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In this research, experimental investigation of the coefficient of the heat transfer has been conducted for a set of rectangular fins with different fin height, 0.27, 0.47 and 0.67 m at air velocity test points of 1.1, 1.3, 1.5, 1.7 and 2 m/s, to meet the Reynolds number (Re). Thirty samples from the two cases with changing fin positions were studied to verify the thermal performance of the system. The study was conducted based on the cross-sectional diameter of 21167, 25016, 28864, 32713, and 38486. Total heat flux in all tubes has been settled as 26.3, 58, and 88.7 W/m2. The experimental results showed that the temperature difference between the surface of the block and flowing air increases with increasing Reynolds number for all heat flow states.

Assessing the energy performance of building components with enclosed airspaces requires accurate determination of the thermal resistance ( R-value) of the airspaces. The R-value of enclosed airspace depends on its size and orientation, direction of heat transfer through the airspace, and temperatures and emissivities of all surfaces that define the airspace. In previous studies, practical correlations were developed to determine the R-values for vertical enclosed airspaces, horizontal enclosed airspaces with upward heat flow and downward heat flow, and 30° and 45° sloped-enclosed airspaces with downward heat flow. However, to the authors’ best knowledge, there is no such practical correlations available to determine the R-values for wide ranges of dimensions and operating conditions for 30° and 45° sloped-enclosed airspaces with upward heat flow. This paper focused on the thermal performance of 45° sloped-enclosed airspaces with upward heat flow, and the predicted R-values were compared with the R-values provided in ASHRAE Handbook of Fundamentals at different conditions. The dependence of the R-value on the aspect ratio of the enclosed airspaces was also investigated. As well, considerations were given to quantify the potential increase in the R-value of enclosed airspace when a thin sheet having different values of emissivity on both sides was placed in the middle of the airspace. The results showed that depending on the value of the effective emittance and the thickness of the airspace, the R-value could be tripled by incorporating thin a sheet in the middle of the enclosed airspace. Finally, practical correlation were developed to determine the effective R-values of 45° sloped-enclosed airspaces with upward heat flow for wide ranges of aspect ratio, temperature difference across the airspace, mean temperature, and effective emittance. The results showed that the calculated R-values using this correlation were in good agreement with the predicted R-values.

Convective heat transfer through a vertically multilayered porous media is examined numerically. The examination is focused upon the effect of the temperature. Flow fields and different regimes of the heat flow. The study was done on a model with vertical isothermal walls at different temperatures and horizontally perfect insulated walls, and for three layered porous medium in which the first and third layers have equal thicknesses and permeabilities. The numerical results are reported for a range of the permeability ratio of the inner sub-layer 0.1 1, the –ve is for the case of kr

Discrete fracture network (DFN) is an effective means of describing the coupling of heat flow in an underground fractured rock mass. In this paper, an improved DFN is proposed by introducing the correlation function of fracture trace length and aperture, which is more consistent with the real fracture data. Next, based on the improved model, the influence of fracture roughness on the fluid flow and heat transmission was evaluated, and the relationship between the fracture aperture and the joint roughness coefficient (JRC) is established. Finally, based on the exponential function between confining pressure and aperture, the influence of confining pressure on the heat‐flow coupling process is considered in the improved model. Besides, the reliability of the model was verified by comparing with the analytical solution of the two‐dimensional single‐fracture heat‐flow coupling problem. The results show that under the same conditions, considering the correlation between the geometric parameters of the fracture, the seepage and heat transfer rates of the model increased, the outlet boundary flow reached the maximum value, and the average outlet temperature dropped rapidly. However, the fracture roughness reduces the outlet flow rate and the decline rate of average temperature. The confining pressure will lead to a decrease of about 3.5% in the outlet flow of the model, which is consistent with the seepage law in practical engineering. The model presented in this paper is an effective supplement to the two‐dimensional fracture network heat‐flow coupling model and can provide a theoretical basis and a numerical calculation tool for related underground rock mass engineering.

