Numerous thermal practical applications utilize shell and tube heat exchanger appliances to transfer heat energy between hot and cold working fluids. Incorporating metal foam to the outer periphery of inner tube improves the heat transfer process from hot water in the tube side to cold water in the shell side and consequently improves heat exchanger performance. In this study, the integration of use of a porous material together with designing a robust adaptive controller could efficiently regulate the outlet cold water temperature to the desired value. This is achieved with respect to the time required for cold water to reach the desired temperature (settling time) and the amount of hot water volume flow during a certain time span. A barrier function-based adaptive sliding mode controller (BF-based adaptive SMC) is proposed, which requires only the information of temperature measurement of cold water. The stability of BF-based adaptive SMC is proved utilizing Lyapunov function analysis. The effectiveness of proposed controller is verified via numerical results, which showed that the proposed controller could achieve considerable accuracy of cold water temperature using suitable design parameters. In addition, the robustness of controller against variation in inlet temperature is also verified. Another improvement to performance of heat exchanger system is achieved by adding the metal foam of aluminum material on inner pipe perimeter with wide range of metal foam to outer inner pipe diameters ratio ($1\le s\le 1.8$). The results showed that the settling time is significantly reduced which enables outlet cold water to reach the required temperature faster. With respect of the case of non-adding metal foam on inner pipe outer circumference, when $s=1.2$, the settling time and hot water temperature are reduced by $1/2$ and $17.3\%$, respectively, while for $s=1.8$, they are decreased by $\le 1/20$ and $35.3\%$ correspondingly. Accordingly, the required volume flow for hot water is reduced considerably.

Based on admirable porous media performance and the popularity of additive manufacturing technology, gradient porous media are progressively being applied in increasing fields. In this study, convection heat transfer within a square vented cavity, partially occupied by two copper metal foam layers of $10$ and $20$ PPI saturated with nanofluid, was assessed numerically. The left wall was heated uniformly and non-uniformly by applying multi-frequency spatial heating following a sinusoidal function. Governing equations, including continuity, the Darcy–Brinkmann–Forchheimer model, and local thermal non-equilibrium energy equations, were adopted and solved by employing the finite volume method. The influences of relevant parameters, including nanoparticle concentrations $\left(0\%\le \phi \le 10\%\right)$, Reynolds number ($1\le Re\le 100$), inlet and outlet port aspect ratios $\left(0.1\le D/H\le 0.4\right)$, three outlet vent opening locations ($\left(S_o=0\right)$ left, ($S_o=\left(H/2-D/2\right)$) middle, and ($S_o=\left(H-D\right)$) right), sinusoidal offset temperature (${\theta }_o=0.5$, $1$), frequency ($f=1, 3, 5$), and amplitude ($A=0-1$), were examined. The results demonstrate that flow and heat transfer fields are impacted mainly by these parameters. Streamlines are more intensified at the upper-left corner when the outlet opening vent is shifted towards the right-corner upper wall. Fluid- and solid-phase Nusselt number increases $Re$, $D/H$, ${\theta }_o$, $A$, and $f$ are raised, specifically when $A\ge 0.3$. The Nusselt number remains constant when the frequency is raised from $3$ to $5$, definitely when $D/H\ge 0.25$. In uniform and non-uniform heating cases, the Nusselt number of both phases remains constant as the outlet port is shifted right for $Re\le 10$ and slightly for higher $Re$ as the outlet vent location is translated from left to right.

The heat exchanger is a device used to transfer heat energy between two fluids, hot and cold. In this work, an output feedback adaptive sliding mode controller is designed to control the temperature of the outlet cold water for plate heat exchanger. The discontinuous gain value of the sliding mode controller is adapted according to a certain adaptation law, where the only information required is the measurement of the outlet cold temperature. A sliding mode differentiator was design to estimate time derivative of outlet hot water temperature. Two constraints which imposed on the volumetric flow rate of the hot water (control input) were considered within the rules of the proposed adaptation law in this work. These are the control input is positive only and has a maximum value. For constructing the sliding variable, the outlet hot water temperature and its time derivative are required. The maximum allowable desired outlet cold water has been estimated as function of heat exchanger parameters and maximum control input. The simulation results demonstrate the performance of the proposed adaptive sliding mode control where the outlet cold water was forced to follow desired temperature equal to . Additionally, the robustness of the proposed controller was tested for the case where the cold inlet temperature is not constant. The results reveal the robustness of the proposed controller.

