Variation Of Average Nusselt Number Research Articles

Free convection of thermodependent non-Newtonian fluids in a square enclosure partially heated at one side

This article exhibits a numerical analysis on free convection cooling of a heater located on the left side of a square enclosure using thermodependent power-law fluids. The temperature of the right sidewall is maintained relatively cold, while the unheated portions of the left wall and the horizontal ones are thermally insulated. The governing differential equations are numerically solved using a finite volume technique based on the iterative Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The objective of this article is to analyze the impacts of the Rayleigh number, the Pearson number, the power-law index, and the location and length of the heat source on the fluid structure and temperature patterns, and to subtract the impact of these control parameters on the cooling efficiency of the cavity. The results reveal that rising the heater size and the Rayleigh number improves free convection inside the cavity. Moreover, using shear-thinning fluids (i.e. n < 1) with high value of the Pearson number enhances the thermal performance of the enclosure. The findings also point to the existence of a peak in the average Nusselt number variation, corresponding to an optimal heater location.

Hydrothermal performance for forced convective flow of viscoplastic fluid through a backward facing step channel

The hydrothermal performance for steady, laminar forced convective flow of viscoplastic fluid through a backward facing step channel is studied. The effect of Bingham number (0 ≤ Bn ≤ 1), Reynolds number (50 ≤ Re ≤ 300), and power law index (0.2 ≤ n ≤ 1) on the thermal and flow characteristics are analyzed. A recirculatory zone is generated at the step corner and the findings depict a decrement in the length of reattachment as n and Bn increases. The temperature drop in the vicinity of the step increases as Bn increases. Also, it is found that the local Nusselt number (Nu) attains a peak in the vicinity of the step and the maximum Nu in this region increases with the increase in Bn. Moreover, for any particular value of Bn, Nu decreases with the increase in n. Also, the average Nusselt number increases significantly for viscoplastic fluids in comparison to shear-thinning and Newtonian fluids, and the heat transfer rate increases as Bn increases. Furthermore, there exists a critical value of Bn that alters the variation of average Nusselt number with the power-law index in case of separated flows.

Investigation of the free convection of nanofluid flow in a wavy porous enclosure subjected to a magnetic field using the Galerkin finite element method

This paper provides a numerical simulation to explore natural convection and fluid flow in a three-dimensional wavy cubical enclosure subjected to a magnetic field along the z-axis. The main emphasis of this research is to discuss entropy generation inside a wavy porous cavity. Brinkman's extended non-Darcy flow model is utilized for studying the free convection in the permeable medium. The equations of the mathematical model were solved using Galerkin finite element method. Isotherms, streamlines, velocity profile, and variation of average Nusselt number are calculated for various values of Ra (103–106), Ha (0–100), and φ (0–0.08). The results show that the streamlines and isotherms increase with the increase of Darcy and Rayleigh numbers. Besides, entropy generation is sensitive to the values of Darcy number, Rayleigh number, Hartmann number, and the number of undulations. Besides, the variation of the Nusselt number is affected by the Rayleigh number and Darcy number. The highest Nusselt number can be obtained for a maximum number of undulations only at the small values of the Rayleigh number. Otherwise, this pattern will be changed in the opposite trend at large values of the Rayleigh number. At the highest values of Ra, increasing Ha from 0 to 100 decreased Nuavg by 23%, while increasing Da from 10−5 to 10−2 enhanced it by 177%. Finally, it was found that the values of Beavg are only being enhanced by only one parameter, namely the Hartmann number. The obtained results from the current non-Darcy flow model agree well with the available literature results.

Prediction of Heat Transport and Drag Force of Ferrofluids around a Sphere in the Presence of Oscillating Magnetic Field

In this article, the heat transfer of magnetic nanofluids over a sphere has been considered in the presence of an external oscillating uniform magnetic field for various range of Reynolds number (Re). The significant difference between the magnetic property of the nanofluid and the heated sphere makes a non-uniform magnetic field around the sphere resulting a significant alteration in the distribution of velocity and temperature around sphere. The variations of average Nusselt number (Nuavg) and drag coefficient (Cd) have been studied to demonstrate the influence of magnetic field frequency and intensity, Re and the relative magnetic permeability of the sphere. It has been found that the magnetic field causes the vortices to appear or grow behind the sphere. These vortices lead to boundary layer distortion and thereby increasing heat-transfer rate and drag force. In addition, the obtained results clearly indicate that there is an optimal frequency at which Nuavg and Cd can be maximized. Moreover, the influence of the applied magnetic field is more noticeable for low Re values and/or frequencies near the optimum value. Furthermore, the obtained results clearly demonstrate that the heat-transfer increase is much higher than the penalty due to the drag force increase for frequencies close to the optimal value.