An analytical thermal model to predict the peak temperature in silicon-on-insulator (SOI)-FinFET-like structures is proposed. The device is divided into two regions based on two separate heat flow paths and each region is analyzed and modeled independently to estimate the corresponding peak temperature. Later both the models are combined to obtain the peak temperature for the device. The temperature dependence of thermal conductivity of the semiconductor material is considered in the model. Modeling results show a high level of correlation with the 3-D COMSOL and electrothermal TCAD simulation for practical range of device dimensions and power densities. Finally, the model is validated with experimental data.

Lubrication and cooling performances of face gears with oil–jet lubrication are closely related to the nozzle layouts. To investigate the influence of the nozzle layouts on the lubrication performance of the face gears, a numerical analysis method based on heat-flow coupling is adopted in this study for predicting the transient temperature characteristics. First, a mathematical model of impingement depth integrating the nozzle spatial layouts, injection parameters, and geometric parameters of the given face gear is presented for determining the nozzle. Then, after accessing the friction heat, the heat-flow-coupled finite element model is built to resemble the oil–jet lubrication process and obtain the temperature field on the tooth surface. Finally, under the same nozzle layouts, the temperature distributions are compared with the oil pressure and oil volume fraction reported in previous studies. The results reveal that the nozzle layouts significantly affect lubrication performance. Specifically, the lubrication performance of the lateral layout parameter near the middle point of the tooth width is better, and there is a certain range for the longitudinal layout parameter and jet elevation angle. This study can provide a reference for further optimizing the nozzle layouts and prolonging the service life of the orthogonal face gear.

The present study investigates the effects of material discontinuities and thermal resistances on the temperature reconstruction and heat flux evaluation via an inverse heat transfer method in hype...

In the present work, a mathematical model was formulated to propose a relationship between the heat flow in thermoelectric material and other physical and thermophysical parameters. The proposed model identifies the dominating factors affecting the heat flow as a function of temperature. This model was validated with various materials to get the trends of variation of heat flow and efficiencies of different thermoelectric materials. The results of the model are in close agreement with the experimentally observed trend in the published works. The model proposed in this work emphasised distinct approach in approximating overall heat flow performance and establishing intrinsic heat flow characteristic of the thermoelectric material.

This study reports on a mathematical model for predicting the fluid and heat flow characteristics of a Z-shaped corrugated foam heat sink. Experiments were carried out to validate local as well as ...

A new method for improving the calculation of the linear conductances of components for lumped parameters thermal models is presented. The here called Conductance Matrix Fitting (CMF) method is based on the generation of a detailed lumped thermal model of the component. After setting-up the detailed model, it is condensed to create a reduced model. The unknown conductances of the reduced model are automatically calculated by correlating the temperature and heat flow of the reduced model with the results of the detailed model. The conductances of the component determined in this way can be used in the modelization of the complete device. A method to determine the temperature uncertainties of the reduced model, compared to the detailed one, is also presented. Finally, the method is validated using a one-dimensional example, and is applied to a real case in the context of the ESA Solar Orbiter mission.

The paper discusses existing models used to estimate the thermal conductivity of the soil medium. The considerations are divided into three general sections. In the first section of the paper, we focus on the presentation of empirical models. Here, in the case of Johansen method, different relations for Kersten number are also presented. In the next part, theoretical models are considered. In the following part, selected models were used to predict measured thermal conductivities of coarse- and fine-grained soils, at different water contents. Based on these predictions as well as on the authors’ experience, a critical assessment of the existing models is provided. The remarks as well as advantages and disadvantages of those models are summarized in a tabular form. The latter is important from a practical point of view; based on the table content, one can simply choose a model that is suitable for the particular problem.

The heat motion in a one-dimensional semi-infinite chain of coupled harmonic oscillators is studied for the Maxwell distribution of initial velocities and zero initial displacements of the chain particles. It is believed that such initial conditions are achieved by an impulse heating of the sample. Exact analytical expressions for the state correlation functions, local temperature, and local heat current of the chain are obtained.

