To enhance the thermofluidic capability of plate pulsating heat pipes (PHPs), a comprehensive and precise analysis of their oscillatory behavior and heat transport performance is essential. A single loop PHP model featuring both horizontal and longitudinal variable-diameter structures was developed. The phase-change and heat transfer processes were simulated using a combined approach of computational fluid dynamics (CFD) and the volume of fluid (VOF) method, providing microscopic insights that address research gaps in numerical modeling of variable-diameter PHPs. Present research systematically investigates the performance enhancement effects of different variable-diameter configurations on the startup and operational behavior of PHPs under varying heat load, filling ratio, and inclination angle conditions. The results showed that non-uniform channel diameters significantly affect the vapor-liquid distribution and pressure distributions within all PHPs. The horizontally variable-diameter PHP (DPHP1) consistently exhibited the lowest thermal resistance across all heating powers, maintaining efficient heat transfer even under high-power conditions. With heat power of 10-70 W, its thermal resistance reached 1.212 K/W and 0.258 K/W, representing reductions of 9.78 % and 26.24 %, respectively, compared to the uniform-diameter PHP (UPHP). The primary reason for faster startup of DPHP1 is the directional growth and rapid coalescence of vapor bubbles. Additionally, condenser-side diameter expansion (DPHP3) enhances vapor transport efficiency, while excessive constriction in the evaporator section (DPHP2) inhibits the momentum of working fluid circulation. Optimizing diameter gradients can help balance flow resistance and phase-change driving forces, thereby enhancing startup performance under low heating power conditions. These findings offer valuable insights for the design and optimization of systems in waste thermal recovery and electronic cooling applications.

Problems of energy storage and rational use are of primary importance in all spheres of human activity. Passive thermal power systems acquire high importance in conditions of constant increase of energy consumption. Phasechange materials are already widely used in electronic devices, batteries, solar collectors, latent thermal energy storage systems, and others, but one of the negative aspects of phase change materials is low thermal conductivity. To improve the thermal conductivity of phase change materials, the metal foam inserts can be used, that can significantly increase thermal conductivity of the system. The porous structure provides a large area of contact with the environment, due to which the temperature difference between phase change material and the solid structure remains small. Consequently, the high thermal conductivity of the metal allows increasing the intensity of heat dissipation. In this numerical study, the process of heat and mass transfer and melting of PCM in a porous insert with anisotropic properties is considered, taking into account convective heat transfer in the melt region. Melting regimes in porous anisotropic media have been little studied and this problem is of interest for modeling and development thermal energy storage systems. The numerical solution is obtained based on the finite difference method using the local thermal equilibrium Darcy-Brinkmann approach and the enthalpy-porosity method to solve the energy equation. The developed computational code has been verified comprehensively. The numerical analysis has shown a significant effect of the anisotropic properties of the porous insert on the convective heat transfer modes and the intensity of material melting. It has been found that the greatest impact of the anisotropy parameters is observed when the heater is located at the top of the region where thermal conduction plays a major role in heat transfer performance. In this case, the anisotropic model shows a decrease in the source temperature by 8 degrees C compared to the isotropic model at high porosity. Furthermore, in almost all observed cases, the model with an anisotropy angle alpha = 0 degrees has demonstrated the best heat transfer performance.

This article presents a study on achieving uniform temperature distribution on a plate surface in mixed convection heat transfer. The study simulated airflow around the plate using RANS equations and k-b) standard turbulence model, validated using experimental studies. Temperature uniformity was achieved by controlling the heat flux into the plate, which was divided into 15 equal-length sections. A comprehensive parametric dataset comprising 2000 numerical simulations was generated for four Reynolds numbers. This dataset was used to construct a surrogate model linking the sectional heat fluxes to the resulting temperature distribution. Several surrogate modeling approaches including KRadiusNeighbor, MultiLayer Prespetron, Random Forest, Extra tress, KNearestNeighbor, and the RSM model of genetic aggregation were evaluated, and the RSM method demonstrated the highest predictive accuracy. The selected surrogate model was subsequently integrated with a multi-objective genetic algorithm to determine the optimal heat-flux distribution required to achieve surface temperature uniformity. The findings indicate that the input heat flux, which creates a uniform temperature field on the surface, has an oscillating nature, and the intensity of the fluctuations of this heat flux increases with increasing Richardson number. The results showed that as the Richardson number augmented, so should the discretization number of heat fluxes enter the plate. The study also observed two decreasing and increasing trends in the graphs of the heat transfer coefficient and output heat flux, which were attributed to the flow transition from laminar to turbulent. RSM model of genetic aggregation type with R 2 = 0.99983 was selected for the optimization process. In Re = 5134, 8557, 10953, and 13692, in Ri = 1.3, 0.79, 0.45, and 0.48, the uniform temperature distribution on the plate is well achieved.