INVESTIGATION ON THE EFFECT OF OSCILLATING MAGNETIC FIELDS ON FLUID FLOW AND FORCED-CONVECTION HEAT TRANSFER AROUND A SPHERE

In this article, the heat transfer of magnetic nanofluids over a sphere has been considered in the presence of an external oscillating uniform magnetic field for a wide range of Reynolds number values (Re). This study incorporates the effect of magnetic permeability and purposes the optimal operating condition for the first time. The significant difference between the magnetic property of the nanofluid and the heated sphere makes a non-uniform magnetic field around the sphere resulting in a significant alteration in the distribution of velocity and temperature around sphere. The variations of average Nusselt number (Nu&lt;sub&gt;avg&lt;/sub&gt;) and drag coefficient (C&lt;sub&gt;d&lt;/sub&gt;) have been studied to demonstrate the influence of magnetic field frequency and intensity, Re, and the relative magnetic permeability of the sphere. It has been found that the magnetic field causes the vortices to appear or grow behind the sphere. This leads to fluid separation even for low Re values in the presence of magnetic field. Local Nu value is minimum at the separation point. This point moves towards the front of sphere as the magnetic field intensity increases. These vortices lead to boundary layer distortion, thereby increasing heat-transfer rate and drag force. In addition, the obtained results clearly indicate that there is an optimal frequency at which Nu&lt;sub&gt;avg&lt;/sub&gt; and C&lt;sub&gt;d&lt;/sub&gt; can be maximized. The dimensionless optimal frequency (&amp;Omega;&amp;tau;) is about 0.6 regardless of Re value or magnetic field intensity. Moreover, the influence of the applied magnetic field is more noticeable for low Re values and/or frequencies near the optimum value. For instance, Nu&lt;sub&gt;avg&lt;/sub&gt; and C&lt;sub&gt;d&lt;/sub&gt; increase by 150&amp;#37; and 50&amp;#37;, respectively, for Re value of 30 while they are three times smaller for Re value of 200. Increase in the magnetic permeability of sphere enhances the Nu&lt;sub&gt;avg&lt;/sub&gt; up to 170&amp;#37; (at Re &amp;#61; 50) close to the optimal frequency, whereas its effect is almost negligible for frequencies far away from the optimal one. Furthermore, the obtained results clearly demonstrate that the heat-transfer increase is much larger than the penalty due to the drag force increase for frequencies close to the optimal value.

Thermo-fluid characteristics and second law analysis of an inclined two-fluid system with variable surface roughness

The present numerical study focuses on the analysis of thermodynamic characteristics of an inclined two-fluid system (Al2O3-water and CuO-water nanofluids) having a heat conducting partition wall of variable surface roughness with constant geometric orientation. A further level of thermal control that results in an optimum system orientation for greater thermo-physical transport along with less entropy generation and thermal optimization is explored by examining the effect of system inclination. Based on the second law of thermodynamics, the quantitative results include the variation of average Nusselt number, average fluid temperature, average entropy generation, and average Bejan number for a wide range of Rayleigh number and inclination angle. Current study realizes that the mean quantitative properties of the system are significantly affected by the change of Rayleigh number and inclination angle, despite having a weak dependency on the partition roughness. The variation of average Bejan number with Rayleigh number assumes a reverse trend compared to the same for average Nusselt number and entropy generation and decreases continuously as the flow circulation strengthens. The rate of thermal transport is significantly regulated by the system orientation. Each Rayleigh number conforms to a critical angle of the system inclination for highest thermal transport and entropy generation.

