Nonhomogeneous Heat Conduction Problem and Its Thermal Deflection Due to Internal Heat Generation in a Thin Hollow Circular Disk

This article is concerned with the determination of temperature and thermal deflection in a thin hollow circular disk under an unsteady-state temperature field due to internal heat generation within it. Initially, the disk is kept at an arbitrary temperature F(r, z). For times t > 0 heat is generated within the thin hollow circular disk at a rate of g(r, z, t) Btu/hr ft³, while the boundary surfaces at (r = a), (r = b), (z = 0) and (z = h) are kept at temperatures f ₁(z, t) and f ₂(z, t), f ₃(r, t) and f ₄(r, t), respectively. The governing heat conduction equation has been solved by using a finite Hankel transform and the generalized finite Fourier transform. The results are obtained in series form in terms of Bessel's functions. As a special case, different metallic disks have been considered. The results for temperature change and the thermal deflection have been computed numerically and illustrated graphically.     

Buckling of stiffened plates and design of stiffeners

This paper presents a closed-form solution of critical instability stresses for simply supported rectangular plates with an arbitrary number of stiffeners in longitudinal and/or transverse directions. It is shown that there are only two buckling modes that are coupled to each other for single direction stiffened plates and four for double direction stiffened plates. The coupling of buckling modes represents the feature of interactions of global and local buckling modes. It is also shown that stiffeners have twofold effects on the critical instability stress, one is by enhancing the “stiffness”, the other is by changing the buckling mode. Because of the twofold effects it becomes difficult to apply the conventional optimum method to design the stiffeners and the optimum design of stiffeners still remains a difficult problem. This paper discusses the way by which the stiffeners can effectively enhance the buckling resistance of plates.     

Nonlinear thermal stability of eccentrically stiffened FGM double curved shallow shells

This article presents analytical solutions for the nonlinear static and dynamic stability of imperfect eccentrically stiffened functionally graded material (FGM) higher order shear deformable double curved shallow shell on elastic foundations in thermal environments. It is assumed that the shell’s properties depend on temperature and change according to the power functions of the shell thickness. The shell is reinforced by the eccentrically longitudinal and transversal stiffeners made of full metal. Equilibrium, motion, and compatibility equations are derived using Reddy’s higher order shear deformation shell theory and taking into account the effects of initial geometric imperfection and the thermal stress in both the shells and stiffeners. The Galerkin method is applied to determine load–deflection and deflection–time curves. For the dynamical response, motion equations are numerically solved using Runge–Kutta method. The nonlinear dynamic critical buckling loads are found according to the criterion suggested by Budiansky–Roth. The influences of inhomogeneous parameters, dimensional parameters, stiffeners, elastic foundations, initial imperfection, and temperature increment on the nonlinear static and dynamic stability of thick FGM double curved shallow shells are discussed in detail. Results for various problems are included to verify the accuracy and e?ciency of the approach.     

Investigation of thermal performance of solar air heater having roughness elements as a combination of inclined and transverse ribs on the absorber plate

An experimental investigation has been carried out to study the heat transfer and friction characteristics by using a combination of inclined as well as transverse ribs on the absorber plate of a solar air heater. The experimental investigation encompassed the Reynolds number (Re) ranges from 2000 to 14 000, relative roughness pitch (p/e) 3–8 and relative roughness height (e/D_h) 0.030. The effect of these parameters on the heat transfer coefficient and friction factor has been discussed in the present paper and correlations for Nusselt number and friction factor has been developed within the reasonable limits. A procedure to compute the thermal efficiency based on heat transfer processes in the system is also given and the effect of these parameters on thermal efficiency has been discussed.     

