Influence Of Nonlinear Thermal Radiation Research Articles

Influence of non-linear thermal radiation on the dynamics of homogeneous and heterogeneous chemical reactions between the cone and the disk

Abstract Purpose The current work presents a theoretical framework to boost heat transmission in a ternary hybrid nanofluid with homogeneous and heterogeneous reactions in the conical gap between the cone and disk apparatus. Furthermore, the impacts of non-linear thermal radiation on the ternary hybrid nanofluid composed of white graphene, diamond, and titanium dioxide dispersed in water are analyzed. Originality/value The combination of cone and disk systems is crucial for designing efficient heat exchange devices in the field of biomedical science for various purposes. For instance, in medical devices, the cone–disk apparatus is used to study the flow and heat transfer characteristics for better design and functionality. Hence, a sincere attempt has been made to study the impact of homogeneous and heterogeneous reactions on the nanofluid flow between the cone and disk in the presence of non-linear thermal radiation. Design/methodology/approach The mathematical model’s governing equations are partial differential equations (PDEs) which are then transformed into non-linear ordinary differential equations through appropriate similarity transformations. These transformed resultant equations are approximated by the Runge–Kutta–Fehlberg fourth/fifth order (RKF45) technique. The influence of essential aspects on the flow field, heat, and mass transfer rates was analyzed using a graphical representation. Findings The interesting part of this research is to discuss the power of parameters in three cases, namely, (1) rotating cone/disk, (2) rotating cone/stationary disk, and (3) stationary cone/rotating disk. Furthermore, the thermal variation of the fluid is analyzed by an artificial neural network with the help of the Levenberg–Marquardt backpropagation algorithm. The regression analysis, mean square error, and error histogram of the neural network are analyzed using this algorithm. From the graph, it is perceived that the flow field climbed up significantly with an increase in the values of radiation parameters in all cases. Also, it is noticed that temperature upsurges significantly by upward values of solid volume fraction of the nanoparticles ( ϕ \phi ).

Model development and heat transfer characteristics in renewable energy systems conveying hybrid nanofluids subject to nonlinear thermal radiation

PurposeIn today’s world, the demand for energy to power industrial and domestic activities is increasing. To meet this need and enhance thermal transport, solar energy conservation can be tapped into via solar collector coating for thermal productivity. Hybrid nanofluids (HNFs), which combine nanoparticles with conventional heat transfer fluids, offer promising opportunities for improving the efficiency and sustainability of renewable energy systems. Thus, this paper explores fluid modeling application techniques to analyze and optimize heat transfer enhancement using HNFs. A model comprising solar energy radiation with nanoparticles of copper (Cu) and alumina oxide (Al2O3) suspended in water (H2O) over an extending material device is developed.Design/methodology/approachThe model is formulated using conservation laws to build relevant equations, which are then solved using the Galerkin numerical technique simulated via Maple software. The computational results are displayed in various graphs and tables to showcase the heat transfer mechanism in the system.FindingsThe results reveal the thermal-radiation-boost heat transfer phenomenon in the system. The simulations of the theoretical fluid models can help researchers understand how HNFs facilitate heat transfer in renewable energy systems.Originality/valueThe originality of this study is in exploring the heat transfer properties within renewable energy systems using HNFs under the influence of nonlinear thermal radiation.

Influence of suction and injection on the electrical magnetohydrodynamic behavior of nano-fluid in a nonlinear radiative flow over an extending surface

The present communication aims to investigate the behavior of a radiative electrical MHD Casson nanofluid flowing over a stretched surface, under the influence of nonlinear thermal radiation, and suction/injection effects. The governing equations include parameters for temperature and concentration, which are adjusted based on the dependence of viscosity and thermal conductivity, thus enhancing the fluid flow properties. By using similarity transformations, the system of PDEs is converted to an ODE, which is then numerically solved using the well-known fourth-order Runge–Kutta integration strategy based on the shooting method. The impacts of operating parameters on velocity, temperature, and concentration profiles were explained and examined through tables and graphs. Temperature and concentration are increased as the injection ( S < 0 ) increases . However, they show decrement when the suction ( S > 0 ) increases . The novelty of this study focuses on the mathematical development of the flow problem with significant results and also investigating the impact of electric field on velocity of the fluid flow and shear stress. These results are applicable in manufacturing of stretchable materials.

