In a previous work [5], we introduced the $G$-transform. This is a generalized Laplace-type integral transform defined by $G(f) = u^{\alpha} \int_{0}^{\infty} e^{-t/u} f(t) \, dt$. This integrates the Laplace, Sumudu, and Elzaki transforms within a single framework parameterized by an integer $\alpha$. The present paper extends this framework to fractional differential equations (FDEs), which are directly applicable to anomalous heat and mass transfer. Many transport phenomena in porous media, nanofluids, and biological tissues deviate from classical Fourier-Fick behavior and are more accurately modeled by time fractional equations involving the Caputo derivative. First, we derive the formula for the $G$-transform for the Caputo fractional derivatives. This formula for the order $\beta \in (0, 1]$ maintains a net algebraic structure similar to classical differential formulas (an extension to $1 < \beta \le 2$, covering the second initial condition $f’(0)$, is given as Corollary 2.4). By applying these results, we solve the time-fractional differential heat conduction equation and the time-fractional mass diffusion equation, demonstrating that the $G$-transform provides an integrated and computationally efficient tool for these problems regardless of the choice of $\alpha$. The parameter $\alpha$ can be adjusted to minimize computational complexity for specific problem types, and we show that choosing $\alpha = -1$ is particularly convenient for fractional relaxation transport equations. Finally, we note that the same fractional relaxation equation underlies fractional-order gradient descent in machine learning, giving a direct bridge between the heat-transfer framework developed here and AI optimization dynamics.
The need for high thermal performance and compact design of heat exchangers in modern energy and industrial systems is prompting current studies in passive heat transfer enhancement techniques. This study investigated, for the first time, the effect of using elliptic-conical tubes on hydrothermal performance compared with traditional straight-circular tubes under identical operating conditions. A well-validated three-dimensional computational fluid dynamics (CFD) model with the shear-stress transport (SST) $k$-$\omega$ turbulence model is used to resolve the turbulent flow and heat transfer characteristics for both elliptic and conical tubes. The Nusselt number $(Nu)$, friction factor $(f)$, and the performance evaluation criterion (PEC) are determined over a Reynolds number $(Re)$ range of 5,000-50,000. The main focus of the study is to evaluate the influence of different diameter ratios $(DR)$ “1, 1.25, 1.5, 1.75 and 2” on these hydrothermal performance parameters. The findings reveal that, at $DR = 2$ and $Re = 50,000$, the elliptic-conical tubes achieve a 43.5% enhancement in the Nusselt number compared to the traditional straight-circular tube. The results confirm that the elliptic-conical tube configuration provides an effective and promising enhancement in thermal performance, with an optimum design at a diameter ratio of 1.5, for which a maximum PEC of 1.206 is achieved at $Re = 50,000$. The results prove that the elliptic-conical tubes offer a more beneficial hydrothermal performance than straight-circular tubes, especially at high Reynolds numbers. These outcomes encourage the use of elliptic-conical tube geometry in proficient, high-performance heat exchangers.
This study aims to compare the exhaust gas flow velocity and pressure among three types of exhaust systems: free flow, HPLPM, and AHLM. The method of research employs comparative analysis using Computational Fluid Dynamics (CFD), with uniform testing parameters applied to all exhaust variants. The analysis results show that the free flow exhaust achieves an average flow velocity of 76.313 m/s and an average pressure of 1.814 kPa. The best-performing AHLM exhaust records a flow velocity of 58.491 m/s with an average pressure of 11.405 kPa, while the best-performing HPLPM exhaust yields an average flow velocity of 58.534 m/s and an average pressure of 12.250 kPa. Based on these findings, it can be concluded that the AHLM exhaust offers better performance than the conventional HPLPM exhaust and delivers results that closely approach the performance of the free flow exhaust system.
This work presents an analysis of the transient heating of a thin circular plate by a small spherical thermal radiant source, assuming a uniform temperature distribution over the plate. The mathematical model is obtained by integrating the governing equations over the plate, assumed here to be gray, and by considering a punctual thermal radiant source represented as a spherical black body. The resulting mathematical model consists of a nonlinear ordinary differential equation that admits an exact solution, explicitly providing time as a function of temperature.
