Prescribed Surface Heat Flux Research Articles

An Improved Non‐Local Planetary Boundary Layer Parameterization Scheme in Weather Forecasting and Research Model Based on a 1.5‐Order Turbulence Closure Model

AbstractPlanetary boundary layer (PBL) modeling is a primary contributor to uncertainties in a numerical weather prediction (NWP) model due to difficulties in modeling the turbulent transport of surface fluxes. The Weather Research and Forecasting model (WRF) has provided many PBL schemes that may feature a non‐local transport component driven by large eddies or a one‐and‐half order turbulence closure model, but few of them possess the two features at once. In the present study, a turbulent kinetic energy (TKE)‐based eddy diffusivity/viscosity method is integrated into the non‐local Asymmetric Convective Model version 2 (ACM2) PBL scheme and implemented in WRF. The original first‐order eddy‐diffusivity term in ACM2 is discarded and an extra prognostic equation for TKE, which considers the tendency of TKE by buoyancy, wind shear, vertical transport, and dissipative processes, is supplied to calculate the diffusivity/viscosity. Non‐local transport is modeled the same as ACM2 using the transilient matrix method. Idealized tests using prescribed surface heat flux and roughness length are performed. TKE‐ACM2 displays advantages over the PBL scheme developed by Bougeault and Lacarrère (hereinafter referred to as Boulac) and ACM2 in the wind speeds (WS) profile because it better matches large‐eddy simulations results in the surface momentum flux. Real case simulations show that TKE‐ACM2 generally outperforms in the diurnal vertical profiles of WS under stable conditions. TKE‐ACM2 also produces a better alignment under moderately unstable conditions in the early nighttime at the urban LiDAR station. However, the model exhibits discrepancies more apparently under a more unstable condition during the winter daytime.

Investigation of heat and mass transfer performance in Casson fluid flow over nonlinear stretching sheet: Impact of novel similarity transformations

This article primarily aims to utilize novel similarity transformations that were created to overcome a limitation found in previous research. These similarity methods have proven to be effective in finding solutions to systems of partial differential equations. The study analyzed mass and heat transfer in a Casson fluid near a boundary on a stretchy, permeable surface, considering radiative heat transmission and non-homogeneous thermal effects. It focused on two heating methods: prescribed surface temperature (PST) and prescribed surface heat flux (PHF). Prior research involving stretchable surfaces has mostly used non-dimensional similarity metrics related to one variable that is not dependent on others (e.g., only or), which resulted in certain errors. To tackle this issue, we have introduced a novel set of similarity transformations that encompass all the independent variables in the equations. that are being studied (that is, x and y ). This novel strategy seeks to significantly improve the accuracy of our results. The equations that dictate the behavior were transformed into nonlinear ordinary differential equations by employing specific similarity transformations. The Runge–Kutta-Fehlberg approach proved to be highly efficient in computing solutions, yielding fourth- and fifth-order approximations. The solutions were found to rely on various physical parameters, including the Casson fluid factor, Prandtl and Schmidt numbers, heat source and sink components, radiation parameters, and suction and injection factors. These parameters elucidate the behavior of velocity, concentration, and temperature profiles. When the Casson parameter increases by 212.5%, the temperature increases by 0.5270% for the PST case and by 1.4050% for the PHF case under suction conditions, and similarly, rises by 1.3238% for the PST case and by 5.7224% for the PHF case under blowing conditions.

Hybrid Nanofluids Flow over a Vertical Cylinder with Heat Source/Sink and Prescribed Surface Heat Flux

This work presents the steady mixed convection in Al2O3-Cu/water hybrid nanofluids along a vertically stretching/shrinking cylinder with the prescribed surface heat flux and the effects of heat source/sink. The governing hybrid nanofluids model was simplified using a similarity transformation. The bvp4c solver in MATLAB software is used to solve the hybrid nanofluids flow problem numerically. It is observed that two outcomes are feasible for the assisting and opposing flow regions as well as stretching and shrinking cases . Besides that, the effects of the dimensionless parameters are analyzed graphically and tabularly. In particular, the critical point is reduced by 3% when the curvature parameter goes from 0 to 0.1 and from 0.1 to 0.2 when the cylinder is stretched. This means that the higher curvature parameter could delay the process of separating the boundary layer. It is noted that the positive heat source will decrease the fluid motions and reduce the shear stress on the surface. Moreover, Al2O3-Cu/water hybrid nanofluids have better performance in heat transfer and velocity of fluid flow than Al2O3/water nanofluids.

