Convective Threshold Research Articles

Thermoconvective instabilities of a non-uniform Joule-heated liquid enclosed in a rectangular cavity

Natural convection produced by a non-uniform internal heat source is studied numerically. Our investigation is limited to a two-dimensional enclosure with an aspect ratio equal to two. The energy source is Joule dissipation produced by an electric potential applied through two electrodes corresponding to a fraction of the vertical walls. The system of conservative equations of mass, momentum, energy and electric potential is solved assuming the Boussinesq approximation with a discontinuous Galerkin finite element method integrated over time. Three parameters are involved in the problem: the Rayleigh number $Ra$, the Prandtl number $Pr$ and the electrode length $L_{e}$ normalized by the enclosure height. The numerical method has been validated in a case where electrodes have the same length as the vertical walls, leading to a uniform source term. The threshold of convection is established above a critical Rayleigh number, $Ra_{cr}=1702$. Due to asymmetric boundary conditions on thermal field, the onset of convection is characterized by a transcritical bifurcation. Reduction of the size of the electrodes (from bottom up) leads to disappearance of the convection threshold. As soon as the electrode length is smaller than the cavity height, convection occurs even for small Rayleigh numbers below the critical value determined previously. At moderate Rayleigh number, the flow structure is mainly composed of a left clockwise rotation cell and a right anticlockwise rotation cell symmetrically spreading around the vertical middle axis of the enclosure. Numerical simulations have been performed for a specific $L_{e}=2/3$ with $Ra\in [1;10^{5}]$ and $Pr\in [1;10^{3}]$. Four kinds of flow solutions are established, characterized by a two-cell symmetric steady-state structure with down-flow in the middle of the cavity for the first one. A first instability occurs for which a critical Rayleigh number depends strongly on the Prandtl number when $Pr<3$. The flow structure becomes asymmetric with only one steady-state cell. A second instability occurs above a second critical Rayleigh number that is quasiconstant when $Pr>10$. The flow above the second critical Rayleigh number becomes periodic in time, showing that the onset of unsteadiness is similar to the Hopf bifurcation. When $Pr<3$, a fourth steady-state solution is established when the Rayleigh number is larger than the second critical value, characterized by a steady-state structure with up-flow in the middle of the cavity.

Time-dependent patterns in quasivertical cylindrical binary convection.

This paper reports on numerical investigations of the effect of a slight inclination α on pattern formation in a shallow vertical cylindrical cell heated from below for binary mixtures with a positive value of the Soret coefficient. By using direct numerical simulation of the three-dimensional Boussinesq equations with Soret effect in cylindrical geometry, we show that a slight inclination of the cell in the range α≈0.036rad=2^{∘} strongly influences pattern selection. The large-scale shear flow (LSSF) induced by the small tilt of gravity overcomes the squarelike arrangements observed in noninclined cylinders in the Soret regime, stratifies the fluid along the direction of inclination, and produces an enhanced separation of the two components of the mixture. The competition between shear effects and horizontal and vertical buoyancy alters significantly the dynamics observed in noninclined convection. Additional unexpected time-dependent patterns coexist with the basic LSSF. We focus on an unsual periodic state recently discovered in an experiment, the so-called superhighway convection state (SHC), in which ascending and descending regions of fluid move in opposite directions. We provide numerical confirmation that Boussinesq Navier-Stokes equations with standard boundary conditions contain the essential ingredients that allow for the existence of such a state. Also, we obtain a persistent heteroclinic structure where regular oscillations between a SHC pattern and a state of nearly stationary longitudinal rolls take place. We characterize numerically these time-dependent patterns and investigate the dynamics around the threshold of convection.