To address the coal gangue fracture heat transfer problem, the law of heat transfers and temperature distribution in the coal gangue fracture is studied. The temperature distribution in a coal gang...

We studied the non-isothermal flow of an incompressible viscous fluid through a porous tube. Motivated by filtration problems, Darcy’s law was incorporated on the walls of the tube and the flow was pressure driven. The main goal was to investigate the thermodynamic part of the system, assuming that the hydrodynamic part is known. In view of the applications we wanted to model, the fluid inside the tube was supposed to be cooled (or heated) by the surrounding medium. Using asymptotic analysis with respect to the small parameter (being the ratio between the tube’s thickness and its length), we constructed the explicit second-order approximation for the temperature distribution of the fluid. Numerical examples are provided to compare the obtained solution with the one derived for a rigid tube and also to show the corrections due to higher-order terms.

The results on the distribution of heat flows coming to the refractory plate of a hypersonic aircraft moving at different distances from the Earth's surface with cosmic velocities are obtained. The results of studies related to the study of phase transitions in the wall boundary layer occurring during the flow of hypersonic flow ablating surface are presented. The influence of the catalytic wall on the heat flow is considered. The main attention is paid to the analysis of the surface entrainment of high-speed aircraft, based on a detailed account of the mechanism of heterogeneous catalytic reactions in the conditions of surface mass transfer. The temperature distribution over the thickness of the boundary layer at the critical point of a blunted body with a refractory coating for a particular section of the flight path is given. Mass entrainment from the surface of crystalline refractory bodies is determined. Ill. 7. Ref. 16.

The physical process of energy transfer in the form of a certain amount of heat from a body with a higher temperature to a body with a lower temperature until the onset of thermodynamic equilibrium is a continuous process and is present in many areas of human activity. Determining the surface heat flux density makes it possible to measure and control the thermal processes of almost any object made of different materials, as well as substances in order to assess their condition. Based on a theoretical review, the article analyzes the current state to determine the critical value of the surface heat flux density depending on environmental conditions. Based on statistics and arrays of fire cards, it was concluded that every fourth fire in Ukraine can spread to adjacent buildings and structures, process equipment and natural ecosystems by spreading thermal energy with subsequent ignition. The authors consider the concept of heat flux and the concept of heat flux density, as well as define the essence of the concept of critical surface heat flux density as characteristics of heat flux. Scientists conducted a detailed analysis of literature sources, regulations and other sources of information related to this topic. Based on the research, the authors analyzed and found that the value of the surface heat flux density significantly depends on environmental conditions, namely the introduction of finely divided water into the space where the heat process and wind exposure. The authors found that to assess the value of the critical surface heat flux density, it is advisable to use the sign of flame combustion of substances and materials for the criterion base. However, to date there is no statistical base of critical values of surface heat flux density for various substances and materials, in particular those that can be used in the decoration of buildings and technological installations. The article analyzes modern approaches to determining the parameters of heat flux, as well as identifies some differences in these approaches, which allowed to formulate the purpose and relevance of further research, and identifies the main tasks to be achieved to achieve this goal.

This research numerically studies the transient cooling of partially liquid magma by natural convection in an enclosed magma chamber. The mathematical model is based on the conservation laws for momentum, energy and mass for a non-Newtonian and incompressible fluid that may be modeled by the power law and the Oberbeck–Boussinesq equations (for basaltic magma) and solved with the finite volume method (FVM). The results of the programmed algorithm are compared with those in the literature for a non-Newtonian fluid with high apparent viscosity (10–200 Pa s) and Prandtl (Pr = 4 × 104) and Rayleigh (Ra = 1 × 106) numbers yielding a low relative error of 0.11. The times for cooling the center of the chamber from 1498 to 1448 K are 40 ky (kilo years), 37 and 28 ky for rectangular, hybrid and quasi-elliptical shapes, respectively. Results show that for the cases studied, natural convection moved the magma but had no influence on the isotherms; therefore the main mechanism of cooling is conduction. When a basaltic magma intrudes a chamber with rhyolitic magma in our model, natural convection is not sufficient to effectively mix the two magmas to produce an intermediate SiO2 composition.