The article examines unstable Magnetohydrodynamics (MHD) transfer of a Casson fluid by advection within a rotating porous medium. The flow occurs over an inclined plate characterized by transverse oscillations, variable surface temperature, and mass diffusion. The mathematical model accounts for the concurrent influences of radiant, generating heat or utilization within the system and first order chemical reactions. We applied Crank-Nicolson finite difference with Thomas algorithm to make nondimensionalize the governing equations and derive their solutions analytically. The numbers indicate that fluid velocity decreases as the inclination angle, magnetic parameter, radiation parameter, Prandtl number, Schmidt number, and chemical reaction parameter increase. On the other hand, it goes up when the thermal and solutal Grashof numbers and the heat source parameter go up. As the radiation and heat generation parameters go up, so does the temperature distribution. But as the Prandtl number goes up, the temperature distribution goes down. Additionally, the concentration profile decreases as the Schmidt number and chemical reaction parameter increase. This is because the mass diffusivity goes down and the chemical interaction gets stronger.
The two-dimensional heat equation is a mathematical model used to describe the process of heat diffusion in a medium over space and time. This equation is a parabolic partial differential equation frequently employed in various fields of science and engineering. This study aims to analyze exact solutions and compare them with numerical solutions using explicit finite difference schemes and the Crank-Nicolson scheme for the two-dimensional heat equation. Exact solutions were obtained using the method of separation of variables, yielding a sine Fourier series form while accounting for the initial and boundary conditions on a rectangular domain. Subsequently, the heat equation was discretized using finite difference methods with forward differences in time and central differences in space, yielding the explicit scheme and the Crank-Nicolson scheme. The results of the numerical simulations show that both numerical methods are capable of approximating the exact solution with a very small error. The explicit method has a simpler computational procedure but requires certain stability conditions regarding the time step, whereas the Crank-Nicolson scheme is unconditionally stable and has a good level of accuracy. Based on the comparison results, both methods provide results that are very close to the exact solution, so the finite difference method can be used effectively in solving two-dimensional heat equations.
Heat sinks are highly efficient devices for cooling and thermal management of electrical and electronic components. Heat sinks are typically installed with the fins oriented upwards to facilitate heat exchange with the surrounding environment. In practice, there are cases where heat sinks are installed with the fins facing downwards, which negatively affect the heat transfer and reduce cooling efficiency. This paper presents the experimental results of evaluating the heat transfer performance of a flat-fin heat sink with a base composed of combined aluminum and copper materials under downward-facing fin conditions. The results show that when the base temperature of the heat sink is 90C, the natural convection heat transfer coefficient of the aluminum based, aluminum based with 1 mm copper layer, and aluminum based with 2 mm copper layer are 3.66, 3.83, and 4.14 W/m2.K, respectively. The addition of a copper layer to the heat sink base improves the thermal conductivity of the base and enhances the natural convection heat transfer performance of the heat sink to the surrounding environment.
This study focused on a drying technical problem of heat and mass transfer in infrared radiation (IR) assisted heat pump (HP) drying of holy basil leaves. The experimental drying of holy basil leaves was carried out to evaluate the effect of IR power on drying rate and heating rate of drying process. The experimental drying was carried out with drying air temperature of 45°C, drying air velocity of 2.0m/s and IR power of 0, 300 and 350W, in which, the HP-only drying mode corresponds to drying mode at IR power of 0W. The experimental drying results showed that the drying rate and heating rate of IR assisted HP drying method could be improved significantly due to the support of IR heating mechanism. The drying mode at IR power 350W obtained the highest drying rate with the shortest drying time of 90 minutes, followed by IR power 300W with drying time of 120 minutes and the HP-only drying mode got the lowest drying rate with drying time of 210 minutes. The IR assisted HP drying mode at IR power 350W and 300W attained the high heating rate with the time duration required for the drying material to reach the drying temperature being about 30 and 40 minutes, respectively, while the HP-only drying mode required about 190 minutes for the drying material’s temperature to reach near drying air temperature value. Besides, the heat and mass transfer equations in IR assisted HP drying process have been established and solved numerically by Matlab software. Statistical comparison between predicted data (the results of numerically solving the heat and mass transfer equations) and experimental drying data was also performed. The statistical analysis results affirmed that the predicted data could be used for predicting the experimental data accurately. Received: December 20, 2025Accepted: February 9, 2026
Steam power plants play an important role in supplying Indonesia’s electricity needs. Steam turbine efficiency is one of the key factors affecting the performance of coal-fired steam power plants. This study aims to analyze the turbine heat rate of the XXX-steam power plant Unit-X based on performance test data obtained before and after an overhaul. The main parameters analyzed include Turbine Heat Rate and High Pressure (HP)-turbine efficiency. Data collection was carried out through a performance test conducted on April 24, 2024 (before overhaul) and July 9, 2024 (after overhaul). The results of the analysis show that the Gross Turbine Heat Rate decreased from 7661.68 kJ/kWh to 7570.63 kJ/kWh after the overhaul, which indicates an increase in energy efficiency. However, the HP turbine efficiency decreased from 83.62% before the overhaul to 82.82% after the overhaul. This is due to time degradation that was not resolved by a simple inspection.