A numerical study integrated with RSM for hydrothermal and entropy performance of porous jet impingement

The thermohydraulic and thermodynamic performance of porous jet impingement under pressure drop effect has not yet been jointly published. Thus, the novelty of this work computationally along with the response surface methodology (RSM) optimization approach considers the porous jet impingement performance linked with a pressure drop simultaneously. Also, the current study used a novel multiobjective optimum design study for various design parameters, such as porosity (ε), Darcy number (Da), and pore per inch (PPI), under numerical simulation assessment of forced laminar convection of jet impingement with full and partial metal foam. The influence of various base plate thicknesses (t = 0, 1, 2, and 3 mm), various nanofluids (Al₂O₃, CuO, SiO₂, and ZnO), and the metal foam size percentage (W/L = 0, 0.25, 0.5, 0.75, and 1) on the improvement of the thermohydraulic and thermodynamic performance is also simulated. Results indicated that utilizing pure water and a metal foam size (W/L) of 1 along with a base plate thickness of 0 mm produced the preferable thermohydraulic and thermodynamic performance. Furthermore, according to an optimization analysis, the current study's objective for the thermohydraulic and thermodynamic performance of jet impingement can be achieved using the parameters porosity ε = 0.1, Darcy number, Da = 1, and the PPI = 15. Therefore, this investigation integrating computational fluid dynamics and RSM offers considerable innovation and useful reference for the optimum design of a porous jet impingement cooling.     

Thermal stability of eccentrically stiffened FGM plate on elastic foundation based on Reddy's third-order shear deformation plate theory

This article studies the nonlinear thermal buckling and postbuckling of eccentrically stiffened functionally graded plates on elastic foundation subjected to mechanical, thermal, and thermomechanical loads. The noticeable point of this study is using the Reddy's higher order shear deformation plate theory and a general formula for the forces and moments of eccentrically stiffened functionally graded material (FGM) plate, which takes into account the influence of temperature on both the FGM plate and stiffeners. The article used the Galerkin method, stress function, and iterative method to determine the thermal buckling loads and postbuckling response of the eccentrically stiffened FGM plates in three different cases of boundary conditions. The effects of material, temperature-dependent material properties, elastic foundations, boundary conditions, outside stiffeners, and temperature on the buckling and postbuckling loading capacity of the FGM plates in thermal environments are analyzed and discussed. A good agreement is obtained by comparing the present analysis with other available literature.     

Analysis of a magnetic field and Hall effects in nanoliquid flow under insertion of dust particles

In this study, the two‐phase hydromagnetic flow of a viscous liquid through a suspension of dust and nanoparticles is considered. The influence of the Hall current is also taken into account. The similarity variables are utilized to transform the problem into one independent variable. The obtained expressions in one independent variable are solved through the Runge–Kutta–Fehlberg scheme connected with the shooting procedure. The computed results are sketched for employing multiple values of physical constraints on the temperature and velocity of the nanofluid and dust phase. The characterization of various nanoparticles like Cu, Al₂O₃, TiO_2, and Ag on velocities and temperatures of both phases is made through plots. A comparative analysis in the limiting approach is presented to justify the present solution methodology. The range of emerging parameters is taken as 0 ≤ l ≤ 3, 0.1 ≤ β_t ≤ 3, 0 ≤ m ≤ 2.5, 0 ≤ M² ≤ 2, 0.1 ≤ β_v ≤ 3, 0 ≤ ? ≤ 0.4, and ?0.8 ≤ λ ≤ 0.8. From the study, it is revealed that β_t has the opposite effect on the temperature of dust and nanofluid phases. The Hall parameter m raises the profiles of velocities in the nanoliquid and dust phases. Also, it is found that the transverse velocities h(η) and H((η) and temperatures θ(η) and θ_p(η) rise for larger ?.     

Heat transfer and bubble characteristics in a fluidized bed with immersed horizontal tube bundle

The effect of gas velocity on the average and local heat transfer coefficients between a submerged horizontal tube (25.4 mm-OD) and a fluidized bed has been determined in a fluidized-bed-heat-exchanger (0.34×0.50×0.6 m-high) of silica sand particles. The heat transfer coefficients and the properties of bubble and emulsion phases were simultaneously measured at the same location around the tube circumference by thermocouples and an optical probe. The average heat transfer coefficient (h_avg) exhibits a maximum value with variation of gas velocity (U_g). The local heat transfer coefficient (h_i) exhibits maximum values at the side of the tube (0°). Bubble frequency (f_b) increases and the emulsion contacting time (t_e) decreases with increasing U_g. The h_i increases with increasing f_b and decreasing t_e. The f_b exhibits higher values and t_e is shorter at the bottom (under each side) than those at the top section of the tube. The t_e and bubble fraction (δ_b) have been correlated with Froude number. The predicted h_avg values of small particles based on the packet renewal model and the emulsion contacting characteristics around the tube well accord to the experimental data.     