Impact of ENSO longitudinal position on teleconnections to the NAO

While significant improvements have been made in understanding how the El Nino–Southern Oscillation (ENSO) impacts both North American and Asian climate, its relationship with the North Atlantic Oscillation (NAO) remains less clear. Observations indicate that ENSO exhibits a highly complex relationship with the NAO-associated atmospheric circulation. One critical contribution to this ambiguous ENSO/NAO relationship originates from ENSO’s diversity in its spatial structure. In general, both eastern (EP) and central Pacific (CP) El Nino events tend to be accompanied by a negative NAO-like atmospheric response. However, for two different types of La Nina the NAO response is almost opposite. Thus, the NAO responses for the CP ENSO are mostly linear, while nonlinear NAO responses dominate for the EP ENSO. These contrasting extra-tropical atmospheric responses are mainly attributed to nonlinear air-sea interactions in the tropical eastern Pacific. The local atmospheric response to the CP ENSO sea surface temperature (SST) anomalies is highly linear since the air-sea action center is located within the Pacific warm pool, characterized by relatively high climatological SSTs. In contrast, the EP ENSO SST anomalies are located in an area of relatively low climatological SSTs in the eastern equatorial Pacific. Here only sufficiently high positive SST anomalies during EP El Nino events are able to overcome the SST threshold for deep convection, while hardly any anomalous convection is associated with EP La Nina SSTs that are below this threshold. This ENSO/NAO relationship has important implications for NAO seasonal prediction and places a higher requirement on models in reproducing the full diversity of ENSO.

Precipitation, Convective Clouds, and Their Connections With Tropical Cyclone Intensity and Intensity Change

AbstractIn this paper, satellite‐based precipitation, clouds with infrared (IR) brightness temperature (BT), and tropical cyclone (TC) data from 2000 to 2015 are used to explore the relationship between precipitation, convective cloud, and TC intensity change in the Western North Pacific Ocean. An IR BT of 208 K was chosen as a threshold for deep convection based on different diurnal cycles of IR BT. More precipitation and colder clouds with 208 K < IR BT < 240 K are found as storms intensify, while TC 24 h future intensity change is closely connected with very deep convective clouds with IR BT < 208 K. Intensifying TCs follow the occurrence of colder clouds with IR BT < 208 K with greater areal extents. As an indicator of very deep convective clouds, IR BT < 208 K is suggested to be a good predictor of TC intensity change. Based upon the 16 year analysis in the western North Pacific, TCs under the conditions that the mean temperature of very deep convective clouds is less than 201 K, and the coverage of this type of clouds is more than 27.4% within a radius of 300 km of the TC center, will more likely undergo rapid intensification after 24 h.

Seasonal and ENSO Influences on the Stable Isotopic Composition of Galápagos Precipitation

AbstractThe origin of stable isotopic variability in precipitation over time and space is critical to the interpretation of stable isotope‐based paleoclimate proxies. In the eastern equatorial Pacific, modern stable isotope measurements in precipitation (δ18Op and δDp) are sparse and largely unevaluated in the literature, although insights from such analyses would benefit the interpretations of several regional isotope‐based paleoclimate records. Here we present a new 3.5 year record of daily‐resolved δ18Op and δDp from Santa Cruz, Galápagos. With a prior 13 year record of monthly δ18Op and δDp from the island, these new data reveal controls on the stable isotopic composition of regional precipitation on event to interannual time scales. Overall, we find Galápagos δ18Op is significantly correlated with precipitation amount on daily and monthly time scales. The majority of Galápagos rain events are drizzle, or garúa, derived from local marine boundary layer vapor, with corresponding high δ18Op values due to the local source and increased evaporation and equilibration of smaller drops with boundary layer vapor. On monthly time scales, only precipitation in very strong, warm season El Niño months has substantially lower δ18Op values, as the sea surface temperature threshold for deep convection (28°C) is only surpassed at these times. The 2015/2016 El Niño event did not produce strong precipitation or δ18Op anomalies due to the short period of warm SST anomalies, which did not extend into the peak of the warm season. Eastern Pacific proxy isotope records may be biased toward periods of high rainfall during strong to very strong El Niño events.

Cross-diffusion induced reaction-convection in a Brinkman porous layer

PurposeThis paper aims to investigate the onset of convection, heat and mass transports in a sparse porous layer saturated with chemically reactive binary fluid mixture heated and salted from below under the influence of Soret and Dufour effects.Design/methodology/approachThe Brinkman model is used for momentum equation. Linear stability analysis based on normal mode technique is used to evaluate the onset threshold for stationary and oscillatory convection. In weak-nonlinear theory, the truncated Fourier series method is used. The resulting system of differential equations is solved numerically by using the Runge–Kutta fourth-order method.FindingsBecause of the competition between the processes of thermal, solute diffusions, chemical reaction and cross-diffusions, the onset of instability is via oscillatory mode instead of stationary. The effect of dissolution/precipitation of reactive component and the cross-diffusions on the stability, heat and mass transports is investigated.Originality/valueBy the proper adjustment of underlying parameters, the onset of convection can either be advanced or delayed as per the requirement. Therefore, the present investigation forms a useful tool for regulating the onset of convection.