Melting effects on steady, two-dimensional mixed convection flow over a vertical surface embedded in a saturated porous medium are numerically investigated for a hybrid nanofluid consisting of copper (Cu) and alumina $\text{(Al}_2 \text{O}_3)$ nanoparticles dispersed in water. The analysis focuses on the assisting flow regime, where buoyancy forces support the external stream. The governing boundary layer equations are formulated and reduced to a coupled system of nonlinear ordinary differential equations using similarity transformations. The resulting boundary-value problem is solved using a shooting scheme implemented in Maple. Numerical results illustrate the influence of the melting parameter, mixed convection parameter, and nanoparticle volume fractions on the velocity and temperature fields, as well as the skin friction coefficient and local Nusselt number. The findings show that assisting buoyancy intensifies the flow and enhances the surface heat transfer rate. In contrast, increasing the melting parameter alters the melt-induced transpiration at the wall, which thickens the momentum boundary layer and reduces the skin friction coefficient, while the velocity field may increase depending on the buoyancy strength.
To address the difficulty of accurately acquiring transient temperature responses at the surface and near-surface region of friction pairs, a shallow subsurface temperature measurement method based on shallowly embedded fine thermocouples is proposed. In this method, NiCr and constantan wires with a diameter of 0.025 mm are used to fabricate E-type fine thermocouples. By combining electrolytic etching and arc-discharge welding, the size of the sensing junction is controlled to approximately 0.02 mm, thereby improving the sensor’s response capability to transient temperature rise. Metal films with a thickness equal to the shallow subsurface depth are covered above the thermocouple to establish equivalent measurement depths between the friction surface and the sensing junction, thus enabling indirect characterization of the shallow subsurface temperature response of the friction pair. To evaluate the performance of the measurement system, static calibration tests and laser step dynamic response tests were carried out for the fine thermocouples. The results show that, after electrolytic etching, the negative-step time constant of the thermocouple decreases from 53.350 ms in the unetched state to 17.338 ms, representing a reduction of approximately 67.5%. This indicates that tip refinement can significantly reduce the thermal inertia of the sensing junction and improve the dynamic response speed. Furthermore, feasibility verification was conducted on a pin-on-disc friction test platform. Under the conditions of a normal load of 30 N and a rotational speed of 0.0785 m/s, the shallowly embedded fine thermocouple produced a clear transient temperature response signal when the friction pin passed over the measurement point. The results demonstrate that the proposed method has the advantages of simple structure, rapid response, and convenient synchronous acquisition. It can be applied to shallow subsurface temperature measurement of friction pairs and provides an experimental basis for analyzing the generation, transfer, and evolution of frictional heat in the near-surface region.
To investigate the effect of inclination angle on saturated pool boiling heat transfer, two correlations are proposed for evaluating the heat transfer coefficient and enhancement factor. The study focuses on a stainless steel tube forming a partial annular space and immersed in water at atmospheric pressure. To enhance heat transfer by promoting fluid motion, one side of the annular space was sealed, allowing fluid to enter and exit only through the open end. A total of 301 experimental data points were collected, and two correlations were developed using the least-squares method. These incorporate the annular gap size, inclination angle, and heat flux. The results confirm that the proposed correlations predict the experimental data within a ±10% accuracy range.