A Lie-Group Adaptive Method to Identify Spatial-Dependence Heat Conductivity Coefficients

We consider an inverse problem for numerically estimating a spatial-dependence heat conductivity α(x) in T _t (x, t) = ?[α(x)T _x ]/? x + h(x, t), 0 < t < t _f , 0 < x < ?; α(x) is assumed to be a continuous function of x, and α(?) is given. An iterative Lie-group adaptive method (LGAM) is developed, which can be used to find α(x) at the spatially discretized locations x _i , requiring only a few measured temperature data at a final time t _f as a target to select a suitable value of the parameter r ∈ [0, 1] appearing in the present method. The new method has three advantages in that no a priori information of the heat conductivity function is required, only a few extra data are measured, and it is robust againt noise. The accuracy and efficiency of the present method are confirmed by comparing the estimated results with some exact solutions.     

Experimental evaluation of the wind convection heat transfer on the glass cover of the single-slope solar still

Accurate evaluation of the wind convection heat transfer coefficient (h_w) for solar-based systems is essential, especially for solar desalination systems. Thermal behavior and productivity of solar stills are highly affected by the external heat loss through the glass cover. This paper describes a new experimental approach to estimate the h_w on the glass cover of the conventional single-slope solar distiller (CSS). Indoor experiments have been conducted under steady-state conditions for a wind speed between 0 and 3 m/s. The h_w has been evaluated through an energy balance performed on the distiller's glass cover. The results showed that increasing the wind speed increases the hw (from 5.64 to 31.57 W/m² K) and enhances the distillation rate (from 5.28 to 7.61 mL/min). A new relationship for the h_w was proposed for the CSS and compared with the experimental data available in the literature. The comparison shows that the obtained results are close to the data from solar systems, with a deviation ranging from 27.4% to 37%. However, a significant deviation was obtained with earlier models derived from flat plates (from 29.5% to 59%).     

Influence of longitudinal obstacle spacing on the deflagration-to-detonation transition through a bank of obstacles in a hydrogen-air mixture

Flame acceleration and deflagration-to-detonation transition (DDT) in a channel containing an array of staggered cylindrical obstacles and a stoichiometric hydrogen-air mixture were studied by solving the fully-compressible reactive Navier-Stokes equations using a high-order numerical algorithm and adaptive mesh refinement. Four different longitudinal spacings (ls) of the neighboring obstacle rows (i.e., ls = 15.28, 19.1, 25.4, and 38.2 mm, corresponding to 1.2, 1.5, 2 and 3 times of obstacle diameter, respectively) were used to examine the effect of obstacle spacing on flame acceleration and DDT. The results show that the main mechanisms of flame acceleration and transition to detonation in all the cases studied are consistent. While the flame acceleration is caused by the growth of flame surface area in the initial stage, it is governed by shock-flame interactions in the later stage when shock waves are generated. The focusing of strong shocks at flame front is responsible for the initiation of detonation. It was found that the flame propagation speed and the DDT run-up distance and time are highly dependent on ls. Specifically, the flame acceleration declines as ls increases, since a larger ls leads to less disturbance of flow by obstacles per unit channel length. For detonation initiation, both the run-up distance and time increase with the increase of ls. It is interesting to note that the DDT distance and time increase significantly as ls increases from 19.1 mm to 25.4 mm. This is related to the slowdown of the increase rate of energy release over a period before DDT occurs under large ls condition, because every time the flame passes over an obstacle row the shock-flame interaction is delayed and numerous isolated pockets of unburned gas material are formed.     