Influence of Sedimentation Length on the Convective Stability of a Colloidal Suspension

The сonvective stability of a colloidal suspension is studied in the case when the vertical dimension of the cavity is less than or comparable with the sedimentation length of nanoparticles. The analysis is carried out within the Boussinesq approximation on the basis of a modified model that takes into account the dependence of a thermodiffusion flow on the local value of impurity concentration. A new parameter of the problem is the ratio of the sedimentation length to the vertical dimension of the cavity. For a quiescent colloidal suspension, exact and approximate (in the case of small concentrations) solutions are obtained that describe the distributions of nanoparticles. A transformation is obtained that allows one to investigate the convective stability of a colloidal suspension stratified in the gravitational field by the Galerkin method with a set of simple trial functions. Instability boundaries and the characteristics of critical perturbations are determined. It is shown that, in the case of negative thermodiffusion, a decrease in the sedimentation length leads to a decrease in the convection threshold and the frequency of neutral oscillations.

Orographic control of the Bay of Bengal cold pool rainfall

In boreal summer (June–September), most of the Indian land and its surroundings experience rainrates exceeding 6 mm day\(^{-1}\) with considerable spatial variability. Over southern Bay of Bengal (BoB) along the east coast of the Indian peninsula (henceforth referred to as the Bay of Bengal cold pool or BoB-CP), the rain intensity is significantly lower (<2 mm day\(^{-1}\)) than its surroundings. This low rainfall occurs despite the fact that the sea surface temperature in this region is well above the threshold for convection and the mean vorticity of the boundary layer is cyclonic with a magnitude comparable to that over the central Indian monsoon trough where the rainrate is about 10 mm day\(^{-1}\). It is also noteworthy that the seasonal cycle of convection over the BoB-CP shows a primary peak in November and a secondary peak in May. This is in contrast to the peak in June–July over most of the oceanic locations surrounding the BoB-CP. In this study, we investigate the role of the Western Ghat (WG) mountains in an Atmospheric General Circulation Model (AGCM) to understand this paradox. Decade-long simulations of the AGCM were carried out with varying (from 0 to 2 times the present) heights of the WG. We find that the lee waves generated by the strong westerlies in the lower troposphere in the presence of the WG mountains cause descent over the BoB-CP. Thus, an increase in the height of the WG strengthens the lee waves and reduces rainfall over the BoB-CP. More interestingly in the absence of WG mountains, the BoB-CP shows a rainfall maxima in the boreal summer similar to that over its surrounding oceans. The WG also impacts the climate over the middle and high latitude regions by modifying the upper tropospheric circulation. The results of this study underline the importance of narrow mountains like the WG in the tropics in determining the global climate and possibly calls for a better representation of such mountains in climate models.

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

We analyze the thermal convection thresholds and linear characteristics of the primary and secondary instabilities for viscoelastic fluids saturating a porous horizontal layer heated from below by a constant flux. The Galerkin method is used to solve the eigenvalue problem by taking into account the elasticity of the fluid, the ratio between the viscosity of the solvent and the total viscosity of the fluid and the lateral confinement of the medium. For the primary instability, we found out that depending on the rheological parameters, two types of convective structures may appear when the basic conductive solution loses its stability: stationary long wavelength instability as for Newtonian fluids and oscillatory convection. The effect of the lateral confinement of the porous medium by adiabatic walls is to stabilize the oblique and longitudinal rolls and therefore selects transverse rolls at the onset of convection. In the range of the rheological parameters where stationary long wave instability develops first, we use a parallel flow approximation to determine analytically the velocity and temperature fields associated with the monocellular convective flow. The linear stability analysis of the monocellular flow is performed, and the critical conditions above which the flow becomes unstable are determined. The combined influence of the viscoelastic parameters and the lateral confinement on the characteristics of the secondary instability is quantified. The major new findings concerning the secondary instabilities may be summarized as follows: (i) For concentrated viscoelastic fluids, computations showed that the most amplified mode of convection corresponds to oscillatory transverse rolls, which appears via a Hopf bifurcation. This pattern selection is independent of both the fluid elasticity and the lateral confinement of the porous medium. (ii) For diluted viscoelastic fluids, the preferred mode of convection is found to be oscillatory transverse rolls for a very laterally-confined medium. Otherwise, stationary or oscillatory longitudinal rolls may develop depending on the fluid elasticity. Results also showed the destabilizing effect of the relaxation fluid elasticity and the stabilizing effect of the viscosity ratio for the onset of both primary and secondary instabilities.