The paper presents solutions for thermo-elasticity problems with an unsteady heat flow for various layered systems typical for Polish traffic categories KR4 and KR7. The tasks were solved assuming a plain strain case for material parameters, which in most cases were determined in a laboratory tests, under thermal type of loading, which simulates an extremely unfavorable weather condition. For the selected structural variants, the resulting stress state was analyzed in relation to the determined tensile stress limits for individual mixture materials. In half analyzed cases, exceeding the material tensile strength in second layer (L2) was observed only as a result of the decreasing temperature.

The Xiong’an New Area is located at the western Bohai Bay Basin, 150 km south of Beijing, China. The area has tremendous high heat flow value within the sedimentary layer, and the average value can reach 90 mW·m-2 within the Niutuozhen Uplift. However, combining the basal heat flow at the top of the metamorphic layer with the heat flow value which was contributed by the radiogenic heat production from the overlying formation, the surface heat flow value was only 65.1 mW·m-2 in this area. Thus, the heat flow value within the sedimentary layer was greatly influenced by other factors. In this study, based on the continuous temperature measurements data from 4 boreholes, thermos-physical parameters (conductivity, radioactive heat production, density, and heat capacity) from 90 rock sample measurements, and the regional stratigraphic development, a two-dimensional thermal-hydraulic modelling was carried out to study the influence of the heat refraction and groundwater convection on the heat flow value. According to calculation results, the heat flow disturbance caused by heat refraction was 10 mW·m-2, and the disturbance value was 20 mW·m-2 for the groundwater convection. Furthermore, when the high-permeability layer thickness was a certain value, with the increasing high-permeability layer buried depth, the influence of the groundwater convection on the temperature field which was used for the heat flow calculation became weak. While when the high-permeability layer buried depth was set up, the influence of the groundwater convection on the above temperature field became stronger with the increasing high-permeability layer thickness.

In this study, the exact transient differential equation was used to calculate the convection heat loss in a heat sink with a rectangular cross section fin. The result of the analytic solution was compared to the result from experiments conducted on a standard heat sink. The experiments were performed at a constant heat flow of 9000 W/m2 and a low airflow rate ranging from 12 to 100 cm3/s in seven steps. The comparative results showed that while there was good agreement between the experimental result and the exact solution, the average error ratio increased with an increase of the airflow rate. However, the maximum average error ratio between the experimental result and the exact solution did not exceed 6.4%. The maximum temperature distribution in the heat sink was obtained at a time of 900 s in all experiments.

This paper concerns the problem of the analysis of properties of the components of a heat flow path in forced cooling systems. Using classical compact thermal model, thermal properties of selected configurations of such systems are characterized. The influence of selected factors on thermal resistances and thermal capacitances occurring in this model are analyzed. Some analytical formulas describing these dependences are proposed. The practical usefulness of these formulas is verified experimentally for selected configurations of forced cooling systems.