NONLINEAR RESPONSE OF GEOMETRICALLY IMPERFECT STIFFENED FLAT PANELS UNDER THERMOMECHANICAL LOADING

A study of the nonlinear response of orthogonally stiffened isotropic flat panels exposed to a temperature rise and a lateral pressure field is presented. A theoretical analysis and the numerical results emphasize the effects played by the bi/uniaxial stiffeners and unavoidable initial geometric imperfections on the thermomechanical load-carrying capacity of stiffened panels, and pertinent conclusions are outlined.     

Nonlinear dynamic response of eccentrically stiffened FGM plate using Reddy’s TSDT in thermal environment

The nonlinear dynamics of an eccentrically stiffened functionally graded material (ES-FGM) plates resting on the elastic Pasternak foundations subjected to mechanical and thermal loads is considered in this article. The plates are reinforced by outside stiffeners with temperature-dependent material properties in two cases: uniform temperature rise and through the thickness temperature gradient. Both stiffeners and plate are deformed under temperature. Using Reddy’s third-order shear deformation plate theory, stress function, Galerkin and fourth-order Runge–Kutta methods, the effects of material and geometrical properties, temperature-dependent material properties, elastic foundations, and stiffeners on the nonlinear dynamic response of the ES-FGM plate in thermal environments are studied and discussed. Some obtained results are validated by comparing with those in the literature.     

Applicability of a simple model for computing diffuse solar radiation to locations of the European, African, Asian and North American areas

It is tested if the correlation type D = K(s/S)^−0.25 (sin h_n)^1.55, 0.2 s/S 0.9 previously proposed by Coppolino for Italian locations using K = 7.0, allows a reliable estimation of the monthly mean daily diffuse solar radiation D (MJ m⁻² day⁻¹), from only the monthly mean daily relative sunshine s/S and the noon altitude of the sun on the 15th of the month h_n (degrees) at locations of the European, African, Asian and North American areas. The test is performed at 14 stations in the above areas displaced at various latitudes L, elevations above sea level E and geographical situations, using K = 7.0 for the stations where 0.48 (s/S)_m, 0.63, K = 8.5 for those where 0.40 (s/S)_m < 0.48 or (s/S)_m > 0.63, and K = 10.0 for those where (s/S)_m < 0.40; (s/S)_m is the yearly mean value of s/S. K = 7.0 is chosen for five stations provided only with sunshine measurements and for three of the other nine stations provided with diffuse radiation measured data as well. K = 8.5 is chosen for five of the above nine stations and K = 10.0 for the remaining one. Moreover the prediction validity of the tested correlation is compared with that of two equations commonly quoted in literature: one of D = f(K_t, G) type and the other of D = f (s/S, G) type, where K_t = G/G₀. G and G₀ are the global and extraterrestrial monthly mean daily solar radiation, respectively. The test results point to a good agreement between the measured data of D and values from the above (D = f(s/S, h_n)) equation for eight of the above nine stations (i.e. with the exception of one with E = 2210 m), and deviations are generally low among D-values from the three considered equations, respectively, for the other five stations. Consequently the tested D = f(s/S, h_n) equation, with K-value chosen by the above guidelines, can be considered applicable, with good reliability, to all locations of the above areas provided 30°S < L < 55°N and E < 2000 m.     

Heat transfer augmentation by swirl generators inserted into a tube with constant heat flux

A novel conical injector type swirl generator (CITSG) is devised in this study. Performances of heat transfer and pressure drop in a pipe with the CITSG are experimentally examined for the CITSGs' angle (α) of 30°, 45° and 60° in Reynolds number (Re) range of 10,000–35,000. Moreover, circular holes with different numbers (N) and cross-section areas (A_h) are drilled on the CITSG. In this way, total areas (A_t = N · A_h) of the holes on the CITSG are equaled each other. Besides, flow directors having three different angles (β = 30°, 60° and 90°) to radial direction are attached to every one of the holes. This study is a typical example for decaying flow. All experiments were conduced with air accordingly; Prandtl number was approximately fixed at 0.71. The local Nusselt number (Nu_x), heat transfer enhancement ratio (Nu_ER) and heat transfer performance ratio (Nu_PR) are calculated and discussed in this paper. It is found that the Nu_ER decreases with increase in Reynolds number, the director angle (β), the director diameter (d), and with decrease in the CITSG angle (α). Likewise, variation of Nu_PR and Nu_ER is also essentially similar for the same independent parameters.     