Soret and dufour effects on unsteady non-linear mixed convection flow past a stretching sheet influenced by non-linear thermal radiation

This article presents a novel mathematical model to analyze the behavior of a time-dependent, incompressible, non-linear (quadratic) mixed convection flow across a stretching surface heated by convection. The model takes into account the influence of non-linear thermal radiation, along with the Soret and Dufour effects. The equations governing the flow characteristics in the boundary layer approximation are derived and transformed into ordinary differential equations (ODEs) using similarity variables. The second-order ODEs are transformed into an initial value problem, which is then numerically solved using the bvp4c solver in MATLAB. The novel findings of the study have been presented using graphs and tables. The intensification of non-linear convection parameters has been shown to lead to the development of velocity near the sheet while simultaneously reducing velocity toward the free stream. The non-linear convection parameters reduce the temperature distribution, while the temperature ratio and the non-linear thermal radiation parameters enhance it. The non-linear convection parameters ( 0.5 ≤ α 1 , α 2 ≤ 2.0 ) , temperature ratio ( 1.2 ≤ θ w ≤ 1.5 ) , and non-linear thermal radiation ( 1.0 ≤ Rd ≤ 1.5 ) , parameters are influential factors in decreasing the surface drag force (by about 15.4%, 28.5%, 4.4%, and 4.3%) and increasing the cooling rate (by about 0.4%, 0.5%, 19.5%, and 23%), respectively. The Biot ( 0.5 ≤ Bi ≤ 1.0 ) number is also found to significantly contribute toward enhancing the cooling rate of the system by about 51.6%.

Magnetohydrodynamic thermo-bioconvective flow of 3D rotating Williamson nanofluid with Arrhenius activation energy in a Darcy–Forchheimer medium over an exponentially stretching Surface

This paper aims to analyze the heat and mass transfer characteristics of the 3D thermo-bioconvective flow of rotating Williamson nanofluid over an exponentially stretching vertical sheet. The flow distribution considers the influence of nonlinear thermal radiation, Hall and ion-slip currents, joule heating, coupled effects of Dufour and Soret diffusion, internal heat generation, Arrhenius activation energy, Brownian, and thermophoresis diffusion in a Darcy–Forchheimer porous medium. The modeled partial differential equations (PDE) in terms of continuity, momentum, energy, concentration, and density of motile microorganisms are reformed into ordinary differential equations (ODE) forms employing similarity variables. The resulting equations are solved numerically using the spectral local linearization method (SLLM). The successive over-relaxation technique is applied to accelerate and enhance the convergence of the method. The obtained results are graphically and tabularly represented and numerically explored for the effects of pertinent parameters on the velocity, temperature, nanoparticle concentration, and motile microorganism concentration profiles. The rotation and mixed convection parameters dropped the primary velocity curve, while the Williamson and heat source parameters uplifted the microbes density distributions. The temperature field rises with an increase in radiation and microbes Brownian motion and declines with an increase in Hall and ion-slip numbers. Furthermore, with the increase in activation energy from 0.5 to 2 and the mixed convection parameter from 0.6 to 1.3, we observe a respective 3.93% rise and 8.30% fall in mass transfer rates. The current investigation has broad applications, including MHD accelerators, biotechnology, the formation of elastic sheets, the production of polymer solutions, and the synthesis of nanoparticles through microbial processes.

Numerical simulations of entropy generation and Arrhenius activation energy on peristaltic transport of Prandtl‐Eyring fluid in a curved conduit

AbstractThe study aims to explore the combined impact of activation energy and entropy generation on Prandtl‐Eyring fluid flow within a curved channel, considering Hall and ion slip effects, alongside the influence of nonlinear thermal radiation on heat transfer. This research is pivotal as it delves into the multifaceted relationship among these factors, offering important implications spanning various fields, from engineering to physics. Notably, the findings highlight that heightened nonlinear thermal radiation does not solely elevate entropy generation but also amplifies the Bejan number, signifying a substantial effect on fluid flow dynamics. Furthermore, the investigation reveals an intriguing correlation: lower concentrations paired with higher Arrhenius activation energy values correspond to heightened chemical reaction rates, presenting valuable insights applicable to reaction engineering and material sciences. Additionally, exploring the impact of activation energy and entropy generation within this fluid model presents a unique approach to understanding complex fluid dynamics and heat transfer phenomena, offering insights crucial for various engineering applications, particularly in fluid dynamics, thermal sciences, and materials engineering.