An application of metal foams to improve the thermal energy transport in organic phase change materials such as paraffins, waxes and fatty acids is one of the most optimal ways to enhance the effective thermal conductivity of these materials. The possibilities of using metal foams can be improved with the combination of layers of different structural topology and thermophysical properties, which allows directing and distributing heat more uniformly throughout the volume. In this paper, computational research on convective thermal energy transfer and melting processes in a two-dimensional cavity including a porous copper medium saturated with a phase change material and heated by a volumetric heat source, is carried out. The results are received employing the finite difference technique, and the main equations are formulated within the framework of the local-equilibrium Darcy-Brinkman approach. The obtained data have allowed to conclude that the location of a foam layer with lower porosity allows more intensive heat dissipation, showing lower source temperatures; however, the best effect has been shown by vertical layers, with a gradient that creates uneven heating, which in turn results in the appearance of an extensive circulation zone and intensive heat removal from the local source.

A computational simulation has been worked out to analyze the flow dynamics and thermal behavior inside a hexagonal enclosure filled with magnetized buoyancy-driven hybrid nanoparticle (MgO-Ag) dispersed in water. The enclosure features thermal boundary conditions such that the lower border is heated, the upper surface is cooled, and the remaining inclined surfaces are adiabatic. Further, the hexagonal chamber contains non-uniformly heated parallel rectangular fins of same size. Two cases are extensively studied. Case I is considered when the partially heated rectangular fins are placed vertically and Case II is held for partially heated rectangular fins placed horizontally within the hexagonal cavity. Rate of heat transport is more in Case II (when fins are placed horizontally) as compared to Case I (when fins are placed vertically). Simulations are done using robust COMSOL Multiphysics software and the validation of the numerical model has been performed against existing standard study to set the accuracy of the calculated outcomes. The influence of Hartmann number (Ha), Rayleigh number (Ra) and fraction of hybrid nanoparticles (ϕ) on streamline patterns, isotherms, Nusselt number, entropy generation and Bejan number is discussed in detail. The ranges of parameters considered for the investigation are 103 ≤ Ra ≤ 106, 0 ≤ Ha ≤ 100, 0.00 ≤ ϕ ≤ 0.04. The investigation reveals that enhancing the Rayleigh number intensifies entropy close to the heated bottom wall and around the partially heated inner plates, whereas the Bejan number weakens in those regions which indicates a swing toward higher irreversibility. The inclusion of MgO-Ag hybrid nanoparticles significantly enhances thermal transport and improving mixing which results in improved thermal performance. Case I is more efficient for thermal stratification while Case II is preferable for uniform wall cooling even with localized heating and entropy. The findings have implications for the creation and optimization of thermal systems including heat exchangers, electronics and solar thermal systems.

The influence of benign and malignant tumors on the temperature profiles of multilayer biological tissue, obtained on the basis of one-dimensional and two-dimensional numerical modeling, has been studied. The mammary gland has been chosen as a model of a multilayer biological tissue. The Pennes biothermal equation has been used to analyze the thermal effects. Various options for the location of tumors, including the superficial and interstitial location, as well as variations in their linear sizes, have been considered. The numerical analysis has been carried out using the finite difference method of the second order of accuracy. It has been established that the nature of the thermal effect significantly depends on the biological nature of the tumor, its size and depth of location. Benign tumors are characterized by local hypothermia, while malignant tumors cause local hyperthermia reaching 311 K. The greatest increase in epidermal temperature has been observed as the size of the malignant tumor increased. For interstitial formations, the effect on surface temperature is determined by the depth of occurrence: benign tumors have virtually no effect on the surface temperature profile, while malignant tumors cause internal thermal peaks, which are partially smoothed out when heat spreads upward. The results obtained can be used to track the spread of heat in the volume of tissues and quantify how the depth of the location and size of the tumor affect the temperature distribution on the surface. Moreover, the obtained correlation of the average temperature of the tumor zone depending on the physiological parameters of the tumor tissue is very important and useful in medical practice.