Magneto-viscous effect on thermal convection thresholds in an Oldroyd magnetic fluid

In magnetic fluids the viscosity can depend on an external magnetic field. We theoretically investigate the influence of this magneto-viscous effect on the thermal convection thresholds for viscoelastic ferrofluids, which are described by a linear Oldroyd model. Such a system is influenced by a static magnetic field not only via the Kelvin force, but also through the magneto-viscous effect. In particular, we find that these two contributions compete oppositely when the threshold for the oscillatory instability is considered. While the Kelvin force tends to decrease the critical Rayleigh number, the magneto-viscous effect increases it. The critical properties at the onset of the oscillatory instability are discussed as a function of the viscoelastic parameters, the external field strength, and the magneto-viscous coefficient. The transition between the stationary and the oscillatory instability is only slightly affected by the magneto-viscous effect. Examples for codimension-2 lines are given.

Representing subgrid convective initiation in the Community Earth System Model

AbstractA widely recognized issue found in most Earth System Models is that of convective precipitation being triggered too early during the day over land, often resulting in persistent light rainfall. In an effort to address this issue, a model‐consistent subgrid convective trigger is demonstrated in the Community Earth System Model (CESM). Subgrid convective initiation is achieved by first calculating a convective threshold within the Community Atmosphere Model (version 5.3). The convective threshold is then passed to each subgrid land cover type within the Community Land Model (version 4.0) and convection is considered to be active if the convective threshold is exceeded and the convective available potential energy (CAPE) exceeds 70 J kg−1 (the default trigger). In total, three simulations are performed: (1) a Control (CTL) with the default CAPE trigger, (2) a simulation with the default CAPE trigger as well as the subgrid trigger (HCF trigger) applied over land and ocean, and (3) a simulation the same as the HCF trigger but only applied over land (HCF land). By including this subgrid trigger, convective onset time is delayed by 1–4 h; however, the time of peak precipitation is unchanged. This diurnal shift improves the number of hours the deep convective scheme is invoked from more than 75% to less than 50%, alleviating the overactivity problem. The delayed onset time of deep convection allows for greater CAPE accumulation and a greater proportion of precipitation generated outside the convective scheme. More CAPE consequently produces an overall increase in intense precipitation events.

Feedback control and heat transfer measurements in a Rayleigh-Bénard convection cell

We report experimental results on the heat transfer and instability onset of a Rayleigh-Bénard convection cell of aspect ratios 6:3:1 filled with a high Prandtl aqueous solution of glycerol under feedback control. We investigate the transient and stationary response of both local temperature readings and heat transfer fluxes on the Rayleigh Bénard cell in both conductive and convective states when we perform two independent feedback control actions on both hot and cold walls. We evaluate the performance of both controllers to maintain a temperature gradient independently if the system is below or above the convection threshold. As the convection cell can be rotated at 180° about the shorter axis of the cell, it was possible to perform transitions between thermal conduction and convection regimes and vice versa under a constant temperature difference maintained by both independent controllers. The experimental setup provided an accurate measurement of the critical Rayleigh number and the evolution of the Nusselt number as a function of the Rayleigh number in the moderately supercritical regime (Ra&amp;lt;104). Flow visualizations show a steady cellular convection pattern formed by 6 transverse rolls throughout the range of Rayleigh numbers.