Exploration of nonlinear radiative heat energy on Buongiorno modeled nano liquid toward an inclined porous plate with heat source and variable chemical reaction

Nanofluids are fluid suspensions of nanoparticles that exhibit a considerable improvement in their characteristics at low nanoparticle concentrations. Numerous research on nanofluids focuses on interpreting their behavior in order to use them in applications where improving straight heat transmission is crucial, such as in various industrial settings, nuclear reactors, transportation, biology, food, and electronics. Thus, this study examines the implementation of a novel numerical technique, namely the shooting method for nonlinear radiative heat energy study on Buongiorno modeled nano liquid confined by an inclined porous plate. The Brownian and thermophoresis diffusions impacts are also accounted. The transmission of thermal and solutal energy is regulated by the considerable influence of nonlinear thermal radiation, heat source, and variable chemical reactions. The dimensional modeled partial differential equations (PDEs), by using precise similarity functions, have been mutated into ordinary differential equations (ODEs). The outcomes for the flow field, thermal, and solutal outlines are captured graphically. The values of the dimensionless parameters are chosen from the literature in such a way that they have significantly affected the dimensionless boundary layer (BL) profiles. Also, the non-dimensional profiles of velocity, temperature, and concentration observe two different trends (increasing and decreasing) for diverse values of the dimensionless parameters.

Numerical study on magnetohydrodynamics micropolar Carreau nanofluid with Brownian motion and thermophoresis effect

ABSTRACT The current work explores the investigation of the influence of nonlinear thermal radiation on unsteady, magnetohydrodynamics boundary layer flow of micropolar Carreau nanofluid past a stretching sheet. Viscous dissipation, internal heating, Brownian motion, heat source/sink, thermophoresis, chemical reaction, and Joule heating effects are considered in the study. To analyze the model, the governing partial differential equations are rephrased and written in the non-dimensional form with the relevant dimensionless quantities. To obtain the solutions, the nonlinear non-dimensional governing equations are numerically solved using finite difference approximation. The impact of every significant flow parameter on fluid motion, micro-rotation, temperature, concentration, surface drag, heat, and mass transfer rates are presented through plotted graphs and tables. It is noted from the study that the fluid flow and angular motion increase, whereas the temperature declines with higher values of the micropolar constant. Further, it is noticed that thermal distribution is a rising function of radiation parameter, and due to the nonlinear thermal radiation effect, there is an increase of 4.903% in temperature distribution when compared to linear thermal radiation. To support the validity of the solutions, a comparison was made with notable results from the existing literature for the specific case of this study.

Two-dimensional nanofluid flow impinging on a porous stretching sheet with nonlinear thermal radiation and slip effect at the boundary enclosing energy perspective

In the current analysis, we examine the heat transmission analysis of nanofluid (NF) movement impinging on a porous extending sheet. The influence of nonlinear thermal radiation (TR), buoyancy force, and slip at the boundary are also examined. The leading partial differential equations (PDEs) are altered to convectional differential equation (ODEs) by suitable transformation. The ODEs are then transformed to first order by introducing the innovative variables and elucidated numerically using bvph2. The Skin Friction (SF) and Nusselt number (NN) are elaborated in detail for Al2O3, Cu, and TiO2 nanoparticles. For validation of the code, ND-solve approach is also applied. The novelty of the current effort is inspect NF flow with heat transfer over extending sheet enclosing thermal and slip effect at the boundary numerically. The thickness of boundary layer increases as the temperature and radiation factors are increased. It is perceived that the fluid velocity decays with the growing values of volume fraction parameter. When permeability and velocity slip parameters are improved the velocity outline enhances. It is investigated that the temperature inside the fluid enhances as the values of velocity slip factor, permeability factor and Biot number are augmented. For the growing values of temperature ratio, volume friction, and thermophoresis factor the temperature is enhances. It is detected that the slip factor causes the friction factor to decrease. Furthermore, the existent study is associated with the preceding.