HCFC22-based vapour absorption refrigeration systems. Part II: Influence of component effectiveness

A thermodynamic analysis was performed on a single-stage vapour absorption refrigeration system (VARS) operating with monochlorodifluouromethane (HCFC22) as a refrigerant and dimethylether of tetraethyleneglycol (DMETEG) or dimethyl acitamide (DMA) as a working fluid. Influence of solution heat exchanger effectiveness (E_h) and mass transfer effectivenesses of absorber (E_a) and generator (E_g) on the performance of VARS were studied. The variations in heat quantities at solution heat exchanger, generator and absorber as well as performance characteristics, namely CR, COP_th and second law efficiency (ϵ) at various operating temperatures are reported. As expected, low CR and high COP_th and ϵ can be obtained at high values of E_h, E_a and E_g. The effects of E_h on the performance is more pronounced when compared to that of E_a and E_g. Also, the change in the circulation ratio (CR) due to a given change in E_a is higher than that due to the same change in E_g. CR is not a function of E_h. A comparison of the influence of E_h, E_a, and E_g on the VARS performance for HCFC22-DMA and HCFC22-DMETEG pairs was made.     

Experimental Study on R-410a Evaporation Heat Transfer Characteristics in Oblong Shell and Plate Heat Exchanger

The evaporation heat transfer experiments were conducted with an oblong shell and plate heat exchanger without oil in the refrigerant loop using R-410A, a mixture of 50 wt% R-32 and 50 wt% R-125 that exhibits azeotropic behavior. An experimental refrigerant loop has been established to measure the evaporation heat transfer coefficient h _r of R-410A in a vertical oblong shell and plate heat exchanger. Four vertical counter-flow channels were formed in the oblong shell and plate heat exchanger by four plates having a corrugated trapezoid shape of a 45° chevron angle. The upflow of the boiling R-410A in one channel receives heat from the hot downflow of water in the other channel. The effects of the refrigerant mass flux, average heat flux, refrigerant saturation temperature, and vapor quality of R-410A on the measured data were explored in detail. The results indicate that a rise in the refrigerant mass flux causes an increase in the h _r . Raising the imposed wall heat flux was found to slightly improve h _r . Finally, at a higher refrigerant saturation temperature, the h _r is found to be lower. Based on the present data, an empirical correlation of the evaporation heat transfer coefficient was proposed.     

Catalytically activated stainless steel plates for the dehydrogenation of perhydro dibenzyltoluene

Hydrogen storage and transport via Liquid Organic Hydrogen Carriers (LOHC) is gaining increasing attention. In this study, we present catalytically activated stainless steel plates as a promising alternative to the commonly used pellet catalysts for the dehydrogenation of perhydro dibenzyltoluene (H18-DBT). These plate catalysts promise better heat transport to the active sites. For improved performance, we modified our Pt/alumina plate catalysts by using i) platinum sulfite impregnation and ii) post-treatment with (NH₄)₂SO₄. Post-treatment with (NH₄)₂SO₄ resulted in a less active catalyst with lower formation of high-boiling side products compared to the S-free plate catalyst. Catalysts prepared with platinum sulfite showed both >35% higher activities and 90% reduction in high-boiler formation compared to the S-free plate catalysts. Our findings pave the way for the development of catalytically activated heat transfer plates that would allow the incorporation of LOHC dehydrogenation units into the geometry of future high temperature fuel cell stacks.     

Rate of change of vorticity covariance in MHD turbulent flow of dusty incompressible fluid

In the paper, the rate of change of vorticity covariance in MHD turbulent flow of a dusty fluid is discussed. The results obtained show that the defining scalars α(r, t), β(r, t) and γ(r, t) of the rate of change of vorticity covariance of MHD turbulence depend on the defining scalars W, T, R, P and F of the tensors W_ij, T_ij, R_ij P_{ik, j}, and F_{kj, i} already defined in the problem.