Laminar natural convection in a 2-D pentagonal house with sloping roof heated by constant heat flux

Natural convection in a pentagonal house with a protruding cooler for summer is numerically investigated. The sloping roof is subjected to constant heat flux, and the cooler maintains at a uniform cold temperature. The remaining walls of the house are insulated. Local multi-quadratic radial basis function (LMQRBF) method is applied in solution of Navier–Stokes equations in stream function-vorticity form. The working fluid in the house is air with Pr = 0.71. The effects of Rayleigh number (103 ≤ Ra ≤ 106), heat flux of the roof (0.1 ≤ q ≤ 2.0), and the cooler’s vertical position (0.65 ≤ H/L ≤ 0.85) are explored. Streamlines, isotherms, velocity profiles, and the distribution of Nusselt number are displayed. Numerical results indicate that for the top and right wall of the cooler, the heat transfer is stronger than that for the bottom wall. It reveals that all the governing parameters efficiently impact the generation and evolution of the secondary and tertiary vortex in the gable roof. It is also observed that the variation of average Nusselt number on the right wall with Rayleigh number is under the combined influence of the heat flux and the cooler’s vertical position.

The effect of plate motion on heat transfer enhancement using turbulent offset jet flow: A conjugate approach

The present research is focused on computational analysis of conjugate heat transfer behavior of a turbulent offset jet flow over a moving flat plate in a quiescent environment. The plate of definite thickness and conductivity is subjected to isothermal condition at the plate bottom surface. The computation is carried out with a low-Reynolds number (LRN) turbulence model proposed by Yang and Shih which involves integration to wall (ITW) approach to capture the thin viscous sub-layer region within the boundary layer. The variation of offset ratio (ranging as 3, 7 and 11) and plate velocity (Up = 0 − 2) plays quite a major role in the distribution of interface temperature and Nusselt number. The conduction heat flow rate in solid depends upon the plate thickness ratio (S) which is varied as 0.5 − 1.5 and the conductivity ratio (K) ranging as 500 − 2000. The variation of average Nusselt number gives evidence of better cooling rate for smaller offset ratios and higher plate to jet velocity ratio.

Rarefaction Effect, Heat Transfer, and Drag Coefficient for Gas Flow Around Square Cylinder in Transition Flow Regime

Abstract In this work, rarefaction effect, heat transfer, and drag coefficient for gas flow around a square cylinder in transition flow regime are numerically studied using unified gas kinetic scheme (UGKS). To reduce computational cost, a mirror symmetry boundary treatment for UGKS is proposed and applied in this study. It is found that: (1) velocity slip is not obvious on upwind and downwind surfaces of square cylinder due to the tangential gas flow being weak in these surfaces; (2) with the increase of local Knudsen number, velocity slip on upper surface always increases, but temperature jump can decrease, which indicates that Knudsen number is not the decisive parameter to characterize temperature jump; (3) the heat transfer between gas and square cylinder enhances with the increase of inflow Knudsen number and cylinder temperature due to the increase of temperature jump and deteriorates with the increase of inflow Mach number on account of gas stagnation; and (4) the drag coefficient increases with the increase of inflow Knudsen number, the decrease of inflow Mach number, and the increase of cylinder temperature. To further predict the variation of average Nusselt number and drag coefficient, correlations for average Nusselt number and drag coefficient with inflow Mach number ranging from 0.05 to 0.3, inflow Knudsen number ranging from 0.1 to 10, and cylinder temperature ranging from 320 K to 380 K are proposed. This research can improve the understanding for mechanisms of gas flow and heat transfer in micro-electromechanical system (MEMS) devices.

Effect of Nanoparticle Shape and Volume Fraction on Nanofluid Flow in Serpentine Microtube

The nanofluid flow in serpentine microtube was numerically investigated in this study. The study has been carried out in three-dimensional laminar flow (750≤Re≤2000) condition. Al2O3 – water nanofluid with different nanoparticle volume fractions (1.0%, 2.0%, 3.0%) have been used as the working fluid in the numerical analyzes. In addition, studies were carried out for blade, platelet and cylindrical nanoparticle shapes. The average Nusselt numbers and the average Darcy friction factors have been used to estimate the flow and heat transfer performance of nanofluid flow in serpentine microtubes. Velocity and temperature distributions inside the microtube were also examined for different cases. Numerical results of the study have been presented as the variation of average Nusselt number and average Darcy friction factor with Reynolds number, nanoparticle shape and nanoparticle volume fraction. As a result, the highest convective heat transfer performance has been obtained for platelet nanoparticle shape of the Al2O3-water nanofluid with 3.0% nanoparticle volume fraction.

