Grashof Number Research Articles

Applications of solar thermal radiation in a bio‐convective Eyring–Powell hybrid nanofluid flow under the influence of electro‐magnetohydrodynamics near a stagnation point: An irreversibility study

AbstractIn this study, we investigate the electromagnetohydrodynamic (EMHD) Eyring–Powell hybrid Nanofluid flowing through a stretching surface, with the effects of copper , aluminum oxide nanoparticles and gyrotactic motile microorganism with polyvinyl alcohol‐water as a base fluid. Heat transfer, joule heating, solar radiation, mass transmission, and entropy generation effects are analyzed on the fluid flow. A numerical model with an analytical methodology for the description of fluid flow and thermal properties of a parabolic trough solar collector (PTSC) installed on a solar plate is underway as the use of solar plates in many devices going to expand. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by using similarity transformations. The higher‐order ODEs are then solved using the analytical scheme known as the homotopy analysis method (HAM) in MATHEMATICA. The effects of different parameters such as magnetic field, electric field, Prandtl number, Eckert number, bioconvection diffusion, Lewis number, chemical reaction parameter, bioconvection, and Grashof number are analyzed with flow characteristics graphically. The velocity of the fluid shows a decrement due to the radiation parameter, Grashof number, and Solutal Grashof number. Thermodynamic properties of the fluid are enhanced with the Prandtl number, Eckert number, and electric and magnetic field. The entropy of the fluid increases with the Prandtl number, Eckert number, and diffusion parameter. Bejan number rises due to diffusion and bioconvection diffusion parameters. The study is about the mathematical analysis of Eyring Powell fluid flowing through a PTSC with the addition of a motile microorganism. PTSC are a main source of energy production for many sectors. Nanoparticles of copper and aluminum oxide are mixed to raise the thermal properties of the fluid used for electricity production engines, solar energy systems, cooling devices. Solar radiation effect, Joule heating, and viscous dissipation are analyzed for the energy production devices.

Magnetized Flow of Maxwell Fluid over a Slippery Stretching Reactive Surface with Thermophoretic Deposition

This manuscript investigated mathematically magnetized Maxwell fluid over slippery stretching reactive surface with thermophoretic deposition. Similarity transformation was used to recast partial differential equations modeling flow problem to nonlinear coupled ordinary differential equations which were solved using fourth order Range-Kutta method and Newton-Raphson shooting technique. Numerical results were compared with literature-based results and found to be in good accord. Skin friction coefficient, Nusselt number, Sherwood number, velocity profiles, temperature profiles and concentration profiles which are of importance to engineers, were found to be influenced by thermo-physical parameters governing the dynamics of flow. Their effects were illustrated in tabular form and graphically. The study found that increasing Thermophoretic deposition parameter, Momentum slip parameter and Biot number amplified rate of heat transfer but decreased rate of mass transfer and Skin friction coefficients. Thermal Grashof, Solutal Grashof, and Damkohler numbers reduced skin friction coefficients but increased heat and mass transfer rates.

Heat and Mass Transfer on Unsteady MHD Chemically Reacting Rotating Flow of Jeffrey Fluid Past an Inclined Plates under the Impact of Hall Current, Diffusion Thermo and Radiation Absorption

An analytical solution for two dimensional unsteady MHD free convective double diffusive heat and mass transfer rotating flow of viscous incompressible optically thin non Newtonian fluid (jeffrey fluid) past a semi-infinite porous plate in the presence of generation of heat absorption with hall current, radiation absorption and Dufour effects are presented in this paper. Lorentz force is applied perpendicular direction to the plate with a first-order chemical reaction. The governing PDEs transformed into ODEs by applying the perturbation technique. The effects of various physical parameters like Hall current, heat absorption, radiation parameter, radiation absorption parameter, Grashof number, modified Grashof number, Dufour effect, magnetic field parameter, inclined angle, chemical reaction parameter, etc., are studied with graphically. Temperature profile is increased by raising the values of Dufour effect, radiation absorption parameter and reverse effect of the heat absorption parameter and also concentration profile distribution is downfall by raising the values of Schmited number, chemical reaction parameter. Another significant finding of the current study is that the numerical data are displayed with the use of Matlab programmes to investigate the outcomes of the skin friction solution. the rate of heat and mass transfer at the wall rising under the influence of Dufour effect. Tables, graphs, and reports can be used to display the impact of all pertinent parameters.