This study investigates the transient thermoelastic response of a three-dimensional homogeneous isotropic half-space subjected to transient thermal shock using a fractional-order generalized heat conduction model. The formulation is based on the Lord-Shulman generalized thermoelastic theory, in which a fractional-order time derivative is introduced in the heat equation to account for memory and non-local effects in heat propagation. The coupled governing equations are solved analytically by applying the Laplace transform with respect to time and the double Fourier transform with respect to spatial variables, yielding closed-form expressions for temperature, displacement, and stress fields. Numerical results obtained for a copper material show that temperature decreases monotonically with depth and that increasing the fractional order leads to faster thermal diffusion. The displacement field exhibits a non-linear profile, reaching a maximum within the medium due to thermoelastic expansion before gradually decaying, while higher fractional orders result in larger peak displacements because of enhanced heat penetration. The stress field is maximum near the thermally shocked surface and decays rapidly with depth, with lower fractional orders producing slower stress relaxation, indicating stronger memory effects in the material. The results smoothly converge to the classical Lord-Shulman model as the fractional order approaches unity, confirming the physical consistency of the formulation. The proposed fractional model provides a more realistic description of thermoelastic behaviour under rapid thermal loading and is relevant to engineering applications such as aerospace structures, nuclear components, and micro-scale thermal systems where classical heat conduction models may not be adequate.
The objective of this study is to develop an advanced model of heat transfer in solids, with a particular focus on applications relevant to the built environment. The proposed framework extends the Dual Phase Lag (DPL) model, providing a comprehensive description of temporal temperature variations, energy flux, and relaxation time required to achieve thermal equilibrium in solid materials. In this approach, the solid is conceptualized as a pulsating thermal string, wherein oscillatory behavior represents temperature fluctuations. The resulting formulation yields an analytical three-dimensional heat transfer equation, the solutions to which are determined by specified boundary and initial conditions. Furthermore, the study introduces the concept of equivalent length, defined according to the intrinsic properties of each material.
This work illustrates the effect of thermal interaction between points located in a thin shell due to heat transfer by thermal radiation. Simple situations are employed to provide explicit comparisons between the temperatures of the plate and the shell with the same heat supply. The temperature increase caused by re-emission and reflection effects due to the non-convexity of the shell is shown. Received: March 22, 2026Accepted: April 2, 2026
Nanofluids have attracted considerable interest in recent years due to their superior thermal properties, evolving from mono-nanofluids and bi-nanofluids to the latest tri-hybrid nanofluid model. This study aims to investigate the significant potential for water-based Williamson tri-hybrid nanofluid specifically for cooling application system in solar energy systems. To achieve the aim, a mathematical model is developed by applying similarity transformation to simplify the governing partial differential equations (PDEs) into dimensionless ordinary differential equations (ODEs). These equations are then solved using the Runge-Kutta-Fehlberg-45 (RKF45) method encoded in MAPLE software. As the Williamson parameter increases, the temperature profile increases. In contrast, the temperature profile decreases with increasing values of the magnetic parameter and injection parameter. Comparative analysis demonstrates that the tri-hybrid nanofluid provides a consistently highest thermal profile compared to mono-nanofluid and bi-nanofluid. It shows an increase of 8% in peak performance for dimensionless temperature compared to the mono-nanofluid model. Furthermore, it was observed that as the Prandtl number $(Pr)$ increases, the thermal boundary layer thickness decreases from mono-nanofluid to tri-hybrid nanofluid. This finding is highly beneficial for the thermal management and renewable energy industry which helps provide a more dependable framework for optimizing the cooling efficiency specifically for producing high-performance solar panel cooling system.