Inclusion of unsteady heat conduction in regular bodies subject to uniform surface heat flux in a heat transfer course

The present study is concerned with the analysis of unsteady heat conduction in regular bodies (large plane wall, long cylinder, and sphere) with constant initial temperature, prescribed surface heat flux and thermal properties of the solid that are invariant with temperature. Surprisingly, this important topic is absent in textbooks on heat transfer. The exact evaluation of the dimensionless surface temperatures varying with the dimensionless time in the regular bodies over the entire dimensionless time domain [Formula: see text] is carried out with a symbolic algebra code. Thereafter, regression analysis is applied to the data gathered for the dimensionless surface temperatures varying with the dimensionless time of the regular bodies inside the dimensionless “small time” time sub-domains [Formula: see text]. The dimensionless threshold time [Formula: see text] is a decisive parameter that establishes the borderline between the “small time” sub-domain [Formula: see text] and the “large time” sub-domain [Formula: see text] comprising the entire dimensionless time domain [Formula: see text]. Based on regression analysis, compact asymptotes are constructed for the dimensionless surface temperatures varying with the dimensionless time inside the dimensionless “small time” sub-domain [Formula: see text]. At the end, agreements with the dimensionless exact, analytical surface temperature distributions (the baseline solutions) valid for the dimensionless time sub-domain [Formula: see text]. are considered of excellent quality.

Consistent ramifications of prescribed surface temperature and prescribed heat flux boundary conditions for the slip flow of Walter B fluid in a stretching channel

ABSTRACT The present work delves into the Walter B fluid flow across the channel with the elongating enclosures when enthralled by linear radiation. The magnetic field is contemplated throughout the examination. The fluid suction and injection is permitted through the lower permeable wall. The slip regime is confined at the boundaries of the channel. Heat transfer in the channel is brought to light under two heating processes, namely prescribed surface temperature and prescribed surface heat flux case. The modeled equations are non-dimensionalized and then solved by the Runge-Kutta Fehlberg method in association with shooting scheme. Results deduce that the Reynolds number magnifies the velocity in the channel. Under two different heat boundary conditions, it is recorded that temperature is more pronounced for prescribed surface temperature case than prescribed heat flux. Flow profile for the varying viscoelastic parameter deciphers that at the lower end of the channel, the velocity is augmented and reverse response is recorded at the upper half of channel. Entropy profile magnifies with the augmentation of the magnetic parameter and shows depleting nature for higher Reynolds number. Examining the Walter B fluid flow in the channel enclosed with stretchable walls deliberates the flow of blood in the arterial wall under the exertion of strong magnetic field.

Prediction of the temperature–time history in ordinary bodies induced by surface heat flux utilizing the enhanced method of discretization in time and the finite difference method