Two-phase simulation of entropy optimized mixed convection flow of two different shear-thinning nanomaterials in thermal and mass diffusion systems with Lorentz forces

This research compares the momentum, thermal energy, mass diffusion and entropy generation of two shear thinning nanofluids in an angled micro-channel with mixed convection, nonlinear thermal radiation, temperature jump boundary condition and variable thermal conductivity effects. The RKF 45 approach was used to solve the Buongiorno nonlinear governing model. The effect of different parameters on the flow, energy, concentration, and entropy generating fields have been graphically illustrated and explained. The hyperbolic tangent nanoliquid has a better velocity than the Williamson nanofluid. The Williamson nanofluid has higher thermal energy and concentration than the hyperbolic tangent nanoliquid in the microchannel. The Grashof number, both thermal and solutal, increases the fluid flow rate throughout the flow system. The energy of the nanoliquid is reduced by the temperature jump condition, while the energy field of the nanoliquid is enhanced by the improving thermal conductivity value. The nanoliquids concentration rises as the Schmitt number rises. The irreversibility rate of the channel system is maximized by the variable thermal conductivity parameter.

Enhancing Magnetohydrodynamic Stability in Channel Flows through Porous Media Incorporating Darcy-Forchheimer Modifications into the Orr-Sommerfeld Analysis

This research paper investigates the stability characteristics of magnetohydrodynamic (MHD) flow within channels filled with porous media. Specifically, the study explores modifications to the classical Orr-Sommerfeld equation using the Darcy-Forchheimer model to account for the presence of porous media. The analysis aims to elucidate the combined influence of porous media and magnetic fields on flow stability in such systems. Numerical simulations and analytical techniques are employed to assess the impact of varying parameters on the stability behavior of the flow. The study revealed that the velocity profile increases with increase in Schmidt and Prandtl’s number and stabilizes with the increase in Grashof number and the buoyancy. The temperature profile increases with Reynold’s Number and Hartmann number. It stabilizes with Schmidt, Prandtl and Grashof number. The profile of species concentration stabilizes with thermo-phoretic parameter, Prandtl number and Darcy-Forchheimer’s parameter augumentation.

DECARBONIZING A THAI COAL POWER PLANT: EFFECT OF FLUE GAS LOADS ON CARBON CAPTURE PERFORMANCE AND ECONOMICS

This study investigated the impact of a cylindrical obstacle on convection in an inclined square cavity filled with water-Al2O3 nanofluid. Using the finite volume method, the problem was resolved by having the inner cylinder rotate adiabatically while other walls were thermally insulated. Additionally, the bottom wall was hotter than the top. The study examined the effects of cylindrical obstacle radius (0.1 ≤ R ≤ 0.2), rotation speed (-500 ≤ Ω ≤ 500), Richardson number (0.01 ≤ Ri ≤ 100), volumetric nanoparticle fraction (0.02), and Grashof number (Gr=104) on heat transfer rate or Nusselt number. The results were compared with previous literature, and the influence of the cylindrical obstacle rotational speed on convection flow was evaluated. An increase in the counterclockwise angular rotating speed resulted in higher nanofluid flux. The heat transmission coefficient increased as the Richardson number decreased. The use of nanofluid in the enclosure increased the coefficient of heat flow through mixed convection. Finally, the study showed that the convection heat exchange is enhanced with the increase in the radius. Moreover, an enhancement of the Nusselt number around 46% was reported for the cylinder, under Gr=10000, ∅=0.02, γ=45° and Ri=10.

Chemical process effects on sloped surface with changing mass and consistent temperature

The research extensively investigated the turbulent flow patterns surrounding an unbounded inclined plate under the conditions of uniform temperature and variable mass dispersion. Throughout this analysis, the study thoroughly considered the impact of chemical reactions within the system. Focusing on the harmonic inclination of the plate within its plane, the study employed the LT approach to accurately solve the non-dimensional governing equations. In scrutinizing various profiles, the investigation examined the impact of several crucial physical factors: chemical response variable, Schmidt number, thermal Grashof number, mass Grashof number, and duration. This study delves into the intricate influence of various factors on the complex flow dynamics surrounding inclined plates, specifically focusing on heat and mass transfer phenomena. By examining these relationships, the research provides crucial insights into improving the efficiency of thermal and mass transmission processes within systems that incorporate tilted surfaces. Moreover, this knowledge can potentially contribute to advancements in various fields, from renewable energy systems to manufacturing processes, where heat and mass transfer play pivotal roles.