Study of non – Newtonian flow, heat transfer and entropy generation characteristics in trapezoidal corrugated channel

This study is focused on the thermo-hydraulic and entropy generation characteristics of a non-Newtonian fluid in a trapezoidal shaped wavy channel. The study has been conducted for different Reynolds number ranging from 25 – 100 and power law index varying from 0.5 – 1.5. The variation of average Nusselt number, pressure drop, thermal entropy generation, viscous entropy generation are being calculated. For the discretization of the governing equations, finite volume method is adopted in Ansys Fluent. Average Nusselt number value increases with an increase in the value of Reynolds number and decreases with an increase in power law index. On the other hand, pressure drop decreases on increasing the value of Reynolds number, whereas on increasing the value of power law index, pressure drop value showing a decreasing trend. Thermal entropy generation and viscous entropy generation follows almost the same trend but both having different order of magnitude. The trend shows that on increasing the value of Re both the entropy generations increases whereas on increasing the power law index, it decreases.

Finite element analysis of mixed convection flow in a trapezoidal cavity with non-uniform temperature

A two dimensional flow analysis in a cavity shaped isosceles trapezium is carried out. Non-parallel sides of a trapezium are adiabatic. A varying sinusoidal temperature is applied to the lower wall while the upper wall is at constant temperature. Upper wall of the cavity moves with a velocity η0 in the positive x-direction. Also, B0 is constant magnetic field of strength aligned in the same x-direction and Newtonian fluid is considered. The values of magnetic field parameter used are Ha=0,50, the Richardson number is Ri=0.1,1,10, Re=100 is Reynolds number used for the analysis, the amplitude of sinusoidal temperature is m=0.25,0.5,1. The impacts of different leading parameters are analyzed by plotting streamlines for flow fields and isotherm contours for temperature of the flow dynamics. The graphs that signify the variation of average Nusselt number and local Nusselt number are sketched for both lower and upper walls of the cavity. Result indicated that with constant temperature the top wall of the boundary layer thickness decreases as Richardson number Ri increases and for bottom wall with variable temperature. The Nusselt number gets higher with an increment in the amplitude of the oscillation of temperature function. Furthermore, the study revealed that the average Nusselt number gets reduced as the intensity of magnetic field is enhanced. The variation in transit of heat at the bottom wall is similar but the maximum value of heat transfer at the bottom wall shows a variation from 3.8 to 20 when Ha=0 and from 3 to 18 when Ha=50. The accuracy of the present numerical algorithms is also established.

Hydrodynamic analysis of nanofluid’s convective heat transfer in channels with extended surfaces

The effects of nanoparticles (NPs) on heat transfer in extended surface channels have been analyzed using a two-component (TC) model. The results show that unlike the single-component model, the TC model leads to more accurate predictions of the system’s heat transfer performance as a result of the direct influence of the NPs’ distribution on the hydrodynamics. It is found that the average Nusselt number varies non-monotonically with the block’s heights, and the trend is explained by the interplay between heat transfer mechanisms and the hydrodynamics. A similar non-monotonic trend observed in the case of the friction factor has been explained by the variations of the concentration- and temperature-dependent viscosity of the nanofluids. A guideline for an optimum design based on the combination of the variation of average Nusselt number and friction factor with respect to the geometrical parameters has also been presented.

A Comparative Numerical Study on Conjugate Natural Convection From Vertical Hollow Cylinder With Finite Thickness Placed on Ground and in Air

Abstract The present work reports a comparative analysis of natural convection heat transfer from a thick hollow vertical cylinder either placed on the ground or suspended in the air. The numerical simulations have been performed by varying the cylinder length to its outer diameter (L/Do) in the range of 0.2–20, the thickness ratio (Di/Do) in a range of 0.5–0.9, and Rayleigh number (Ra) from 104 to 108. The flow and heat transfer characteristics have been delineated precisely with the presentation of the thermal plume and flow field in the vicinity of the cylinder. The variation of average Nusselt number (Nu), local Nu, and contribution to total heat loss from different surfaces with the pertinent parameters have been elucidated graphically. The average Nu is always more for the cylinder in the air compared with the case when it is on the ground. However, the difference between the Nu for these two cases diminishes, as the L/Do increases. It has also been found that the contribution to total heat loss from the inner surface of the hollow cylinder suspended in air increases with L/Do, attains a peak, and decreases sharply. Cooling time curves for the cylinder placed in air or on the ground have been described precisely. Finally, a correlation for the average Nusselt number as a function of all the pertinent parameters has been proposed that can be useful for industrial and academic purposes.