Purpose The purpose of this paper is to address unsteady heat conduction in two subsets of ordinary bodies. One subset consists of a large plane wall, a long cylinder and a sphere in one dimension. The other subset consists of a short cylinder and a large rectangular bar in two dimensions. The prevalent assumptions in the two subsets are: constant initial temperature, uniform surface heat flux and thermo-physical properties invariant with temperature. The engineering applications of the unsteady heat conduction deal with the determination of temperature–time histories in the two subsets using electric resistance heating, radiative heating and fire pool heating. Design/methodology/approach To this end, a novel numerical procedure named the enhanced method of discretization in time (EMDT) transforms the linear one-dimensional unsteady, heat conduction equations with non-homogeneous boundary conditions into equivalent nonlinear “quasi–steady” heat conduction equations having the time variable embedded as a time parameter. The equivalent nonlinear “quasi–steady” heat conduction equations are solved with a finite difference method. Findings Based on the numerical computations, it is demonstrated that the approximate temperature–time histories in the simple subset of ordinary bodies (large plane wall, long cylinder and sphere) exhibit a perfect matching over the entire time domain 0 < t < ∞ when compared against the rigorous exact temperature–time histories expressed by classical infinite series. Furthermore, using the method of superposition of solutions in the convoluted subset (short cylinder and large rectangular crossbar), the same level of agreement in the approximate temperature–time histories in the simple subset of ordinary bodies is evident. Originality/value The performance of the proposed EMDT coupled with a finite difference method is exhaustively assessed in the solution of the unsteady, one-dimensional heat conduction equations with prescribed surface heat flux for: a subset of one-dimensional bodies (plane wall, long cylinder and spheres) and a subset of two-dimensional bodies (short cylinder and large rectangular bar).

Entropy formation analysis for magnetized UCM fluid over an exponentially stretching surface with PST and PSHF wall conditions

<abstract> <p>This article aims to demonstrate the formation of entropy due to variable thermal conductivity, radiation, and fluid friction irreversibilities for a three-dimensional upper-convected Maxwell (UCM) fluid. The fluid motion occurs as a result of exponential stretching sheets. Separate discussions are held regarding the entropy generation related to the prescribed surface temperature and prescribed surface heat flux. Additionally, the heat transport mechanism is examined in the presence of thermal radiation. The governing physical situation is first modeled and then solved by using the homotopy analysis method to acquire the solution. The physical importance of relevant flow parameters is shown graphically and in tabular form. It is noted that the entropy generated is reduced with an increase in the thermal radiation parameter. Streamline patterns are also drawn for two- and three-dimensional UCM fluid models. Finally, the current analytical solution is found to be in agreement with the solutions in the literature.</p> </abstract>

The effects of redistributed heat flux on ocean climate change in FAFMIP heat flux anomaly experiments

The Flux–Anomaly-Forced Model Inter-comparison Project (FAFMIP) aims to study the response of the ocean to changes in prescribed surface flux (heat, freshwater, and wind) caused by atmospheric CO2 increase. Among these surface flux perturbations, the heat flux has the greatest effect on ocean heat uptake (OHU), the Atlantic Meridional Circulation (AMOC), and sea level changes. This occurs in part because of the redistributed heat flux (Qr’), which is the component of the heat flux driven by ocean circulation changes and almost nearly doubles the initial heat flux perturbation (F) prescribed by FAFMIP in the North Atlantic (NA). In this study, we used a standalone ocean model to quantitatively investigate the impact of Qr’ on OHU and the AMOC in prescribed heat anomaly experiments (faf-heat experiment in FAFMIP). We also showed that whether the other two FAFMIP heat flux anomaly experiments (faf-heat-NA50pct and faf-heat-NA0pct) can reasonably simulate the ocean’s response to prescribed surface heat flux, especially OHU and AMOC. Our findings show that faf-heat-NA50pct is better because the redistribution-feedback (Qr’) nearly equals the initial perturbation (50%F) in the NA and thus recovers the total perturbation F in faf-heat. Although direct comparisons cannot be drawn, both faf-heat-NA50pct and faf-heat experiments with no effect of Qr’ cause AMOC weakening that is roughly comparable with the 1pctCO 2 experiments. The magnitude of simulated AMOC weakening in faf-heat-NA50pct is 3.9Sv, accounting for about 29% of the AMOC intensity in unperturbed experiment, which is closer to the faf-heat experiment (about 31%) with no effect of Qr’ relative to the faf-heat experiment. Because of negative Qr’ in all regions except the NA region especially for the Central and Eastern Equatorial Pacific and Southern Ocean, the simulated global OHU in faf-heat-NA50pct is reduced by 10% as compared to the added OHU in the faf-heat experiment. The Qr’ in the faf-heat experiment increases OHU by approximately 13% of the total OHU and further reduces AMOC intensity by 3.4 Sv, accounting for 26% of the AMOC strength in an unperturbed experiment. Faf-heat-NA0pct results in a significant reduction in OHU (approximately 26%), and the magnitude of AMOC weakening is only approximately 1.9 Sv, despite no F being added in the NA.