SUMMARY Previous geodynamic studies have indicated that the presence of a compositionally anomalous and intrinsically dense (CAID) mantle component can impact both core heat flux and surface features, such as plate velocity, number and size. Implementing spherical annulus geometry mantle convection models, we investigate the influence of intrinsically dense material in the lower mantle on core heat flux and the surface velocity field. The dense component is introduced into a system that features an established plate-like surface velocity field, and subsequently we analyse the evolution of the surface velocity as well as the interior thermal structure of the mantle. The distribution and mobility of the CAID material is investigated by varying its buoyancy ratio relative to the ambient mantle (ranging from 0.7 to 1.5), its total volume (3.5–10 per cent of the mantle volume) and its intrinsic viscosity (0.01–100 times the ambient mantle viscosity). We find at least three distinct distributions of the dense material can occur adjacent to the core–mantle boundary (CMB), including multiple piles of varying topography, a core enveloping layer and two diametrically opposed provinces (which can on occasion break into three distinct piles). The latter distribution mimics the morphology of the seismically observed large low shear wave velocity provinces (LLSVPs) and can occur over the entire range of CAID material viscosities. However, diametrically opposed provinces occur primarily in cases with CAID material buoyancy numbers of 0.7–0.85 (corresponding to contrasts in density between ambient and CAID material of 130 and 160 kg m−3, respectively) in our model (with an effective Rayleigh number of order 106). Steep and high topography piles are also obtained for cases featuring buoyancy ratios of 0.85 and viscosities 10–100 times that of the ambient mantle. An increase in relative density, as well as larger volumes of CAID material, lead to the development of a core enveloping layer. Our findings show that when two provinces are present core heat flux can be reduced by up to 50 per cent relative to cases in which CAID material is absent. Surface deformation quantified by Plateness is minimally influenced by variation of the properties of the dense material. Surface velocity is found to be reduced in general but mostly substantially in cases featuring high CAID material viscosities and large volumes (i.e. 10 per cent) or buoyancy ratios.

Heat flow for laminar mixed convection in a triangular enclosure with uniformly heated bottom wall is solved using Galerkin weighted residual method of finite element formulation. A fluid with Prandtl number (Pr = 0.71) is also used to investigate the effects of heat flow for Reynolds number(40 ≤ Re ≤ 110) varying Rayleigh number (103≤ Ra ≤ 104) in that enclosure. In the enclosure, the left wall is considered cold; bottom wall is uniformly heated while the other inclined wall is insulated. The geometry of physical problems is represented mathematically by different sets of governing equations along with appropriate boundary conditions. Results are shown in terms of streamlines, isotherms, average Nusselt number and average temperature of the fluid in the cavity for uniform heating of bottom wall. It is seen that heat transfer rate from the heat source is higher for increasing value of Re. On the other hand, average bulk temperature declines significantly. It is also indicated that for fixed Prandtl number and various Ra, the buoyancy force and heat transfer rate inside the enclosure are increased for the greater value of Re. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 27-43

We suggested a new approach for describing heat transfer in thermosyphons and determining the characteristic temperatures. The processes of thermogravitation convection in the coolant layer at the lower cap, phase transitions in the evaporation zone, heat transfer as a result of conduction in the lower cap are described at the problem statement. The main assumption, which was used during the problem formulation, is that the characteristic times of steam motion through the thermosyphon channel are much less than the characteristic times of thermal conductivity and free convection in the coolant layer at the lower cap of the thermosyphon. For this reason, the processes of steam motion in the thermosyphon channel, the condensate film on the upper cap and the vertical walls were not considered. The problem solution domain is a thermosyphon through which heat is removed from the energy-saturated equipment. The ranges of heat flow changes were chosen based on experimental data. The geometric parameters of thermosyphon and the fill factors were chosen the same as in the experiments (height is 161 mm, diameter is 42 mm, wall thickness is 1.5 mm, ε=4-16%) for subsequent comparison of numerical simulation results and experimental data. In the numerical analysis it was assumed that the thermophysical properties of thermosyphon and coolant caps do not depend on temperature; laminar flow regime was considered. The dimensionless equations of vortex, Poisson and energy transfer for the liquid coolant under natural convection and the equations of thermal conductivity for the lower cap wall are solved by the method of finite differences. Numerical simulation results showed the relationship between the characteristic temperatures and the heat flow supplied to the bottom cap of thermosyphon. The results of the theoretical analysis are in satisfactory agreement with the known experimental data.