The determination of airflow rate in a fluidized bed drying system is a critical requirement in fluidized bed drying operations, as it directly governs the fluidization regime and the efficiency of heat and mass transfer, particularly for high-quality agricultural products. This study developed and evaluated an experimental airflow measurement system using a cluster of three ISA 1932 standard nozzles integrated into a rectangular plenum chamber. The system’s performance was investigated across a fan operating frequency range of 20 Hz to 60 Hz. Airflow rates calculated from differential pressure $(\Delta p)$ at eight different static pressure tapping positions were cross-validated against reference values derived from duct centerline velocity measurements. Experimental results demonstrate a strong linear correlation between fan frequency and airflow velocity, consistent with centrifugal blower characteristics. The relative error between the two measurement methods fluctuated between 5.94 % and 24.31 %. Notably, the highest precision (error < 10 %) was consistently achieved at higher operating frequencies (55 – 60 Hz) and specifically at tapping positions 4 and 5, located toward the lower boundaries of the plenum chamber. This study identified an optimal pressure tapping configuration, demonstrating that while the multi-nozzle arrangement is a viable method for extending measurement ranges, accuracy is highly sensitive to the spatial location of the taps. To achieve optimal measurement accuracy, the static pressure taps were strategically positioned at the lower edges of the plenum chamber, where flow redistribution was most stable and less affected by localized turbulence. These findings provide a technical foundation for optimizing drying kinetics and enhancing energy efficiency in post-harvest processing.
Due to the flow path constraints of the lubrication oil cooling system on the NY6240ZJA diesel engine, the oil cooler is positioned downstream of the oil filter. This configuration poses a potential risk to the lubrication system. To prevent debris in the piping and heat exchanger from entering the main oil gallery, installing a filter element at the oil cooler outlet has been identified as an effective countermeasure. However, the addition of such filter element significantly increases the flow resistance on the oil side. It is therefore necessary to investigate the feasibility of their installation and to characterize the resistance behavior of filter element with specific mesh sizes. This paper presents an experimental investigation into the resistance characteristics of filter element with varying mesh numbers under different temperature conditions. The results indicate that, regardless of the oil temperature, the strainer - due to its limited flow area - induces an excessive system pressure drop and restricts the flow rate, thereby preventing the system from achieving the rated flow. During a temperature sweep from 50°C to 90°C, the flow-resistance characteristics of filter element with different mesh sizes were systematically measured. The experimental results demonstrate that with the filtration devices installed, the pressure drop increases with higher mesh numbers and higher flow rates, and decreases with rising oil temperature. An empirical correlation for the resistance coefficient of the filter element was derived. The findings of this study provide valuable reference data for the process improvement of the lubrication oil cooling system and the design of oil coolers for the NY6240ZJA diesel engine.
Bile movement obstruction is a common severe disease in people. This study aims to find the effects of stenosis on the peristaltic transport of bile fluid within an inclined duct of permeable nature. This is a bile transport application through an inclined channel (duct) with calculus and stenosis. Bile flow is examined from a wave frame of reference that travels with the wave speed. In this investigation, equations for continuity and motion are developed for theoretical analysis, and the equations so formed are solved under the assumption of a less Reynolds number value, long wavelength, along with a non-dimensionalization process. The study examines the velocity profile, pressure gradient, and pressure rise, with a specific emphasis on the permeability parameter, amplitude ratio, gravity parameter, angle of inclination, and height of stenosis. The findings indicate that the velocity component of bile in the axial direction diminishes for the increasing permeability parameter and the height of the stenosis, with respect to axial distance.
This study is part of an effort to improve the performance of photovoltaic panels by focusing on predicting surface soiling losses and evaluating the effect of dew water cleaning on glass transmittance. The experiments were conducted in Takaddoum-Rabat (Morocco) on three glass samples subjected to different conditions, including an uncleaned sample (i), a sample cleaned with tap water (ii), and a sample cleaned with dew water (iii). Transmittance measurements showed that dew water significantly reduces soiling losses on glass treated with dew at a variable angle compared to uncleaned glass. The study also analyzed the influence of meteorological parameters such as temperature, relative humidity, wind speed, and clearness index to examine their correlation with soiling losses. The results indicate a complex interaction between these parameters and soiling dynamics. Statistical modeling based on the backward stepwise selection method resulted in a highly predictive model, with a coefficient of determination $(R^2)$ of 93.86%. The analysis revealed that relative humidity and clearness index are key factors, with higher values associated with reduced soiling losses. This study enhances the understanding of the mechanisms affecting photovoltaic performance and provides insights for more efficient and sustainable solar solutions.
