinabo Magnus,3Dappa Jane Aselenyeofori
1Department of Mathematics and Statistics,
Ignatius Ajuru University of Education, Rivers State Nigeria 2School of Foundation Studies,
Rivers State College of Health Science and Management Technology,
Rumueme, Port Harcourt, Nigeria
3Department of Mathematics and Statistics,
Federal Polytechnic of Oil and Gas Bonny
For the optimization process to start, traditional statistical methods for nonlinear regression models
need a starting point (initial parameters or guess values). The parameters must first be predicted using
an iterative process after the nonlinear regression model expression has been written, the parameter
names have been expressed, and the initial parameter values have been defined. The Gauss-Newton
and Levenberg-Marquardt methods (algorithms) for solving non-linear regression models were used
in a computer program for predicting three growth models (Logistic, Gompertz, and Weibull models).
The multiplicative error terms used to decompose the growth models help specify the best algorithm
and model for growth studies. Before using an iterative approach, second-order regression techniques
were used to solve the problem of the initial parameters. The final estimate of the parameters,
standard errors, p-values, and model adequacy metrics like (R2
, Adj.R2
, MSE, SSE, AIC, and BIC)
that were used to select the best algorithm and growth model are displayed in the result. The Weibull
Growth Model with Multiplicative Error Terms was determined to be the ideal growth model by this
study. The Gauss-Newton Algorithm was once again found to be the best algorithm for solving nonlinear regression models in this study. Finally, this study suggest/recommend using the Gauss-Newton
algorithm to solve non-linear regression models and the Weibull Growth Model for additional growth
studies.
keywords: Algorithms, Gompertz Model, Logistic Model, Non-linear Regression, Weibull Model
1Amadi, Ugochukwu, 2Biu, O. Emmanuel,3,*Nkpordee, Lekia
1,3Department of Mathematics Statistics,
Ignatius Ajuru University of Education, Rivers State Nigeria
2Department of Mathematics and Statistics,
University of Port Harcourt, Nigeria
The issues concerning global rainfall distribution and warming/climate change cannot be over emphasized
since it affects virtually every part of live. The study used rainfall pattern in two states of Nigeria. Data on
the monthly rainfall distribution in Imo and Rivers state, for a period of 37 years was examined. The
result showed a continuous increase in the pattern of rainfall for a period of thirty seven years within the
period under study. However the pattern was inconsistence for the remaining years with some kind of
fluctuations. The monthly mean series plots showed a clear presence of trend with the peak period being
September annually in both series with coefficient of determination- R square value of 83% and 86% for
Imo and Rivers series respectively. The yearly mean series plots showed a clear irregular variation over
the years in both series. The irregularity in the pattern of rainfall calls for serious commitment in joining
the force for climate change abatement process. Pearson correlation coefficient between the two series is
0.80 (substantial correlation), which is the same result with cross correlation between the two rainfall
series (0.79988 approx. 0.80). The series reveal the following characteristics: high correlations appear
seasonality of order 12 in the monthly mean plots (every September), irregular variation and trend curve
which is quadratic trend. ARIMAX model with independent variable was employed to identify the best
bivariate time series model for prediction purpose. The result reveal an increase in Rivers series (Yt)
would tend to a linear combination of some increase of the preceding Imo series (It) values which is vise
visa. SARIMAX (1, 2) and SARIMAX (2, 1) models are identified as the best model with respect to
Rivers on Imo series rainfall; via Imo on Rivers series rainfall.
keywords: Rainfall Distribution Data, Cross Correlation, Seasonality, SARIMAX model, Model
Selection Criteria
In this study, Autoregressive integrated moving average with exogeneous variables (ARIMAX) model
was used to investigate the impact of inflation rate and unemployment rate on poverty level in
Nigeria. These variables were subjected to the usual model building steps in linear time series. The
Kwiatkowski, Philips, Schmidt and Schin (KPSS) test was used to test the variables for stationarity.
Differencing technique was used to obtain stationarities for the non – stationary series. Then, several
ARIMAX models were built to identifiy the best model. The result showed that ARMAX (2,0) fitted
the series best and was used to generated forecasts for the next five years. Its shows a decrease in
poverty level for the years 2022, 2023 and 2024 then a slightly increase for the year 2025. A
comparative analysis was carried out with Peter et al (2016) which applied vector Autoregressive
model of order 2 to the aforementioned variables. The result further confirmed that ARMAX (2.0)
performed best.
keywords:ARIMAX model, Stationary, Poverty Level, Inflation Rate, Unemployment Rate and
Vector Autoregressive Model
In this study, the problem of unsteady incompressible flow was analyzed using collocation technique to
find the most accurate solution for the velocity and energy distribution of the Newtonian fluid flow. The
flow experienced a gradual decrease with a retarded flow and afterwards increases but not a steady
increase. It is revealed that a little increase in the Darcy number leads to an increase in the velocity of the
fluid flow, indicating that porosity increase enhances the fluid flow. Results further show that increase in
the Hartman parameter decreases the fluid velocity which is due to the strength the Lorentz force.
Temperature decreases with increase in the Prandtl number and the Brinkman parameter.
keywords: Collocation, heat transfer, cylindrical pipe, porous media
In this research work on numerical analysis of reactive third grade fluid in cylindrical pipe, collocation
procedure were applied to analyze the flow regime. Results show that increase in the third grade,
magnetic field, Eckert and Brinkman parameters increased both the velocity of the fluid flow and
temperature of the system.
keywords: Reactive, Non-Newtonian, Third Grade Fluid, Cylindrical pipe
In this study on flow of third grade fluid in channel filled with porous media in the presence of heat
generation, the researcher considered and analyzed the effects thermo-physical parameters involved the
momentum and energy equations. The nonlinear momentum and energy equations arising from the flow
regime is solved analytically using perturbation technique. Explicit expression for the velocity field and
energy balance have been obtained Results show that a little increase in the third grade parameter
β ,
Grashof number,
G
, and the magnetic field parameter,
M , reduces the velocity of fluid flow but
enhances the temperature of the system greatly.
keywords: Third grade fluid, Channel, Porous media, heat source