Transverse magnetic effects of hybrid nanofluid flow over a vertical rotating cone with Newtonian/non-Newtonian base fluids

The main objective of this work is to investigate the convective flow of three hybrid nanoparticles with different base fluids on a spinning down pointed vertical cone in the presence of magnetic field along with prescribed surface heat flux and also analyzed the behavior on non-Newtonian profiles by using Casson model. The governing equations are transformed into nonlinear ordinary differential equations and then solved numerically using the fourth-order Runge–Kutta method with shooting technique. The effects of various physical parameters are examined graphically. Numerical values of Skin friction coefficient and Nusselt number are given in tabular form. From the results, one can conclude that tangential and swirl velocity profile gets detracted when its magnetic parameter hikes in the three hybrid nanofluids.

Nanofluid Flow on a Shrinking Cylinder with Al2O3 Nanoparticles

This study investigates the nanofluid flow towards a shrinking cylinder consisting of Al2O3 nanoparticles. Here, the flow is subjected to prescribed surface heat flux. The similarity variables are employed to gain the similarity equations. These equations are solved via the bvp4c solver. From the findings, a unique solution is found for the shrinking strength λ≥−1. Meanwhile, the dual solutions are observed when λc<λ<−1. Furthermore, the friction factor Rex1/2Cf and the heat transfer rate Rex−1/2Nux increase with the rise of Al2O3 nanoparticles φ and the curvature parameter γ. Quantitatively, the rates of heat transfer Rex−1/2Nux increase up to 3.87% when φ increases from 0 to 0.04, and 6.69% when γ increases from 0.05 to 0.2. Besides, the profiles of the temperature θ(η) and the velocity f’(η) on the first solution incline for larger γ, but their second solutions decline. Moreover, it is noticed that the streamlines are separated into two regions. Finally, it is found that the first solution is stable over time.

Enhanced transport properties and its theoretical analysis in two-phase hybrid nanofluid

This study explores the issue of micropolar fluids and heat transfer in a hybrid nanofluid through a moving thin needle with prescribed surface heat flux. Here, SWCNT and MWCNT are referred to as hybrid nanoparticles, and Engine oil and Refrigerant-134A as a working fluid. Similarity transformation is implemented to acquire the similarity equations, and then numerically solved by utilizing the shooting technique bvp4c function. Hybrid nanofluids enhance the heat transfer coefficient when their concentrations and nanoparticle volumes increase. The graphical results are made for different involved parameters such as material parameter, micro-gyration parameter, moving parameter, and index parameter. It is found that the heat transfer and friction drag are improved for hybrid nanofluid than nanofluids. It is further seen that increase in the size of the needle axial and angular velocity and temperature distribution diminishes.

Analytic Treatment for Electrical MHD Non-Newtonian Fluid Flow over a Stretching Sheet through a Porous Medium

In this study, an attempt has been made to investigate the mass and heat transfer effects in a BLF through a porous medium of an electrically conducting viscoelastic fluid subject to a transverse magnetic field in the existence of an external electric field, heat source/sink, and chemical reaction. It has been considered the effects of the electric field, viscous and Joule dissipations, radiation, and internal heat generation/absorption. Closed-form solutions for the boundary layer equations of viscoelastic, second-grade, and Walters’ B ′ fluid models are considered. The method of the solution includes similarity transformation. The converted equations of thermal and mass transport are calculated using the optimal homotopy asymptotic method (OHAM). The solutions of the temperature field for both prescribed surface temperature (PST) and prescribed surface heat flux (PHF) are found. It is vital to remark that the interaction of the magnetic field is found to be counterproductive in enhancing velocity and concentration distribution, whereas the presence of chemical reaction, as well as a porous matrix with moderate values of the magnetic parameter, reduces the temperature and concentration fields at all points of the flow domain.