LTNE effect on non-linear radiative MHD mixed convective flow in an annular porous medium: Intelligent Computing Paradigm

In this study, the back-propagated Levenberg-Marquardt algorithm-based neural network intelligent computing paradigm is used to examine the influence of non-linear thermal radiation, induced magnetic field and local thermal non-equilibrium effect on the magnetohydrodynamic mixed convective flow in the vertical annular porous region. In the annular porous region the inner cylinder is considered as electrically conducting and the outer cylinder as electrically non-conducting. The heat transfer is expected due to mixed convection and non-linear thermal radiation. The Galerkin finite element method is adopted to solve the governing equations. In the vertical annulus an increase in the magnetic Prandtl and Hartmann number reduces the velocity and induced magnetic field due to a strong external magnetic field and the Lorentz force. The higher Brinkmann values decelerate the conduction of heat generated by viscous dissipation hence, the temperature increases. The fluid and solid temperature increase with the buoyancy parameter. The non-linear radiation term enhances the fluid temperature, whereas it decelerates the solid temperature. The ANN model utilises finite element method output for training, validating and testing to predict the heat transfer characteristics. The performance of the BLM-NN algorithm is assessed using mean square error, error histogram and regression.

Thermal analysis and entropy generation of Darcy-Forchheimer ternary nanofluid flow: A comparative study

Ternary nanofluid is a novel class of working fluids with excellent heat transfer properties. A combination of three solid nanoparticles consisting of SWCNTs, TiO2, and MoS2 is investigated for Darcy-Forchheimer water-based ternary nanofluids. The related mathematical models are established by considering linear, quadratic and nonlinear thermal radiations. Numerical results and entropy generation analysis reveal the considerable influence of nonlinear thermal radiation on temperature and the reduced Nusselt number of ternary nanofluids. With the help of multiple quadratic regression, the impact of relevant parameters on the reduced Nusselt number is studied in depth. The results show that the temperature and Nusselt number are always the highest in the nonlinear thermal radiation model compared with the linear and quadratic ones, and they are most sensitive to the changes of Rd and δ. The thermal radiation properties of ternary nanofluids may potentially lead to more efficient solar energy conversion. This comparative study illustrates the advantages of ternary nanofluids in improving solar radiation utilization efficiency with nonlinear thermal radiation.

Numerical simulation of MHD two‐dimensional flow incorporated with joule heating and nonlinear thermal radiation

AbstractThe current investigation presents a numerical simulation of boundary layer flow with heat transfer. The study primarily emphasizes heat generation due to the influence of nonlinear thermal radiation. Moreover, the simultaneous effects of Joule heating and viscous dissipation have been incorporated for the thermal enhancement of the magnetohydrodynamics (MHD) on the convective boundary layer flow over a flat plate. Dimensional analysis is brought into use to determine the hydro and thermal boundary layer thickness for the two‐dimensional flow. Subsequently, the application of the suitable similarity transformation yields a nonlinear coupled flow problem with is solved numerically with the help of the Runge–Kutta Fehlberg (RKF) method incorporated with the Shooting technique. Moreover, this theoretical study highlights the immense mechanical and aeronautical applications of thermal radiation. In view of computational findings and simulating results, linear and nonlinear thermal radiation effects can also be investigated on fluids passing through a cylinder and channels. Finally, computational data tabulated against some pertinent parameters and parametric study reveal that non‐linear thermal radiation is more effective for highly viscous fluids.

Non-uniform heat generation and Stefan blowing on nonlinear radiative Casson-nanofluid flow through microorganisms through leading-edge accretion or ablation

The effect of Stefan blowing on bioconvection of microorganisms mixed on non-Newtonian fluid with water-based nanofluids to an accretion/ablation of the leading edge was investigated in this current analysis. The effects of convective heat boundary conditions are one more important physical parameter in the flow investigation and have been studied for that analysis. Furthermore, the influence of nonlinear thermal radiation and irregular heat source or sink was more integrated. Even systems of conservative governing PDEs were transformed within the dimensionless structure of equations by utilising the appropriate conversion. The recent systems of equations including comparable transformed boundary conditions were again defined numerically for the use of the finite element method. It is notable about the accuracy and validity of the current numerical solution was an attractive understanding of the actual definite results in the literature. It is observed that velocity decreases by increasing Casson fluid parameter.