The emergence of a reaction cycle in a mixture of reacting molecules may require naturalized regulation of the constituent material elements. One source of naturalized regulation could be sought in updating the constituent elements through exchanging with those available from the outside under the conditions of unidirectional heat flow. One physical vehicle for implementing constant material exchange could be a durable reaction cycle serving as a necessary precursor to the phenomenon called life. Each constituent element circulating around a durable reaction cycle moves causally until it comes to eventually leave the cycle. At the same time, the circulation is also retrocausal in letting the reaction flow in the downstream pull in and being cohesive to those reactants in the immediate upstream. The onset of a reaction cycle as a precursor to the origins of life must have corresponded to a unique historical event taking advantage of the likelihood of retrocausal cohesion propagating backward along the reaction sequence. Physical underpinning of biology may be found in the operation of retrocausal cohesion.

This article deals with the improvement of thermal efficiency of heating boilers with furnace wall waterflow. During one cycle in a PK-38 boiler the average level of the heat flow decreases by 25–30 %. The incident heat flux is measured with a thermal probe which, however, gives a large error in the measurement results. Experiments show that the error depends on the penetration of the thermal probe into the outer surface of thermal zone as well as on cavities in sealing the thermal probe, and different thermophysical properties of the latter and metal material of the heating surface. The accuracy of the measured parameters is affected by the thermal probe sealing. It is found that the distortion of temperature fields is more significant at the lower boundary of the thermal probe junction at frequently used sealing. Studies show that the waterflow leads to the restoration of local coefficients of thermal efficiency to the previous values. The obtained results can be used in boiler design and allow improving the measurement methods for thermal efficiency of heating boilers with furnace wall waterflow.

The solution of the problem of heat flow in heat exchangers from the surface of collective finning at different temperatures of its ends is given. The obtained analytical formulas allow us to quantify the influence of the asymmetry of the boundary conditions on the heat transfer through the finned heat exchange surface. Calculated dependencies can be used in the design of high-performance heat exchangers for power engineering, agricultural process equipment, air conditioning systems, ventilation and heat supply.

It is proposed to use an imitation model with a black globe thermometer to analyze the processes of the room thermal regime formation. The model is verified by the results of a physical experiment. The indicators of the radiation factor are taken into account in the dependences of the average radiation temperature difference on the deviation of the temperature of the globe thermometer. On the basis of the proposed model, numerical experiments are performed on the example of a room model with heat-emitting panels and a cooled ceiling

The operation of an electrode under transient conditions, in particular the possibility for instabilities is considered. Various simplified models are analysed to determine whether or not instabilities might occur, and if so, over what parameter ranges.

Many physical and engineering problems can be modeled using partial differential equations such as heat transfer through conduction process in steady and unsteady state. Perturbation methods are analytical approximation method to understand physical phenomena which depends on perturbation quantity. Homotopy perturbation method (HPM) was proposed by Ji Huan He. HPM is considered as effective method in solving partial differential equations. The solution obtained by HPM converges to exact solution, which are in the form of an infinite function series. Biazar and Eslami proposed new homotopy perturbation method (NHPM) in which construction of an appropriate homotopy equation and selection of appropriate initial approximation guess are two important steps. In present work, heat flow analysis has been done on a rod of length L and diffusivity α using HPM and NHPM. The solution obtained using different perturbation methods are compared with the solution obtained from most common analytical method separation of variables.

Gas flow and heat transfer in confined geometries at micro and nano scales differ considerably from those at macro-scales, mainly due to nonequilibrium effects such as velocity slip and temperature jump. The nonequilibrium effects enhance with a decrease in the characteristic length-scale of the fluid flow or the gas density, leading to the failure of the standard Navier-Stokes-Fourier (NSF) equations in predicting thermal and fluid flow fields. The direct simulation Monte-Carlo (DSMC) method is employed in the present work to investigate pressure-driven nitrogen flow in divergent microchannels with various divergence angles and isothermal walls. The thermal fields obtained from numerical simulations are analysed for different inlet-to-outlet pressure ratios (1.5 $\leq \Pi \leq$ 2.5), tangential momentum accommodation coefficients and Knudsen numbers (0.05 $\leq \mathrm{Kn} \leq$ 12.5), covering slip to free-molecular rarefaction regimes. The thermal field in the microchannel is predicted, heat-lines are visualised, and the physics of heat transfer in the microchannel is discussed. Due to the rarefaction effects, the direction of heat flow is largely opposite to that of the mass flow. However, the interplay between thermal and pressure gradients, which are affected by geometrical configurations of the microchannel and applied boundary conditions, determines the net heat flow direction. Additionally, the occurrence of thermal separation and cold-to-hot heat transfer (also known as anti-Fourier heat transfer) in divergent microchannels is explained., Comment: 18 pages, 11 figures