Materials with low phase transition temperatures have proven themselves in the construction industry as a source of increased heat capacity and passive regulator of energy exchange. The scope of application covers air conditioning systems, thermal control, PV panels and others. This paper numerically investigates the heat transfer phenomena through a wall element containing air cavities and enclosures filled with technical paraffin. An algorithm based on the finite difference method is used as a tool for modeling the thermal and hydrodynamic processes. Non-stationary problems of conjugate convection with the phenomenon of phase transformation in phase change material (PCM) are solved and results have been obtained in a wide range of Rayleigh numbers for several configurations of the bricks with different volume fraction of air and Rubitherm of a melting point of 22 degrees C. Present study, for the first time, provides detailed examination of the influence of hydrodynamic phenomena in the melt on the ability of hollow brick containing PCM to smooth out daily temperature fluctuations. The effect of various convective heat transfer conditions depending on the volume of the material has been studied. It has been shown that with an increase in the outdoor temperature, the presence of solid PCM in the cavities significantly inhibits the growth of temperatures in the region, delaying and reducing temperature peaks on the indoor surface. At high thermal loads for the double PCM cavities in a brick, a reduction of 87% in daytime heat losses and a time delay of more than 4 h have been obtained. It has also been shown that natural convection, even in small cavities, can intensify the heat transfer due to heating of the upper part of the region. As a result of temperature stratification in the melt, it has been discovered that the surface temperature in the room can have a difference of 1.5 degrees C in height.

PurposeThe purpose of this study is to investigate the onset of convection in microelectronics cooling in a trapezoidal thermal system saturated with a H2O based Ag-MgO (50-50%) binary hybrid nanofluid via stream function-vorticity (psi-zeta) analysis and numerical simulation.Design/methodology/approachA uniformly heated block is positioned in the middle of the trapezoidal system. The block is considered in three different sizes, measured by aspect ratios of 25%, 50% and 75% of the trapezium height. The flow transport in the domain is magnetically controlled. The governing formulas are solved by using a fourth-order accurate compact finite difference scheme, which captures flow physics on low computational grids with high spatial resolution.FindingsQuantitatively, the maximum heat transfer enhancement is achieved at AR = 0.75 and gamma=75 degrees, with corresponding increases in average Nusselt number (Nuav) ranging from 9.5% to 34.12% at Ra = 104, 8.43% to 29.78% at Ra = 105 and 7.27% to 35.21% at Ra = 106. The results reveal that the heated block significantly alters the thermal and flow structure, especially under higher Rayleigh numbers and inclined boundary configurations. These outcomes offer promising implications for real-world applications requiring efficient thermal management within confined enclosures.Originality/valueThis work's originality is found in five key areas: the role of hybrid nanofluids with experimental correlations, the geometrical effects of the trapezoidal cavity, the influence of heated block aspect ratios (0.25 <= AR <= 0.75), the interaction with applied magnetic fields, and the implementation of higher-order compact computational techniques over a wide range of parameters.

PurposeThe extraction and application of renewable energy are significant for breaking through traditional energy structures. Geothermal energy is an illustrated clean and renewable energy source that possesses enormous reserves, wide distribution and safety and stability. The purpose of this study is to improve the internal tube structure of smooth coaxial heat exchangers and innovatively proposes spiral finned and double slanted finned structures for the improvement of convective thermal energy transport inside the pipeline.Design/methodology/approachThe computational fluid dynamics (CFD) numerical research investigates the impacts of three different internal tube structures on the exit temperature of the heater system, the energy extraction power and the surrounding soil temperature field, and analyzes the enhanced energy transport performance of the new coaxial thermal exchangers.FindingsThe outcomes illustrate that the spiral finned coaxial thermal energy exchanger demonstrated superior convective energy transport enhancement through comparative analysis under different conditions. Subsequently, the study explores the different effects of inner tube diameter, pitch and fin height of spiral finned heat exchanger on its heat transfer performance. The better efficiency inner tube structure increases the thermal energy extraction intensity by 4.49% in comparison with the smooth one. Under equal extraction conditions, the heat exchanger can obtain more geothermal energy by choosing soil heat sources with a larger temperature gradient. When the local temperature gradient rises between 0.025 and 0.045 K/m, the thermal energy extraction power can be increased by 66.7%.Originality/valueThe present study provides theoretical support for improving the thermal energy extraction efficacy of a novel coaxial heater system in practical applications.