Hydrothermal performance of nanofluid flow in a sinusoidal double layer microchannel in order to geometric optimization

In this investigation, laminar flow with a hybrid nanofluid as a working fluid in a newly designed double layer microchannel with sinusoidal walls is investigated. The nanofluid is Al2O3-Cu/water hybrid nanofluid. Results indicate that changing the geometry of fluid route (wavelength of the sinusoidal wall), usage of nanofluid and increasing fluid velocity can alter Nusselt number, the maximum temperature distribution in the microchannel, Performance Evaluation Criterion and friction factor. The presence of sinusoidal wavelength across the entire microchannel can improve mixing between surface and fluid, and this mixing happens because of the slow flow of fluid in low Reynolds number (Re = 50) and the average Nusselt number variation is the same for similar wavelengths. For Re = 300, 700 and 1200, the decrease in PEC is the same for the higher volume concentration of solid nanoparticles and the change in the level of curves for each wavelength are close together compared with Re = 50. When the difference temperature between surface and fluid is reduced, the heat transfer value is reduced, and the maximum temperature of the lower layer increases sharply so that for Re = 50 the value of maximum temperature is noticeable compare with Re = 1200.

Numerical and Experimental Investigation of Phase Change Heat Transfer in the Presence of Rayleigh–Benard Convection

Abstract This research investigates the melting rate of a phase change material (PCM) in the presence of Rayleigh–Benard convection. A scaling analysis is conducted for the first time for such a problem, which is useful to identify the parameters affecting the phase change rate and to develop correlations for the solid–liquid interface location and the Nusselt number. The solid–liquid interface and flow patterns in the liquid region are analyzed for PCM in a rectangular enclosure heated from bottom. Numerical and experimental results both reveal that the number of Benard cells is proportional to the ratio of the length of the rectangular enclosure over the solid–liquid interface location (i.e.,, the liquified region aspect ratio). Their effect on the local heat flux is also analyzed as the local heat flux profile changes with the solid–liquid interface moving upward. The variations of average Nusselt number are obtained in terms of the Stefan number, Fourier number, and Rayleigh number. Eventually, the experimental and numerical data are used to develop correlations for the solid–liquid interface location and average Nusselt number for this type of melting problems.

Natural convection heat transfer and fluid flow around a thick hollow vertical cylinder suspended in air: A numerical approach

The present study reports numerical investigation on natural convection heat transfer and fluid flow from a thick hollow vertical cylinder suspended in air within laminar regime for a Rayleigh number (Ra) of 104 to 108. Numerical simulations have been performed by changing the length to outer diameter ratio (L/Do) of the cylinder from 0.2 to 20 and thickness ratio (Di/Do) from 0.5 to 0.9. Variation of average Nusselt number (Nu) and local Nusselt number with the above parameters has been elucidated graphically. Subsequently, the influences of Ra, L/Do, Di/Do on mass-flow rate and velocity profile inside the cylinder has also been investigated. Temperature contour and velocity vector plot around the cylinder have been represented pictorially to describe the thermal and velocity field around the vertical thick hollow cylinder. It has been observed that the average Nu of a thick hollow cylinder increases with L/Do, attains a peak and then decreases to a minimum and then again increases with L/Do. This phenomenon is very well observed at high Ra of 106 compared to lower Ra of 104. The Nu of the inner surface is found to be always lower compared to the outer surface and as L/Do increases beyond 8 the inner surface Nu falls drastically at high Ra compared to lower Ra. It has also been observed that the non-dimensional mass-flow rate due to buoyancy driven flow inside the thick hollow cylinder increases with L/Do, attains a peak and then decreases for all Ra. Cooling curve and a correlation for Nusselt number as a function of geometrical and thermal parameter have been presented which are useful for industrial purposes.