The inductive component is the only missing components in thermal circuits unlike their electromagnetic counterparts. Herein, we report an electrically controllable reverse heat flow, which can be regarded as a proper equivalent of the “thermoinductive” effect. The underlying concept is the heating and cooling of the ends of the material by the Peltier effect under an applied ac current; this form a negative temperature gradient in the opposite direction in a controllable manner. We have derived the exact solution indicating that this reverse heat flow occurs universally in solid-state systems, even in conventional metallic Cu, and that it is considerably enhanced by thermoelectric properties (i.e., a large Seebeck coefficient and low thermal conductivity). A local cooling of 25 mK was demonstrated in (Bi,Sb)2Te3, which was explained by our exact solution. This electrically controlled reverse heat flow is directly applicable to the fabrication of a “thermoinductor” in thermal circuits.

Evaporation from bare soil is an important hydrological process which influences the water and energy budget at all scales. Modelling soil evaporation is complex because it involves coupled liquid, vapor and heat flow. Although high-quality experimental data and use of different boundary conditions is mandatory to validate theory and to discriminate between models, many controlled experiments are still restricted to single boundary conditions. We conducted laboratory bare-soil evaporation experiments with a sand and a silt loam with three atmospheric forcings, (i) wind, (ii) wind and short-wave radiation, and (iii) wind and intermittent short-wave radiation. The soil columns were instrumented with temperature sensors, mini-tensiometers, and relative humidity probes, and evaporation rates were measured gravimetrically. The evaporation experiments were then simulated with a coupled water, vapour and heat flow model. We show that the coupled model reproduces measured evaporation rates and soil state variables (pressure head and temperature) of the evaporation experiments very well. In particular, the onset of stage-two evaporation, characterized by a decrease in evaporation rate and an increase in soil temperature is predicted correctly. Notably, a soil surface resistance, which has been suggested in the literature as a necessary component of evaporation models, led to a gross underestimation of the evaporation rate and a mismatch of the transition to stage-2 evaporation for both soils, for all boundary conditions, and for different soil surface resistance models. This illustrates that the use of resistance factors in coupled water, vapor and heat flow modelling studies is not justified.

The present study highlights an analytical hybrid scheme consisted of a shift of variables and finite integral transform for analysing a local thermal non-equilibrium (LTNE) bioheat model. This model can have utilised to be a betterment of prediction of the temperature field in the localised hyperthermia therapy (LHT) for the treatment of cancer patients. As the hyperthermia treatment is only the application in living tissues, an appropriate initial condition for the therapeutic thermal response is proposed instead of a constant temperature taken in the previous studies based on the 1-D heat flow. The present analysis suggests the therapeutic exposure time of 7776.8s (2.16 h) with constant heat flux and the exposure time of 10969.9s (3.06 h) with a sinusoidal heat flux within the usual temperature range of the hyperthermia (in a combination of thermal ablation and medium temperature hyperthermia) to be more effective in the treatment protocol. The presented results show that fatal injuries (tissue trauma, thermal burn, etc.) of internal organs might be possible to avoid by the current therapeutic condition. Therefore, this study may nullify the adverse effect of the existing model with the constant heating and consequently, the repercussion of the several therapeutic variables is to estimate with the development of a thermal profile for the suitability of a therapeutic condition. On the other hand, the present study well matches with the published analysis in case of both the theoretical and experimental (live tissues of the pig due to unavailability of real-time data on the human body) studies and it found the maximum deviation of the thermal response as 2.26% and 2.66%, respectively.