This numerical study investigates natural convection phenomenon in a rotating porous cubical cavity, analyzing the coupled effects of rotation, temperature difference and porous medium characteristics on heat transfer dynamics. The governing equations, formulated using vector potential and vorticity variables, incorporate the extended Darcy-Brinkman model to account for porous media effects. A second-order finite difference method with successive over relaxation and Thomas algorithm solves the discretized system, validated against benchmark solutions for both hydrodynamic and thermal fields. The analysis explores a broad parameter space, including Taylor numbers, Rayleigh numbers, and porosities. Key findings reveal that two distinct regimes exist: buoyancy-dominated (low Ta) with oscillatory Nusselt numbers and rotation-dominated (high Ta) with stabilized Nu. Porosity-enhanced heat transfer persists across all Ta, although centrifugal forces modulate its efficiency, while Ra significantly intensifies convection only at low Ta, demonstrating rotational suppression of thermal effects. The results demonstrate that angular velocity and porosity can serve as effective control parameters for thermal management, with practical implications for rotating machinery and energy systems employing porous media. The study establishes a validated numerical framework to analyze three-dimensional convection in rotating porous environments. This study identifies optimal rotation-porosity configurations that enhance thermal efficiency in heat exchangers and passive cooling systems, outperforming conventional designs. The findings enable sustainable heat recovery in industrial applications and next-generation microelectronics thermal management, reducing energy consumption.

The production of a various engineering systems is accompanied by studies of liquid flow structures and thermal energy patterns. Many engineering systems in electronics and energy are affected by rotation and an important task becomes the description of physical phenomena under rotational effects. This investigation is dedicated to convective-radiative thermal and mass transport inside a rotating cube having a flat heated element placed on the bottom surface. The rotation of the cube around each of the axes of Cartesian coordinates has been considered. Governing equations based on mass, momentum and energy conservation laws are written employing the non-primitive variables. The set of control equations is resolved by the finite difference schemes. The influences of angular velocity, rotation axis orientation, and emissivity of surfaces on the intensity of heat transfer have been shown. Temperature patterns for various rotation angles are presented and described in detail. The results demonstrate that rotation around the vertical axis shows a steady-state of the Nusselt numbers, while rotation around the horizontal axis shows the periodic changes. It is interesting that similar heat exchange modes are formed during rotation around horizontal axes. More intensive convective and radiative heat exchange is observed in the case of rotation around an axis at which the cooling walls change their position.

Nowadays effective cooling of heat-generating elements can be obtained using suitable working heat transfer fluid and/or optimal extended heat transfer surface e.g. fins. A combination of these two approaches can allow preparing an effective cooling system for heat-generating elements in electronics and power engineering. The present investigation deals with mathematical modeling of heat transfer performance in an engineering system having a local heater of constant internal volumetric heat flux and a heat sink with fins as well as a pseudoplastic nanofluid as a working heat transfer liquid. Additionally in the present research a comparison between solid and porous fins influence on the cooling effect has been conducted. A combination of carboxymethylcellulose with H2O and Cu nanoparticles has been used as a working power-law liquid. The partial differential governing equations written employing the conservation laws for mass, momentum and energy have been worked out employing the finite difference schemes and non-primitive variables. The in-house numerical code has been verified comprehensively. The calculated data are analyzed by the distributions of local isolines for stream function and temperature combined with average temperature of the heat-generating element. It has been revealed that porous fin is more effective compared to the solid one due to more essential heat transfer surface. From another side it is possible to control the thermal energy removal by optimal choosing the porosity and permeability of the metal foam fin.

Natural convection, driven by buoyancy, is utilized for the heat transport in various applications including thermal exchangers, cooling of heat sources, solar collectors, geothermal power systems, electronic devices, microelectronics, and nuclear industries. This research focuses on the free convection of a hybrid nanoliquid containing Ag–MgO nanoparticles in an enclosure having partially active borders. The hybrid nanosuspension utilized is a mixture of MgO and Ag nanoparticles in equal proportions, suspended in water as the base liquid. The square enclosure is subject to the Lorentz force impact. The study examines two cases. In Case 1, the left wall experiences heat dissipation via a heat sink at a fixed temperature T c , whilst the right wall is partly affected by the active chamber borders with a heater at temperature T h (where T h > T c ). The rest sections of vertical borders are adiabatic. In addition, the cavity is thermally insulated on both the upper and lower surfaces. In Case 2, the chamber's vertical sides are heated to a certain extent ( T h ), whereas the bottom wall is somewhat cold ( T c ) and has some level of activity. The remaining inactive sections of the cavity are adiabatic. The control flow equations were resolved with the help of COMSOL Multiphysics, which is complex modelling software for computational fluid dynamics (CFD). The computational study has been performed with the following parameters, Rayleigh number ( Ra ) = 10 3 –10 6 , Hartmann number ( Ha ) = 0–80, and nanoparticles volume fraction (ϕ) = 0.01, 0.02. The effect of important variables, such as Hartmann and Rayleigh numbers, in conjunction with the concentration of nano additives has been examined by analyzing streamlines and isotherms to understand their effect on thermal convection. It is found from the isotherms within the cavity in Case 2, that increment in Ha leads to slight rise the temperature within the cavity. Further, in Case 1, Nu avg is decreasing function of Ha and Q . While in Case 2, the average Nu is decreasing function of Q and increasing function of Ra and ϕ.

