Conjugate natural convection-conduction heat transfer in a square enclosure with a finite wall thickness is studied numerically in the present paper. The governing parameters considered are the Rayleigh number (5 × 10(3) ≤ Ra ≤ 10(6)), the wall-to-fluid thermal conductivity ratio (0.5 ≤ Kr ≤ 10), and the ratio of wall thickness to its height (0.2 ≤ D ≤ 0.4). The staggered grid arrangement together with MAC method was employed to solve the governing equations. It is found that the fluid flow and the heat transfer can be controlled by the thickness of the bottom wall, the thermal conductivity ratio, and the Rayleigh number.
Nano-cryosurgery is one of the effective ways to treat cancerous cells with minimum harm to healthy adjacent cells. Clinical experimental research consumes time and cost. Thus, developing a mathematical simulation model is useful for time and cost-saving, especially in designing the experiment. Investigating the Casson nanofluid's unsteady flow in an artery with the convective effect is the goal of the current investigation. The nanofluid is considered to flow in the blood arteries. Therefore, the slip velocity effect is concerned. Blood is a base fluid with gold (Au) nanoparticles dispersed in the base fluid. The resultant governing equations are solved by utilising the Laplace transform regarding the time and the finite Hankel transform regarding the radial coordinate. The resulting analytical answers for velocity and temperature are then displayed and visually described. It is found that the temperature enhancement occurred by arising nanoparticles volume fraction and time parameter. The blood velocity increases as the slip velocity, time parameter, thermal Grashof number, and nanoparticles volume fraction increase. Whereas the velocity decreases with the Casson parameter. Thus, by adding Au nanoparticles, the tissue thermal conductivity enhanced which has the consequence of freezing the tissue in nano-cryosurgery treatment significantly.
The effect of radiation on magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet was studied. The governing system of partial differential equations was transformed into ordinary differential equations before being solved numerically by an implicit finite-difference method. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. It was found that the local heat transfer rate at the surface decreases with increasing values of the magnetic and radiation parameters.
The aim of the present numerical study is to analyze the conjugate natural convection heat transfer in a differentially heated square enclosure containing a conductive polygon object. The left wall is heated and the right wall is cooled, while the horizontal walls are kept adiabatic. The COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parameters considered are the polygon type, 3 ≤ N ≤ ∞, the horizontal position, 0.25 ≤ X 0 ≤ 0.75, the polygon size, 0 ≤ A ≤ π/16, the thermal conductivity ratio, 0.1 ≤ K r ≤ 10.0, and the Rayleigh number, 10(3) ≤ Ra ≤ 10(6). The critical size of the solid polygon was found exists at low conductivities. The heat transfer rate increases with the increase of the size of the solid polygon, until it reaches its maximum value. Here, the size of the solid polygon is reaches its critical value. Further, beyond this critical size of the solid polygon, will decrease the heat transfer rate.
The solar flat plate collector operating under different convective modes has low efficiency for energy conversion. The energy absorbed by the working fluid in the collector system and its heat transfer characteristics vary with solar insolation and mass flow rate. The performance of the system is improved by reducing the losses from the collector. Various passive methods have been devised to aid energy absorption by the working fluid. Also, working fluids are modified using nanoparticles to improve the thermal properties of the fluid. In the present work, simulation and experimental studies are undertaken for pipe flow at constant heat flux boundary condition in the mixed convection mode. The working fluid at low Reynolds number in the mixed laminar flow range is undertaken with water in thermosyphon mode for different inclination angles of the tube. Local and average coefficients are determined experimentally and compared with theoretical values for water-based Al2O3 nanofluids. The results show an enhancement in heat transfer in the experimental range with Rayleigh number at higher inclinations of the collector tube for water and nanofluids.
Magnetic field influence on unsteady free convection flow of a second grade fluid near an infinite vertical flat plate with ramped wall temperature embedded in a porous medium is studied. It has been observed that magnitude of velocity as well as skin friction in case of ramped temperature is quite less than the isothermal temperature. Some special cases namely: (i) second grade fluid in the absence of magnetic field and porous medium and (ii) Newtonian fluid in the presence of magnetic field and porous medium, performing the same motion are obtained. Finally, the influence of various parameters is graphically shown.
Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions.
This paper studies the heat transfer analysis caused due to free convection in a vertically oscillating cylinder. Exact solutions are determined by applying the Laplace and finite Hankel transforms. Expressions for temperature distribution and velocity field corresponding to cosine and sine oscillations are obtained. The solutions that have been obtained for velocity are presented in the forms of transient and post-transient solutions. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. Numerical computations and graphical illustrations are used in order to study the effects of Prandtl and Grashof numbers on velocity and temperature for various times. The transient solutions for both cosine and sine oscillations are also computed in tables. It is found that, the transient solutions are of considerable interest up to the times t = 15 for cosine oscillations and t = 1.75 for sine oscillations. After these moments, the transient solutions can be neglected and, the fluid moves according with the post-transient solutions.
Over the last few decades, cubic splines have been widely used to approximate differential equations due to their ability to produce highly accurate solutions. In this paper, the numerical solution of a two-dimensional elliptic partial differential equation is treated by a specific cubic spline approximation in the x-direction and finite difference in the y-direction. A four point explicit group (EG) iterative scheme with an acceleration tool is then applied to the obtained system. The formulation and implementation of the method for solving physical problems are presented in detail. The complexity of computational is also discussed and the comparative results are tabulated to illustrate the efficiency of the proposed method.