Hybrid nanofluid flow on a shrinking cylinder with prescribed surface heat flux

PurposeThis study aims to investigate the flow impinging on a stagnation point of a shrinking cylinder subjected to prescribed surface heat flux in Al2O3-Cu/water hybrid nanofluid.Design/methodology/approachUsing similarity variables, the similarity equations are obtained and then solved using bvp4c in MATLAB. The effects of several physical parameters on the skin friction and heat transfer rate, as well as the velocity and temperature profiles are analysed and discussed.FindingsThe outcomes show that dual solutions are possible for the shrinking case, in the range , where is the bifurcation point of the solutions. Meanwhile, the solution is unique for . Besides, the boundary layer is detached on the surface at , where the value of is affected by the hybrid nanoparticle and the curvature parameter . Moreover, the friction and the heat transfer on the surface increase with the rising values and . Finally, the temporal stability analysis shows that the first solution is stable in the long run, whereas the second solution is not.Originality/valueThe present work considers the problem of stagnation point flow impinging on a shrinking cylinder containing Al2O3-Cu/water hybrid nanofluid, with prescribed surface heat flux. This paper shows that two solutions are obtained for the shrinking case. Further analysis shows that only one of the solutions is stable as time evolves.

Hybrid Nanofluid Flow Past a Shrinking Cylinder with Prescribed Surface Heat Flux

This numerical study was devoted to examining the occurrence of non-unique solutions in boundary layer flow due to deformable surfaces (cylinder and flat plate) with the imposition of prescribed surface heat flux. The hybrid Al2O3-Cu/water nanofluid was formulated using the single phase model with respective correlations of hybrid nanofluids. The governing model was simplified by adopting a similarity transformation. The transformed differential equations were then numerically computed using the efficient bvp4c solver with the ranges of the control parameters 0.5%≤ϕ1,ϕ2≤1.5% (Al2O3 and Cu volumetric concentration), 0≤K≤0.2 (curvature parameter), 2.6<S≤3.2 (suction parameter) and −2.5<λ≤0.5 (stretching/shrinking parameter). Dual steady solutions are presentable for both a cylinder (K>0) and a flat plate (K=0) with the inclusion of only the suction (transpiration) parameter. The real and stable solutions were mathematically validated through the stability analysis. The Al2O3-Cu/water nanofluid with ϕ1=0.5% (alumina) and ϕ2=1.5% (copper) has the highest skin friction coefficient and heat transfer rate, followed by the hybrid nanofluids with volumetric concentrations (ϕ1=1%,ϕ2=1%) and (ϕ1=1.5%,ϕ2=0.5%), respectively. Surprisingly, the flat plate surface abates the separation of boundary layer while it enhances the heat transfer process.

Significances of prescribed heat sources on magneto Casson nanofluid flow due to unsteady bi-directionally stretchable surface in a porous medium

In this communication, bidirectional flow of Casson nanomaterial driven by an unsteady moveable surface in the region of boundary layer is analyzed. Moreover, the significances of porous space, magnetic field, prescribed surface temperature (PST), and prescribed surface heat flux are also incorporated. Furthermore, the aspects of Brownian motion and thermophoresis are also comprised through Buongiorno nanofluid model. Governing equations are firstly transformed into system of ordinary differential equations by using a suitable combination of variables, and then computational assessment is made through Keller-Box method. Graphical illustrations for temperature distribution, concentration distribution, local Nusselt number and local Sherwood number against escalating amounts of pertinent parameters are presented. It is observed that escalating amounts of unsteady parameter and temperature controlled indices reduce the temperature distribution, as well as the concentration distribution. It is also observed that increasing amounts of Casson parameter enhances the rate of heat transfer, and reduces the rate of mass transfer for PST case. Finally, a comparison benchmark for limited case has been presented to validate the present methodology.