Purpose: Applying external magnetic fields and employing porous media are both common approaches to control the heat transfer characteristics of magnetic fluids. To optimize such control strategies, the present study proposes the use of anisotropic media with structured design in the heat transfer domain and assesses its impact. In particular, the natural convection of a magnetic fluid through an anisotropic porous medium under a non-uniform magnetic field is investigated. Design/methodology/approach: In order to model the phenomena at play, the governing partial differential equations including mass, momentum, and conservation laws for the anisotropic porous medium taking into account the use of local thermal non-equilibrium approach are developed and solved employing the finite volume technique. Findings: Different combinations of parameters related to fluid motion and energy transfer performance, like the thermal conductivity ratio, interface heat transfer coefficient, permeability ratio and orientation angle for the permeability tensor within the anisotropic porous cavity, are evaluated. The results indicate that the most important factors to manage heat transfer and flow structures are changes of thermal conductivity ratio and interface heat transfer coefficient. The influence of permeability tensor is found to be essential for flow structures, but its influence on heat transfer rates remains weak.

The latent heat thermal energy storage devices can store a notable amount of energy in a fairly compact space with minimal environmental impact. However, the heat transfer rate in these systems is limited by inherited low thermal conductivity of most organic materials such as paraffins. This research focuses on addressing the impact of using an engineered anisotropic metal foam layer on heat transfer improvement of latent heat thermal energy storage (LHTES) units. The comprehensive two heat equation models, together with a finite element method, were employed to simulate the energy storage in LHTES unit. The study demonstrates that increasing the size of the Anisotropic Metal Foam Layer (AMFL) significantly enhances the melting of paraffin. The orientation of the AMFL also plays a crucial role, with the larger side positioned near the hot wall contributing more effectively to PCM melting. This optimal arrangement led to a reduction in melting duration by up to 5.28%. AMFL reduced the melting time by 8.2% in case d2 compared to a case with uniform metal foam.

Purpose - The purpose of this paper is to numerically examine the influence of inclined fins and the porosity of porous media on the melting heat transfer of phase change material (PCM) in a latent heat thermal energy storage (LHTES) system. Design/methodology/approach - Under the assumption of a constant inlet water rate, the alterations in fluid velocity within the bed as a result of temperature fluctuations during system operation were deemed negligible. To minimize computational time, steady-state water velocity distributions were used in combination with the heat transfer modeling techniques. The packed-bed, which includes microencapsulated PCM, is characterized as a porous medium with a defined porosity determined by the diameter of the PCM pellets. The fluid flow in the PCM packed-bed porous medium is governed by the partial differential equations based on the conservation laws of mass, momentum and energy. The computational fluid dynamics (CFD) model is developed and simulated using COMSOL Multiphysics software. The analysis extends the range of fin lengths (L = D/8 to 3D/4) and inclination angles (theta = pi/6 to pi p/6), while systematically examining variations in porosity (epsilon = 0.2 to 0.8). Findings - It is observed that an increase in fin length enhances the fluid velocity near the tank axis, leading to a faster temperature rise in that region. Furthermore, an increase in fin length yields a nonuniform temperature distribution within the tank, resulting in different melting rates of PCM. The variation in the inclination angle of the fins primarily affects the melting rate of PCM at the base of the fins, with a slower melting rate observed for PCM within a narrower angle. The porosity governs the flow rate within the tank, whereby a higher porosity leads to a reduced flow rate and a more uniform temperature rise. Additionally, an increase in porosity diminishes the temperature disparity between different substances (fluid, PCM and porous medium) within the tank. Originality/value - To the best of the authors' knowledge, previous studies have not thoroughly investigated the combined effects of inclined fins, porous media and PCM on heat transport in a LHTES system. Therefore, the current work aims to investigate the influence of inclined fins and the porosity of porous media on the melting heat transfer of PCM in a unit. This study can contribute to enhancing the overall melting-solidification process of PCM in LHTES systems.