Jeffrey fluid flow past inclined stretchable sheet with magnetic dipole and suction/injection

Jeffrey fluid flow past an inclined stretchable sheet affected by magnetic dipole and suction/injection was investigated. The applicable equations were changed into nonlinear ordinary differential equations by similarity transformations. With the Chebyshev spectral collocation approach, solutions were obtained for fluid velocity and temperature. Considering the prescribed surface temperature (PST) and prescribed heat flux (PHF) heat processes, the effect of inclination angle, the Grashof number, and other parameters on the velocity and temperature of the fluid were documented by graphs and tables. Without the angle of inclination, the solutions from this paper were found to agree with those of the Generic algorithm and Nelder Mead method. The fluid is slower when the plate is inclined at a larger angle and this tends to allow for higher fluid temperature. The ferromagnetic interaction parameter and the ratio of relaxation to retardation time have the same effect on fluid velocity and temperature as the angle of inclination. The suction parameter and Prandtl number amplify the Nusselt number, while, as the suction increases, the skin friction increases for all inclination angles. With these results, engineers in chemical/polymer industries can make appropriate changes that can lead to more quality production.

ACTIVATION ENERGY EFFECT ON MHD CONVECTIVE MAXWELL NANOFLUID FLOW WITH CATTANEO-CHRISTOVE HEAT FLUX OVER A POROUS STRETCHING SHEET

The current article investigates the heat and mass transfer of convective magnetohydrodynamics (MHD) Maxwell nanofluid flow over a porous stretching sheet with Cattaneo-Christove heat flux. The influences of heat sources, radiation, and viscous dissipation are investigated. Also, the activation energy with binary chemical reaction and suction/injection are considered into the account. The dimensional governing equations are transmitted into nondimensional form by similarity transformations. Further, the obtained mathematical model is solved numerically in MATLAB. The effects of physical parameters pertaining in flow regime are investigated through figures and tables. It is noticed that the fluid velocity drops with an increase in the magnetic field, porosity, and suction parameter. The increased Brownian motion, heat generation, and radiation improves the temperature field, while it declines with an upsurge in values of thermal relaxation time. An increasing thermophoresis and activation energy lead to an increase in the concentration, whereas the opposite trend is seen for increasing chemical reaction. The Nussult number enhances due to the larger values of thermal Grashof number, solutal Grashof number, and Biot number, whereas it declines with the escalating values of Brownian motion, thermophoresis, and Eckert number. The comparison of the present results is carried out with the published results and noted a good agreement. These findings are useful for the space technology, metal thinning, power generation, water purification in the soil, polymer extrusion, and the thermal control of heat exchangers in upcoming technologies.

Mixed convection analysis in a dual-driven cavity with a stable vertical temperature gradient using the lattice Boltzmann method

The complex dynamics of mixed convection circumstances, concentrating on two examples. In the first case, mixed convection was investigated in a single-sided lid-driven cavity with a top and bottom walls arrangement and the second scenario explores parallel and anti-parallel topologies, focusing on mixed convection in a double-sided lid-driven cavity. The main parameters in this study are the Reynolds, Rayleigh, Prandtl, Grashof, and Richardson numbers. Calculation of numerical solutions to the Navier-Stokes equations over wide ranges in parameters, 0 ? Gr ? 106, 0 ? Re ? 3000, Pr~O(1), and an aspect ratio approximately O(1). The study analyzes these results systematically to understand the relative importance of natural convection and forced convection. As a result of this study, a two-dimensional cavity with specific boundary conditions was created. In a square domain with adiabatic side walls, a top wall is maintained at a higher temperature than the bottom wall. The flow characteristics approach those of a typical driven-cavity of a non-stratified fluid when Gr/Re2 ? 1. There are low fluctuations in temperature and well-mixed fluids throughout the majority of the interior. Much of the inner cavity?s middle and bottom are stationary when Gr/Re2?1. Temperature patterns in these areas are vertically linear and isotherms are nearly horizontal. Lattice Boltzmann method considers the effect of gravity on mixed convection by adjusting the y-velocity using a temperature-dependent forcing factor. The calculation of the Nusselt number at the top wall reveals enhanced heat transfer, with the results suggesting increased intensity when Gr/Re2?1.