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau–Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

Thermal instability in a nanofluid saturated horizontal porous layer subjected to g-gitter

An analytical investigation of the onset of convection in a horizontal porous saturated by a nanofluid, and subjected to g-gitter (or vertical vibration) is presented. The Darcy model is used for the porous layer and a linear stability analysis is used to determine the convection threshold in terms of the key parameters for the nanofluid in a homogenous porous medium. The results are presented for the special case when the porosity to heat capacity ratio is unity. The critical Rayleigh number and wavenumber is presented in terms of the nanofluid parameter.

Bistability and hysteresis induced by form drag in nonlinear subcritical and supercritical double-diffusive Lapwood convection in shallow porous enclosures

This paper considers natural Lapwood convection in a shallow porous cavity filled with a binary fluid. The investigation is mainly focused on the nonlinear behaviour of subcritical convection and the bistability phenomenon caused by the combined effects of porous medium form drag and double-diffusive convection. The Dupuit–Darcy model, which includes the effect of the form drag at high Reynolds flow, is used to describe the convective flow in the porous matrix. The enclosure is subject to vertical temperature and concentration gradients. The governing parameters of the problem under study are the Rayleigh number, $R_{T}$, the buoyancy ratio, $\unicode[STIX]{x1D711}$, the Lewis number, $Le$, the form drag coefficient, ($1/P_{r}^{\ast }$), where $P_{r}^{\ast }$ is a modified Prandtl number, and the aspect ratio of the cavity, $A$. An analytical solution, valid for shallow enclosures ($A\gg 1$), is derived on the basis of the parallel flow approximation. Among other things, this work focuses on the effects of the form drag parameter on the convective flows that occur when the thermal and solutal buoyancy forces are opposing each other. For this situation, in the absence of the form drag effect, the onset of motion is known to occur at a subcritical Rayleigh number, $R_{TC}^{sub}$, which depends upon $\unicode[STIX]{x1D711}$ and $Le$ only. The effects of $P_{r}^{\ast }$ on $R_{TC}^{sub}$ and on the subsequent convective heat and mass transfer rates are found to be significant. A new bistability phenomenon arises when the onset of subcritical convection is shifted close to or beyond the threshold of supercritical convection, whether heating or cooling isothermally or upon applying constant heat and solute fluxes, regardless of the enclosure aspect ratio value. It is demonstrated, on the basis of linear stability theory, that the form drag parameter has a stabilizing effect and considerably affects the threshold for Hopf bifurcation, $R_{TC}^{Hopf}$, which characterizes the transition from steady to unsteady convection. In the range of governing parameters considered in this study, the heat, solute and flow characteristics predicted by the analytical model are found to agree well with the numerical study of the full governing equations.

Stability analysis of Rayleigh-Bénard convection in a cylinder with internal heat generation.

The flow instabilities of Rayleigh-Bénard convection in a cylinder with effect of uniform internal heat source are investigated numerically. The instabilities of the static state and of axisymmetric flows are investigated by linear stability analysis. The convection threshold depends on the strength of internal heat source q and the aspect ratio of the cylinder Γ. The stability of axisymmetric flows is strongly affected by these two parameters, as well as the Prandtl number Pr. Depending on the value of q, three regimes are identified: weak internal heating, moderate internal heating, and strong internal heating regime. In a weak internal heating regime, the instability characteristics are similar to Rayleigh-Bénard convection. In a moderate internal heating regime, intense interaction of buoyancy instability and hydrodynamic instability result in complex instability curves. When q is large enough, the internal heating effect overwhelms the boundary heating effect. Specifically, the influence of Pr on instability is studied at a moderate internal heat strength q=6.4. An extremely multivalued stability curve is observed. At most five critical Rayleigh numbers can be determined for the axisymmetry-breaking instability at a certain Prandtl number. An axisymmetric unsteady instability mode is observed as well. By nonlinear simulation, the oscillatory flow patterns are obtained, and the axisymmetry-breaking bifurcation of the unsteady toroidal flow is studied.