Darcy-Forchheimer flow of Prandtl-Eyring nanofluid subjected to a Riga plate of varying thickness along with Brownian diffusion, thermophoresis and non-uniform heat source/sink effects

This article is subjected to the characteristics of an electro-magnetohydrodynamic (EMHD) boundary layer movement of a nanofluid induced by a Gailitis device with variable thickness. A viscous incompressible Prandtl-Eyring nanofluid saturates the porous medium through Darcy-Forchheimer expression. Heat transfer process involves the influence of non-linear thermal radiation, viscous dissipation, non-uniform heat source/sink, and convective boundary conditions. Moreover, Brownian motion and thermophoresis mechanisms are taken into consideration. The governing mathematical model is transmuted with appropriate similarity transformations into a non-dimensional system of ordinary differential equations (ODEs). Numerical solution for this system is acquired through the bvp4c solver in MATLAB software. Velocity, temperature, and concentration profiles are scrutinized through graphical representation for various flow controlling parameters. The impact of these parameters on local values of skin friction coefficient, Nusselt number, and Sherwood number is analyzed through computational data specified in a tabular form.

Statistical Modelling for the Darcy–Forchheimer Flow of Casson Cobalt Ferrite-Water/Ethylene Glycol Nanofluid under Nonlinear Radiation

Current research is focused on the utilization of a numerical solution of Casson cobalt ferrite nanofluid flow by taking two forms of base fluid. This investigation includes the gradual influence of nonlinear thermal radiation on the improvement of heat transfer related to the flow of nanofluids over a stretched rotating surface by the Darcy–Forchheimer law. The model constructed by a Casson nanoliquid in the boundary layer’s flow is studied for its symmetric behaviour, including cobalt ferrite nanomaterials. Two base liquids named as ethylene glycol and water are considered. The rate of heat transport is examined by considering Newtonian heating conditions. By utilizing similarity transformations, a partial differential system that governs the said model has been transformed into a highly nonlinear ordinary differential system, and numerical outcomes are obtained by implementing the RK4 via shooting methodologies. All obtained results, including local skin friction coefficients and local Nusselt number, are defined and discussed in the paper. The study’s findings ensure that the Casson cobalt ferrite nanofluid flowing towards a stretching plate has a unique solution: A variation of the solid volume fraction corresponds to the decrease in various values of the Casson nanofluid parameter for both type of nanofluid. Furthermore, a similar behaviour is noted for various values of the solid volume fraction, which corresponds to various values of the inertia coefficient parameter. Moreover, for the highest values of the solid volume fraction and all values of R1 and Ni taken into account, the rate of heat transfer upsurges. The data from the local skin friction coefficient (LSFC) and local Nusselt number (LNN) have been analysed using various statistical distributions, and it has been determined that both datasets generally fit the exponentiated Weibull distribution for various values of considered parameters. The findings would serve as a starting point for the manufacture of devices.

Influence of nonlinear thermal radiation on mixed convective hybrid nanofluid flow about a rotating sphere

AbstractThe present study investigates the mixed convective hybrid nanofluid flow over a rotating sphere under the impact of nonlinear thermal radiation. A model is built to examine the heat transport performance of ferrimagnetic magnetite and copper nanoparticles over a rotating sphere. Nonsimilar transformations are used to nondimensionalize the coupled nonlinear governing equations and the flow model's boundary conditions. Furthermore, the nondimensional governing equations were solved using implicit finite difference approximation and the quasilinearization technique. The impacts of the flow regime on many controlling parameters are then thoroughly addressed. Temperature patterns improve when nonlinear thermal radiation and hybrid nanofluid values increase. The fluid velocity and skin friction coefficient increase in the streamwise direction while decreasing in the rotating direction. The separation of the boundary layer is delayed as the sphere's rotation weakens. The stationary sphere has a larger boundary layer separation than the revolving sphere. The velocity distribution improves with increasing rotation parameter values while decreasing with increasing combined convection parameter values in the rotating direction. An increase in the temperature ratio parameter makes the fluid get hotter, and the Nusselt number goes down simultaneously. Nusselt number and skin friction coefficient in the rotation direction increase, while skin friction coefficient in streamwise direction reduces for increasing values of hybrid nanofluid. The velocity of the fluid enhances in the stream‐wise direction while reducing in the rotational direction with the increasing values of the combined convection parameter.