Optimization of system parameters during conjugate mixed convective flow in a square domain with an oscillating spinning cylinder

A computational analysis has been executed to analyze the combined conduction-mixed convection heat transfer of a rotationally oscillating solid cylinder in a differentially heated square box filled with air. The conjugate mixed convective flow initiates the heat transfer process, where the left-side boundary is isothermally kept to a higher temperature, and the right-side boundary is maintained at a lower temperature. Conduction heat transfer takes place inside the solid cylinder. Navier-Stokes and heat energy conservation equations model the system in the dimensionless pressure-velocity formulation. All these equations are solved via the Galerkin finite element approach. Three different combinations of Grashof (103-105), Reynolds (32–316), and Richardson (0.1–10) numbers are examined to systematically investigate the variations of governing parameters on instantaneous Nusselt numbers and the respective time-averaged values along the hot wall. In each combination, the impacts of the oscillating amplitude and frequency and the variation of cylinder diameter are examined to perform the optimization study. Power spectrum analysis is also done using the Fast Fourier Transform in the frequency domain to visualize the principal frequency of the system. The instantaneous values of the Nusselt number exhibit a wavering pattern over time owing to the recurrent waning and waxing of the thermal boundary layer. For all the cases, the maximum diameter and oscillating amplitude of the cylinder are found to maximize the heat transfer. However, the optimized frequency of the oscillation strongly depends on the selection of the governing parameters. In addition, the principal thermal frequency of the system is determined to be independent of the oscillation frequency.

HORIZONTAL SINUSOIDAL WAVY FORM PLATE-FIN HEAT SINKS FOR NATURAL CONVECTION HEAT DISSIPATION

The plate-fin heat sink geometry was modified to have the fin form sinusoidal wave shape in the horizontal direction with twelve variations by amplitude and period changes. Three different wave periods and four different wave amplitudes were used. The purpose was to alter natural convection motion in favor of heat transfer effectiveness. The main performance indicator was the base-plate average temperature. The independent geometric parameters were experimentally examined in terms of the effectiveness of natural convection heat transfer by the measured average temperature values. Heat transfer by radiation was calculated by an analytical algebraic approach in order to obtain the Nusselt number solely based on convective heat transfer. Eight different heat inputs were used for each tested geometry to change the Grashof and Rayleigh numbers in a laminar flow interval. As reference geometries, a flat plate and a heat sink with straight/flat-plate fins were utilized. The heat sinks were also oriented to three different angles by a test stand. Accordingly, thirty six unique experimental cases were examined as a result of 327 trials and 1100 hours of testing. It was realized that the wavy fin geometry enhances natural convection heat transfer compared to the base-plate and flat-plate-fin heat sinks. However, increasing period and amplitude of the wave form more than initial values deteriorated the gains by the modifications on the fins. Since a single-period, 2-mm-amplitude heat sink resulted in the highest Nusselt number for all orientations, an optimum may be sought about this setting. As a general evaluation, computational simulations for spatial resolution of the event physics and dimensional optimization are standing as future study targets.

Convection boundary layers with transpiration: Non-similar solutions and scaling

We present a new formulation and novel scaling relations for natural convection boundary layers on horizontal surfaces with weak transpiration velocities Vi, for intermediate Schmidt numbers (or Prandtl numbers Pr) 1<Sc<20. Using characteristic scales derived from integral boundary layer equations, we define a new similarity variable η=(y/x)(Rex/Grx)1/4/Sc1/5 that has Vi within it, where Rex and Grx are the local Reynolds and Grashof numbers based on Vi and the concentration difference ΔC, respectively. Using η, and the dimensionless transpiration velocity ξ=(Rex/Grx1/5)5/4 as a non-similarity variable, we obtain novel, reduced, non-similar boundary layer equations. Numerical solution of these reduced boundary layer equations using a local non-similarity approach gives us the profiles of horizontal velocity and concentration, boundary layer thicknesses, wall shear stress, and mass flux as functions of Sc, for various ξ in the range ξ<1. Using normalizing functions, we then obtain scaling relations for these parameters; we observe extended similarity where the non-similarity parameter ξ itself appears in the obtained similarity scaling relations.