Heat Transfer Characteristics of Twin Circular Jet Impingement Cooling on the Strip Surface after Rolling

The heat transfer characteristics of the strip surface due to the twin circular jet impingement were numerically investigated by a three-dimensional finite element program. Systematic parametric research is conducted by varying the jet velocity of nozzle exit of 7.5 m/s, nozzle to the steel plate surface distance (H = 6.7, 11.7, 16.7), and the nozzle to nozzle centre spacing (W = 10, 15). The general trend of the distribution of the local Nusselt number and the average Nusselt number variation on the impingement surface of strip was obtained under the various parameters. The results show that, the heat transfer capacity of the strip surface perpendicular to the centre of the two jets decreases with the increase of the nozzle to nozzle centre spacing. The average Nusselt number increases by about 2%-20% with the increase of nozzle to the steel plate surface distance from 6.7 to 11.7 for the nozzle to the steel plate surface distance of 100mm and 200mm, while the average Nusselt number decreases by about 11%-25% with the increase of nozzle to the steel plate surface distance from 11.7 to 16.7.

Conjugate heat transfer in a duct using nanofluid by two-phase Eulerian–Lagrangian method: Effect of non-uniform heating

The underlying physics behind the effect of non-uniform heating on the heat transfer characteristics for flow of Al2O3-water nanofluid through a duct having finite wall thickness subjected to sinusoidal heat flux has been numerically investigated in this study. The nanofluid is modelled as a single fluid with two phases using the Eulerian-Lagrangian formulation. The concomitant implications of thermal conductivity ratio of solid to fluid, outer tube diameter to inner tube diameter ratio, amplitude of sinusoidal heat flux and volume fraction of nanoparticles on the thermal attributes have been explored and quantified by local and average Nusselt number. The results elucidate a close resemblance between the nature of the variation of local Nusselt number and the applied heat flux, particularly at the intermediate region of the channel. The results also reveal a damping effect on the conjugate heat transfer due to the increase in conducting wall thickness, irrespective of the volume fraction of nanofluid. The confluence of various key parameters on the variation of the magnitudes of the crests and troughs of local Nusselt number are analyzed and this variation proves to be a prime factor in determining the variation of average Nusselt number. Furthermore, the average Nusselt number decreases with amplitude of heat flux. The rate of heat transfer for flow of base fluid through a duct having finite wall thickness is always lower in case of non-uniform heating. However, the use of nanofluid as the heat transfer medium can compensate the decrement in heat transfer due to non-uniform heating.

Effects of moving wall on the flow of micropolar fluid inside a right angle triangular cavity

PurposeThe main purpose of this study is to examine the effects of moving wall on the mixed convection flow and heat transfer in a right-angle triangular cavity filled with a micropolar fluid.Design/methodology/approachIt is assumed that the bottom wall is uniformly heated and the right inclined wall is cold, whereas the vertical wall is adiabatic and moving with upward/downward velocity v0/−v0, respectively. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the Galerkin finite element method. The Penalty method is used to eliminate the pressure term from the momentum equations. To accomplish the consistent solution, the value of the penalty parameter is taken 107. The simulations are performed for a wide range of Richardson number, micropolar parameter, Prandtl number and Reynolds number.FindingsThe results are presented in the form of streamlines, isotherms and variations of average Nusselt number and fluid flow rate depending on the Richardson number, Prandtl number, micropolar parameter and direction of the moving wall. The flow field and temperature distribution in the cavity are affected by these parameters. An average Nusselt number into the cavity in both cases increase with increasing Prandtl and Richardson numbers and decreases with increasing micropolar parameter, and it has a maximum value when the lid is moving in the downward direction for all the physical parameters.Research limitations/implicationsThe present investigation is conducted for the steady, two-dimensional mixed convective flow in a right-angle triangular cavity filled with micropolar fluid. An extension of the present study with the effects of cavity inclination, square cavity, rectangular, trapezoidal and wavy cavity will be the interest of future work.Originality/valueThis work studies the effects of moving wall, micropolar parameter, Richardson number, Prandtl number and Reynolds number parameter in a right-angle triangular cavity filled with a micropolar fluid on the fluid flow and heat transfer. This study might be useful to flows of biological fluids in thin vessels, polymeric suspensions, liquid crystals, slurries, colloidal suspensions, exotic lubricants, solar engineering for construction of triangular solar collector, construction of thermal insulation structure and geophysical fluid mechanics, etc.