The aim of the research is to numerically compare the flow patterns and temperature distributions within two- and three-dimensional cavities having a solid or porous rib on the hot border as a heat transfer intensifier. The comparison has been realized in a wide range of Rayleigh number (Ra = 104–106). The size, position, structure and thermal conductivity of the fin remain the same for all Ra (d = 0.4, l = 0.4, λs/λf = 15251, ɛ = 0.9) with a fixed Darcy number (Da = 10−2). Note, that the last two parameters are for porous fin only. The results have shown that solid fin in cubical (3D) cavities enhances the heat transfer much more intensively than those in two-dimensional (2D) cavities (up to 53.5% for 3D chamber with a solid rib at Ra = 106). Moreover, the drop in energy transport strength between 2D and 3D cavities with a solid fin rises with Rayleigh number. Meanwhile, the variations of heat transfer rate in 2D and 3D cavities for the cases of finless cavities and cavities with a porous fin are insignificant and the difference is within 10%, especially at high Rayleigh numbers (Ra > 105). Therefore, it is possible to use 2D models instead of 3D ones for finless cavities and for chambers with a porous rib at the heated boundary for the considered range of Ra.

Purpose The exploration of thermogravitational convection within trapezoidal chambers has accumulated significant interest owing to its wide-ranging applications in both engineering and natural systems. This study aims to optimize thermosolutal transmission rates by using advanced radiative hybrid nanofluids. Design/methodology/approach This work delves into the effects of constant, linear, quadratic and sinusoidal (with varying amplitudes and periods) thermal and species profiles on the complex dynamics of thermosolutal convection within a trapezoidal porous chamber. The cavity is filled with a Cu-Al2O3 hybrid nanofluid, where the lower boundary is high in temperature and concentration, while the left and right boundaries remain low in temperature and concentration. The top wall is insulated both thermally and solutally. The governing Navier Stokes, thermal and species equations are solved using a higher order compact procedure. This investigation systematically examines the influence of control parameters, including the Hartmann number, Lewis number, inclination angle, buoyancy ratio, Darcy number, Rayleigh number, radiation parameter and the concentration of solid particles of the hybrid nanoliquid. Findings The findings reveal that the constant heating profile yields the most effective thermal dissipation, while the sinusoidal temperature distribution demonstrates the least efficiency. These outcomes, depicted through comprehensive graphical and tabular representations, provide novel insights into enhancing thermal and solutal transport processes within such configurations. Originality/value This study provides significant insight into those thermal systems that are used in the manufacturing industry like automobiles, refrigerators, insulators and food processing industry.

There are numerous real-world applications of phenomena caused by abruptly started or stopped object motion. One such illustration is an application of airbags in motor vehicles. The primary purpose of this research is to investigate impulsive mixed convective Williamson ternary nanofluid flow over a rotating rough sphere in the presence of periodic magnetic effects. The external stream is primarily responsible for the time-dependent flow. A sinusoidal waveform mathematically models the rough surface of the sphere with small amplitude and high frequency. Thus, surface gradient and skin-friction exhibit wavy effects in the boundary layer regime. Under suitable initial and boundary conditions, the governing equations of the Williamson fluid flow, which in the current flow problem include the effects of heat diffusion and rotation, are highly coupled nonlinear PDEs. These are converted to non-dimensional forms by applying the semi-similar transformations, for which numerical semi-similar solutions are produced using the quasi-linearization technique followed by implicit finite difference approximation. The ranges of some important parameters considered are 2 ≤ Ri ≤ 10 (Richardson number), 0 ≤ M ≤ 4 (magnetic), 0 ≤ ϕi ≤ 0.04, i = 1, 2, 3 (nanoparticles volume fraction), 0 ≤ Wp ≤ 1 (Williamson parameter), 0 ≤ λ ≤ 5 (rotation parameter). The streamwise velocity ( F( ξ ,η)) , skin-friction ( Re^1 / . -0pt 2 Cf_x) and rotational skin-friction ( Re^1 / . -0pt 2 Cf_y) are all enhanced by increasing Ri and λ values. The upsurging λ values from 0 to 4 amend the Re^1 / . -0pt 2 Cf_x approximately by 17 Re^1 / . -0pt 2 Cf_x for n = 50 is enhanced by about 98