The Newtonian heating effect on MHD free convective boundary layer flow of magnetic nanofluids past a moving inclined plate

The effect of magnetic strength on the MHD free convection flow of nanofluids over a moving inclined plate with Newtonian heating is analyzed. The governing partial differential equations with Newtonian heating boundary conditions are transformed into a system of nonlinear coupled ordinary differential equations (ODEs) by using similarity transformations. The Keller Box method was used as a solvation method for ODEs. The skin friction and Nusselt number are evaluated analytically as well as numerically in a tabular form. Numerical results for velocity and temperature are shown graphically for various parameters of interest, and the physics of the problem is well explored. The significant findings of this study are promoting an angle of an aligned magnetic field, magnetic strength parameter, the angle of inclination parameter, local Grashof number, the volume fraction of nanoparticles, and Newtonian heating parameter. The result shows that the moving inclined plate in the same direction increases the skin friction coefficient and reduces the Nusselt number. It is also observed that the velocity of moving an inclined plate with the flow is higher compared to the velocity of moving an inclined plate against the flow. The temperature of a moving inclined plate with the flow is decreased much quicker than the temperature of a moving inclined plate against the flow. The other noteworthy observation of this study demonstrates that the Nusselt number in the Newtonian heating parameter shows that Fe3O4-kerosene is better than Fe3O4-water.

Magneto-Williamson nanofluid flow past a wedge with activation energy: Buongiorno model

The current investigation explores the effect of activation energy on the MHD radiative Williamson nanofluid flow across a wedge using heat generation and binary chemical reactivity. The flow model consists of partial differential equations (PDEs) by transforming them into ordinary differential equations (ODEs). Numerical computations have been carried out through the bvp4c MATLAB package. The most effective solutions for flow profiles have been displayed through graphs, while the numeric solutions for the drag friction, heat, and mass transport have been displayed via tables. Numerical findings demonstrate that the temperature field is accelerated by the increase in radiation parameter. In addition, it is intriguing to discover that the concentration boundary layer thickness improves as the activation energy increases. A fundamental study further reveals that the local skin friction coefficient is a rising function of thermal and concentration Grashof numbers. Moreover, it is concluded that the enhanced Brownian motion, thermophoresis, and Eckert number decline the heat transfer rate.

Implementation to cardiovascular disorders under the action of magnetohydrodynamics in a non‐Newtonian peristaltic blood flow of nanofluid

AbstractThe issue of vascular stenosis has recently received significant innovative interest among researchers. Due to the buildup of adipocytes and other constituents of atherosclerotic, arteries can generate an abnormal condition called arterial stenosis. It optimizes blood circulation to prevent myocardial illness. In light of this, the current scientific report assembled a Casson fluid model to assess the MHD peristaltic transit of blood supply via a mildly stenotic artery when copper nanoparticles are added. A relevant simulation model is often used to outline the issue, acquiring non‐dimensional variables and approximations for the stenosis. Temperature has quantitative approaches, and the result for velocity is derived numerically in MATHEMATICA. The expressions for Nusselt number, wall shear stress, flow resistance distribution and stream function are attained. The under action of copper nanoparticles, the consequences of several new physiological measures on arterial blood circulation properties are visually displayed and explained briefly. A pictorial explanation of the trapping phenomena is also provided. In comparison to arteries devoid of stenosis, arteries with stenosis have a higher temperature distribution throughout the fluid flow and velocity. In addition, high temperature and velocity increase in the middle of the artery and decrease as one gets closer to the arterial wall. Further, the concentration, Grashof number and heat source and sink parameters of the nanoparticles reduce the wall shear stress of the blood in the arteries since the arterial wall contributes heat to the flow zone. The discovery could have medical applications as well as bioinformatics. Furthermore, the current work contributes to the cure of different cardiac illnesses.

Hydrothermal characteristics of ferrofluid in a wavy chamber with magnetic field-dependent viscosity: Effects of moving walls