Effect of Phase Thermal Modulation Without Stationary Temperature Gradient on the Threshold of Convection

The convective instability of a horizontal fluid layer subject to a time varying gradient of temperature is investigated. The stationary component of the temperature gradient is considered equal to zero and the oscillating components imposed on the horizontal boundaries are in phase and with the same amplitude. The aim of the present paper is to examine the effect of this type of modulation on the onset of convective instability. We show that unlike the case where the equilibrium configuration is stable in the absence of modulation, we have instability when the temperature at the horizontal boundaries is modulated in phase. Also, we observe that in the limit of low and high dimensionless frequency of modulation, ω &lt; 0.5 and ω &gt; 140, the basic state tends to a stable equilibrium configuration and for an intermediate dimensionless frequency, the system is potentially unstable. The results obtained from analytical asymptotic study for low and high dimensionless frequency are in good agreement with the numerical ones.

Thermal Instability of Convection in a Rotating Nanofluid Saturated Porous Layer Placed at a Finite Distance From the Axis of Rotation

An analytical investigation for the onset of convection in a vertical porous layer saturated by a nanofluid is presented when the porous layer is placed some finite distance from the axis of rotation. A linear stability analysis is used to determine the convection threshold in terms of the key parameters for the nanofluid. This study reconfirms that the Taylor number and gravity effects are passive, and that the most critical mode is roll cells aligned with the vertical axis of rotation. The critical Rayleigh number is presented in terms of the nanofluid parameters and offset distance for stationary convection.

Numerical investigation of electrohydrodynamic instability and bifurcation in a dielectric liquid subjected to unipolar injection

The electroconvection of dielectric liquids subjected to unipolar injection is numerically studied in a two-dimensional cavity. To understand the Coulomb force driven electroconvective instabilities and bifurcations in the closed cavity, a high resolution upwind scheme is applied to carry out linear stability analysis and numerical simulation of nonlinear electrohydrodynamic equations. We focus on the strong injection case, where the non-dimensional injection parameter C is fixed at C=10. The length to height ratio of the cavity is fixed at 0.614. The numerical simulations are performed subject to free and rigid lateral wall boundary conditions. Two dimensionless mobility parameters M=5 and M=10 are considered for each kind of the lateral boundary conditions. Our linear stability analysis result is consistent with previous theoretical predictions. The nonlinear behaviors of the investigated system beyond the convection threshold are carefully examined. Abundant bifurcation phenomena, such as the pitchfork bifurcation, Hopf bifurcation, quasi-periodic Hopf bifurcation and heteroclinic bifurcation, have been observed. Some nonlinear flow features, such as the hysteresis loops, coexistence of multiple solutions and transition to chaos, have also been demonstrated. Our simulation results show that flow structure and bifurcation sequence can be greatly affected by the specified lateral boundary conditions and the chosen mobility parameters. Besides the static state, a series of steady and unsteady solutions has been calculated, like the one-cell steady state, one-cell periodic state, one-cell quasi-periodic state, and the one-cell chaotic state. All these convective states with two-cell structure are also obtained. Moreover, a periodic state oscillating between the one-cell structure and the two-cell structure has been found in flow domain bounded by rigid walls.

The effects of short-lived radionuclides and porosity on the early thermo-mechanical evolution of planetesimals

The thermal history and internal structure of chondritic planetesimals, assembled before the giant impact phase of chaotic growth, potentially yield important implications for the final composition and evolution of terrestrial planets. These parameters critically depend on the internal balance of heating versus cooling, which is mostly determined by the presence of short-lived radionuclides (SLRs), such as 26Al and 60Fe, as well as the heat conductivity of the material. The heating by SLRs depends on their initial abundances, the formation time of the planetesimal and its size. It has been argued that the cooling history is determined by the porosity of the granular material, which undergoes dramatic changes via compaction processes and tends to decrease with time. In this study we assess the influence of these parameters on the thermo-mechanical evolution of young planetesimals with both 2D and 3D simulations. Using the code family i2elvis/i3elvis we have run numerous 2D and 3D numerical finite-difference fluid dynamic models with varying planetesimal radius, formation time and initial porosity. Our results indicate that powdery materials lowered the threshold for melting and convection in planetesimals, depending on the amount of SLRs present. A subset of planetesimals retained a powdery surface layer which lowered the thermal conductivity and hindered cooling. The effect of initial porosity was small, however, compared to those of planetesimal size and formation time, which dominated the thermo-mechanical evolution and were the primary factors for the onset of melting and differentiation. We comment on the implications of this work concerning the structure and evolution of these planetesimals, as well as their behavior as possible building blocks of terrestrial planets.