Significance of Stefan blowing effect on flow and heat transfer of Casson nanofluid over a moving thin needle

The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model. The influences of Stefan blowing, Dufour and Soret effects are also considered in the model. The equations which represent the described flow pattern are reduced to ordinary differential equations (ODEs) by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg’s fourth fifth-order method (RKF-45) with shooting process. The impacts of pertinent parameters on thermal, mass and velocity curves are deliberated graphically. Skin friction, rate of heat and mass transfer are also discussed graphically. Results reveal that, the increase in values of Brownian motion, thermophoresis, Dufour number, heating and radiative parameters improves the heat transfer. The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number. Finally, the escalating values of the radiative parameter decays the rate of heat transfer.

Effects of aligned magnetic field on heat transfer of water-based carbon nanotubes nanofluid over a stretching sheet with homogeneous–heterogeneous reactions

The present analysis deals with the heat transfer of chemically reactive magnetic-nanofluid over a stretching surface by considering the aligned magnetic field in a porous medium under the influence of nonlinear thermal radiation, variable thermal conductivity and suction. An isothermal model of homogeneous–heterogeneous reactions is used to regulate the solute concentration profile. It is assumed that the water-based nanofluid is composed of single and multi-walled carbon nanotubes. By applying a suitable set of similarity transformations, the system of partial differential equations is first transformed into a system of nonlinear ordinary differential equations before being solved numerically. The impact of various pertinent parameters on the velocity, temperature, concentration, skin friction and local Nusselt number coefficient is discussed. It is found that the increase in the rate of heterogeneous and homogeneous reactions retards nanoparticle concentration distribution. The existence of variable thermal conductivity and an inclined magnetic field realise a decrease in heat transfer.

Interfacial layer and shape effects of modified Hamilton’s Crosser model in entropy optimized Darcy-Forchheimer flow

In this analysis, the interfacial layer and shape effects has been inspected numerically for the Darcy Forchheimer electromagnetic flow of single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNTs) with base fluid (water) nanofluids. The influence of nonlinear thermal radiation and homogenous and heterogeneous chemical reactions are also taken into account. A revised Hamilton Crosser model is implemented for measuring interfacial layer and shape effects of carbon nanotubes-water nanofluid. The flow problem for examining the heat transfer features has been modeled in term of nonlinear equations by incorporating the Hamilton–Crosser model. The main objective for performing the current work is to analyze how the shapes of nanoparticles effect towards the flow of considered fluid with various thermal features. The entropy generation analysis is performed as novelty. The governing dimensionless equations are numerically solved by fourth order Runge–Kutta method computational shooting technique. The relevant parameter variations on axial, radial, tangential velocity, temperature, concentration, skin friction, Nusselt number, entropy generation rate and Bejan number are highlighted. The enhanced shape factor of nanoparticles contributes to accelerated flow along axial and radial directions while it yields decelerated flow along tangential direction of lower and upper disks. The augmented interfacial layer parameter enhances heat transportation from the surfaces of lower and upper disks.

Impact of Nonlinear Thermal Radiation and the Viscous Dissipation Effect on the Unsteady Three-Dimensional Rotating Flow of Single-Wall Carbon Nanotubes with Aqueous Suspensions

The aim of this article is to study time dependent rotating single-wall electrically conducting carbon nanotubes with aqueous suspensions under the influence of nonlinear thermal radiation in a permeable medium. The impact of viscous dissipation is taken into account. The basic governing equations, which are in the form of partial differential equations (PDEs), are transformed to a set of ordinary differential equations (ODEs) suitable for transformations. The homotopy analysis method (HAM) is applied for the solution. The effect of numerous parameters on the temperature and velocity fields is explanation by graphs. Furthermore, the action of significant parameters on the mass transportation and the rates of fiction factor are determined and discussed by plots in detail. The boundary layer thickness was reduced by a greater rotation rate parameter in our established simulations. Moreover, velocity and temperature profiles decreased with increases of the unsteadiness parameter. The action of radiation phenomena acts as a source of energy to the fluid system. For a greater rotation parameter value, the thickness of the thermal boundary layer decreases. The unsteadiness parameter rises with velocity and the temperature profile decreases. Higher value of ϕ augments the strength of frictional force within a liquid motion. For greater R and θ w ; the heat transfer rate rises. Temperature profile reduces by rising values of Pr .