The present investigation aims to scrutinize the role of different moving walls on the hydrothermal characteristics and thermal performance of a Fe3O4-H2O ferrofluid within a wavy chamber under mixed convection. Notably, the study also takes into consideration the effects of a magnetic field and internal heat generation or absorption phenomena. To achieve this, a numerical simulation employing a compact finite difference method is conducted, focusing on key factors such as the Richardson number (0.1≤Ri≤100), Hartmann number (0≤Ha≤30), magnetic orientation (00≤γ≤900), Grashof number (Gr=104), solid concentrations (0≤ϕnp≤0.04), magnetic number (0≤δ0≤1), Prandtl number (Pr=6.8377), and internal heat generation parameter (−2≤Q≤2). All of this is undertaken while carefully managing the ferromagnetic particle volume fraction. The primary aim is to assess how different types of moving walls affect the transport behavior of the ferrofluid and to determine the impacts of the magnetic field on the hydrothermal characteristics of the ferrofluid. The outcomes of this investigation reveal that the presence of moving walls leads to a non-uniform temperature distribution within the ferrofluid, significantly affecting the overall transport behavior. The addition of ferrofluid particles to the base fluid results in noteworthy enhancements in the average Nusselt numbers, signifying improved convective heat transfer efficiency. Specifically, Case-I experienced an increase of up to 3.21%, Case-II showed an improvement of 0.93%, Case-III exhibited a rise of 1.70%, and Case-IV demonstrated the highest enhancement of 20.71%. Furthermore, the inclusion of magnetic field-dependent viscosity and the internal heat generation coefficient significantly influences the behavior of the ferrofluid. The findings from this study hold paramount importance for the design and optimization of heat transfer systems that employ ferrofluids and have the potential to contribute to the development of novel technologies with a wide range of industrial applications.

Role of internal heat generation, magnetism and Joule heating on entropy generation and mixed convective flow in a square domain

This study has computationally inspected the role of internal heat generation, magnetism, and Joule heating on mixed convective flow and entropy generation in an air-filled square domain. The right cold wall of the differentially heated domain is sliding in its plane at a fixed speed, giving rise to two distinct flow configurations: aiding and opposing flows based on the direction of the sliding wall. In addition, a uniform magnetic field is applied horizontally parallel to the domain with the facility of Joule heating and volumetric heat generation. The fluid flow and the heat transfer within the square domain are formulated by continuity, momentum, and heat energy conservation equations, which are solved using the Galerkin finite element method after imposing appropriate boundary conditions. Numerical simulations are carried out under five distinct cases over a specific range of Reynolds number (31.623 ≤ Re ≤ 316.23), Grashof number (103 ≤ Gr ≤ 105), Richardson number (0.1 ≤ Ri ≤ 10) for mixed convective laminar flow consideration, Hartmann number (0 ≤ Ha ≤ 17.783), and Stuart number (0 ≤ N ≤ 3.162) for the variation of the strength of the uniform magnetic field under Joule heating, and volumetric heat generation coefficient (0 ≤ Δ ≤ 2) for internal thermal generation. The detailed quantitative results incorporate both the thermal and mechanical performances of the system, leading to several important conclusions outlined in their respective cases. It is found that increasing both Re and Ha or increasing Re and decreasing N with fixed Gr lead to higher heat transfer and reduction of the average fluid temperature inside the domain with less experienced drag and higher total entropy generation. Meanwhile, pure mixed convection exhibits higher heat transfer with increasing Gr, particularly when no internal heat is generated.

Numerical investigation of the maximum temperature zone for liquid–vapour flow during reflooding

High-temperature deformation caused is a major problem during reflooding. To describe the heat transfer behaviour, relationship between the maximum temperature zone and influencing factors are investigated. Good agreement between the numerical predictions and experimental data is observed. The results are obtained. (1) The Euler number and Grashof number influence the maximum temperature zone, the Strouhal number has a greater influence. (2) There is no correlation between the maximum temperature zone and velocity distribution waveform. (3) The power distribution changes the flow and temperature field and shifts the position of the highest temperature from the middle to the top. (4) The change in initial temperature directly leads to PCT mutations and changes in the maximum temperature zone. An excessively large Grashof number initial power, a top-enhanced power distribution, and a linear power distribution leads to an excessively high PCT and the maximum temperature zone at higher positions, which requires significant attention.

Role of suction/injection on electromagnetohydrodynamics natural convection flow in a porous microchannel with electroosmotic effect

This paper examined the role of suction/injection on time-dependent electromagnetohydrodynamics (EMHD) natural (free) convection flow in a vertical microchannel with electroosmotic effect. With the aid of Laplace transformation method, the governing energy and momentum equations are converted from partial differential equation (PDE) into ordinary differential equation (ODE) to obtain fluid temperature and velocity in Laplace domain. The semi-analytical solutions of the velocity profile and temperature distribution have been derived using the Riemann sum approximation. After which a MATLAB program was written to study the effects of Prandlt number Pr, Hartmann number Ha, electric field strength on x and z directions (Ex and Sz) and Grashof number Gr in fluid velocity, temperature, skin-friction and mass flow rate in terms of line graphs. Result shows the role of suction/injection parameter alters the temperature distribution and velocity profile, so also how effective the governing parameters contribute to the flow formation. .