Thermal Analysis of a Hydromagnetic Viscoelastic Fluid Flow Over a Continuous Curved Stretching Surface in the Presence of Radiative Heat Flux

This study deals with the flow and heat transfer of 2-D Maxwell fluid due to linear stretching of a curved surface. The heat transfer happens when temperature is specified on the boundary as prescribed surface temperature, PST, and prescribed surface heat flux, PSHF. The radiation and dissipation effects are incorporated in the energy equation. The modeling of the curved structure for a linear stretching velocity of Maxwell fluid is developed. The fluid is electrically conducted in the presence of varying applied magnetic field. The field quantities which describe the velocity, pressure, and temperature are calculated numerically. The effects of the radius of curvature, magnetic field, and non-Newtonian parameters are investigated and explained physically. This analysis adds to the mathematical understanding of boundary-driven flows in non-Newtonian fluids and enlarges the scope of its applications in the polymer industry for curved structures.

On the stability of the flow over a shrinking cylinder with prescribed surface heat flux

This study investigates the steady stagnation point flow and heat transfer passes a horizontal shrinking permeable cylinder. The free stream velocity and the prescribed surface heat flux are assumed to vary linearly with the distance from a fixed point on the cylinder. The partial differential equations governing the flow and heat transfer are transformed into a system of ordinary differential equations via similarity transformation. These equations are solved numerically for several values of the governing parameters, such as suction parameter s, curvature parameter γ, and shrinking parameter λ. The equations are solved numerically by employing the boundary value problem solver package available in MATLAB software, bvp4c. The effects of the governing parameters on the skin friction coefficient, surface temperature, velocity, and temperature profiles are examined. Given the existence of dual solutions in the present study for a certain range of the curvature parameter, stability analysis is carried out to determine which one of the solutions is stable as time passes. The outcome of the stability analysis demonstrates that only the first solution, with lower boundary layer thickness, appeared to be stable and thus physically reliable, while the other is not. It is also discovered that the boundary layer separation is delayed by reducing the curvature parameter.

Mixed Convective Hydromagnetic Stagnation Point Flow of Nanofluid over an Inclined Stretching Plate with Prescribed Surface Heat Flux

Mixed Convective Hydromagnetic Stagnation Point Flow of Nanofluid over an Inclined Stretching Plate with Prescribed Surface Heat Flux

Dual solutions for boundary layer flow and heat transfer of biomagnetic fluid over a stretching/shrinking sheet in presence of a magnetic dipole and a prescribed heat flux

This paper analyzes the steady boundary layer flow and heat transfer of biomagnetic fluid over a stretching/shrinking sheet with prescribed surface heat flux under the influence of a magnetic dipole. The governing equations are transformed into a set of ordinary differential equations (ODEs) by using similarity transformations. Numerical results are obtained using the boundary value problem solver bvp4c of MATLAB. The effects of various physical parameters on the velocity and temperature profiles as well as skin friction coefficient are discussed. The paper shows that dual solutions exist for certain values of stretching/shrinking sheet and suction parameters. Stability analysis is performed to determine which solution is stable and physically valid. Results of the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

Natural convection flow of Sodium Alginate based Casson nanofluid about a solid sphere in the presence of a magnetic field with constant surface heat flux

In this paper, we examined a free convection flow of Sodium Alginate (SA) as a host Casson fluid with three different types of nanoparticles specifically, Silicon Dioxide (SiO2), Copper oxide (CuO), and Copper (Cu) on a solid sphere in the presence of magnetic field along with prescribed surface heat flux. The Keller-box method was carried out for solving the transformed governing partial differential equations. Numerical results for the local skin friction coefficient are obtained and compared with literature. Also, the influences of Casson parameter, magnetic parameter, nanoparticles volume fraction, on local skin friction coefficient, local Nusselt number, temperature, and velocity are analyzed graphically. Our study revealed that the local Nusselt number, local skin friction coefficient and velocity profiles of SiO2 - SA based Casson nanofluid are higher than the other nanoparticles - SA based Casson nanofluid, as well as it has the lowest temperature profiles.