Practical applications such as solar power energy systems, electronic cooling, and the convective drying of vented enclosures require continuous developments to enhance fluid and heat flow. Numerous studies have investigated the enhancement of heat transfer in L-formed vented cavities by inserting heat-generating components, filling the cavity with nanofluids, providing an inner rotating cylinder and a phase-change packed system, etc. Contemporary work has examined the thermal performance of L-shaped porous vented enclosures, which can be augmented by using metal foam, using nanofluids as a saturated fluid, and increasing the wall surface area by corrugating the cavity’s heating wall. These features are not discussed in published articles, and their exploration can be considered a novelty point in this work. In this study, a vented cavity was occupied by a copper metal foam with $PPI=10$ and saturated with a copper–water nanofluid. The cavity walls were well insulated except for the left wall, which was kept at a hot isothermal temperature and was either non-corrugated or corrugated with rectangular waves. The Darcy–Brinkman–Forchheimer model and local thermal non-equilibrium models were adopted in momentum and energy-governing equations and solved numerically by utilizing commercial software. The influences of various effective parameters, including the Reynolds number ($20\le Re\le 1000$), the nanoparticle volume fraction ($0\%\le \phi \le 20\%$), the inflow and outflow vent aspect ratios ($0.1\le D/H\le 0.4$), the rectangular wave corrugation number ($N=5$ and $N=10$), and the corrugation dimension ratio ($CR=1$ and $CR=0.5$) were determined. The results indicate that the flow field and heat transfer were affected mainly by variations in $Re$, $D/H$, and $\phi$ for a non-corrugated left wall; they were additionally influenced by $N$ and $CR$ when the wall was corrugated. The fluid- and solid-phase temperatures of the metal foam increased with an increase in $Re$ and $D/H$. The fluid-phase Nusselt number near the hot left sidewall increased with an increase in $\phi$ by $\left(25–60\right)\%$, while the solid-phase Nusselt number decreased by $\left(10–30\right)\%$, and these numbers rose by around $3.5$ times when the Reynolds number increased from $20$ to $1000$. For the corrugated hot wall, the Nusselt numbers of the two metal foam phases increased with an increase in $Re$ and decreased with an increase in $D/H$, $CR$, or $N$ by $10\%$, $19\%$, and $37\%$. The original aspect of this study is its use of a thermal, non-equilibrium, nanofluid-saturated metal foam in a corrugated L-shaped vented cavity. We aimed to investigate the thermal performance of this system in order to reinforce the viability of applying this material in thermal engineering systems.

An ambit of enhancing heat transfer throughout thermal convection in a cavity is explored numerically in this study, contemplating the heat dispersal from a segmental heat source circumscribed in a square-vented porous cavity with a moving lid. The cavity can be used as a heat sink for electronic cooling, material processing, and convective drying. Aluminum $10$ PPI metal foam saturated by aluminum oxide–water nanofluid is occupied in this lid-driven vented cavity system. The bottom cavity wall is fully and partially heated by a heat source of specific length $L_H$, and the left wall and inlet fluid are kept at the same cold temperature, while the right wall and top-driven wall are thermally insulated. Thermal dispersion and local thermal non-equilibrium effects are included in an energy equation, and continuity and Darcy–Brinkmann–Forchheimer momentum equations are implemented and resolved by utilizing the finite volume method with the aid of a vorticity–stream function approach operation. The inspirations behind pertinent parameters, including the Reynolds number ($Re=10–50$), Grashof number ($Gr={10}^3–{10}^6$), inlet and outlet ports’ aspect ratio ($D/H=0.1–0.4$), outlet port location ratio ($S/H=0.25–0.75$), and discrete partial heating ratio ($L_H/L=0.25–1$) are scrutinized. The baseline circumstance corresponds to full-length heating $L_H/L=1$ and the outlet port location ratio $S/H=0.25$. The results reveal that the fluid and heat flow domains are addressed mostly via these specification alterations. For $Gr={10}^3$, increasing $Re$ from $10$ to $40$ does not alter streamlines or the isotherm field, but when $Re=50$ it is detected that streamlines increase monotonically. Streamlines are not altered when $L_H/L$ and $S/H$ are amplified but strengthened more when the opening vent aspect ratio is increased. A greater temperature difference occurs as $L_H/L$ is raised from $0.25–0.75$ and isotherms are intensified, and the thermal boundary layer becomes more distinct when $S/H$ is augmented. The average Nusselt number rises as $Re$, $Gr$, $L_H/L$, and $D/H$ are increased by about $30\%$, $3.5\%$, $23\%$, and $19.4\%$, respectively, and it decreases with $S/H$ amplifying is increased by around $5.5\%$.