This study offers the numerical solutions for the problem of mixed convection stagnation-point flow along a permeable
vertical flat plate in an Oldroyd-B fluid. The present investigation considers the effects of thermal radiation and heat
generation/absorption in the fluid flow. The similarity transformation simplifies the complex model and the bvp4c function
generates the numerical solutions according to the variations in the governing parameters. A higher degree of shrinking
hastens flow separations. The dual solutions are visible in the range of buoyancy opposing flow. The results from this study
may be useful for the scientist to understand the behaviour of the dilute polymer solutions in the industrial applications,
for example, the drag reduction in pipe flows.
In this study, the effects of suction and injection on the mixed convection flow of a nanofluid, over a moving permeable
vertical plate were discussed. A similarity variable was used to transform the governing equations to the ordinary
differential equations, which were then solved numerically using the bvp4c programme from MATLAB. Dual solutions
(upper and lower branches) were found within a certain range of the mixed convection parameter in assisting and
opposing flow regions. A stability analysis was implemented to confirm that the upper branch solution was stable, while
the lower branch solution was unstable.
Effects of radiation on free convection about a heated horizontal circular cylinder in the presence of heat generation is investigated numerically. The cylinder is fixed and immersed in a stationary fluid, in which the temperature is uniformly heated about the temperature of the surrounding fluid. The governing equations are transformed into dimensionless non-linear partial differential equations and solved by employing a finite difference method. An implicit finite difference scheme of Crank Nicolson method is used to analyze the results. This study determined the effects of radiation parameter, heat generation parameter, and the Prandtl number, on the temperature and velocity profiles. The results of the local heat transfer and skin-friction coefficient in the presence of radiation for some selected values of and are shown graphically.
In this paper, the problem of free convection boundary layer flow on a horizontal circular cylinder in a nanofluid with viscous dissipation and constant wall temperature is investigated. The transformed boundary layer equations are solved numerically using finite difference scheme namely the Keller-box method. Numerical solutions were obtained for the reduced skin friction coefficient, Nusselt number and Sherwood number as well as the velocity and temperature profiles.The features of the flow and heat transfer characteristics for various values of the Brownian motion parameter, thermophoresis parameter, Lewis number and Eckert number were analyzed and discussed.
The heat and mass transfer of steady magnetohydrodynamics of dusty Jeffrey fluid past an exponentially stretching sheet in the presence of thermal radiation have been investigated. The main purpose of this study is to conduct a detailed analysis of flow behaviour of suspended dust particles in non-Newtonian fluid. The governing equations hav been converted into dimensionless form, and then solved numerically via the Keller-box method. The expression of Sherwood number, Nusselt number and skin friction have been evaluated, and then displayed in tabular forms. Velocity, temperature and concentration profiles are presented graphically. It is observed that large value of dust particles mass concentration parameter has reduced the flow velocity significantly. Increase in radiation parameter enhances the temperature, whereas the increment in Schmidt number parameter reduces the concentration.
The control effects on the convection dynamics in a viscoelastic fluid-saturated porous medium heated from below and cooled from above are studied. A truncated Galerkin expansion was applied to balance equations to obtain a four-dimensional generalized Lorenz system. The dynamical behavior is mainly characterized by the Lyapunov exponents, bifurcation, and isospike diagrams. The results show that within a range of moderate and high Rayleigh numbers, proportional controller gain is found to enhance the stabilization and destabilization effects on the thermal convection. Furthermore, due to the effect of viscoelasticity, the system exhibits remarkable topological structures of regular regions embedded in chaotic domains.
Background: The thermally-induced urine flow can generate cooling that may alter the treatment outcome during hyperthermic treatments of bladder cancer. This paper investigates the effects of natural convection inside the bladder and at skin surface during gold nanorods (GNR) - assisted photothermal therapy (PTT) of bladder cancer in mice. Methods: 3D models of mouse bladder at orientations corresponding to the mouse positioned on its back, its side and its abdomen were examined. Numerical simulations were carried out for GNR volume fractions of 0.001, 0.005 and 0.01% and laser power of 0.2 and 0.3 W. Results: The obtained results showed that cooling due to natural convection inside the bladder and above the skin depends on the mouse orientation. For a mouse positioned on its back, on its side or on its abdomen, the maximum temperature achieved inside the tumour at 0.001% GNR volume fraction and 0.2 W laser power was 55.2°C, 50.0°C and 52.2°C, respectively compared to 56.8°C when natural convection was not considered. The average thermal gradients when natural convection was considered were also lower, suggesting a more homogenous temperature distribution. Conclusions: Natural convection inside the bladder can be beneficial but also detrimental to GNR-assisted PTT depending on the level of heating. At low levels of heating due to low GNR volume fraction and/or laser power, flow inside the bladder may dissipate heat from the targeted tissue; making the treatment ineffective. At high levels of heating due to high GNR volume fraction and/or laser power, cooling may prevent excessive thermal damage to surrounding tissues.
This study analysed mixed convection heat transfer for thermally developing flow in a side heated square duct with varying inclination angles. The test section consists of one-side heated isothermal wall and three adiabatic walls. The inclination angle varied from 00C, and heat flux ranging from 252 W/m2C to 100o30o 858 to 1788 and the wall surface emissivity was considered to be 0.05 and 0.85. Flow visualizations were carried out to obtain the flow structure of natural convection and mixed convection for three inclination angles. The variation of surface temperature along the length of the test section was studied to calculate the convective Nusselt number. The result showed that the heat transfer enhancement and convective Nusselt number was significantly affected by the variations of inclination angle, flow velocity, Reynolds number, and the surface radiation. It was also observed that the increase in the inclination angle improved convection rate and hence significantly enhanced heat transfer. to 200, with hot wall temperature ranging from to 872 W/m2
Linear stability analysis was used to investigate the onset of Marangoni convection in a two-layer system. The system comprised a saturated porous layer over which was a layer of the same fluid. The fluid was heated from below and the upper free surface was deformable. At the interface between the fluid and the porous layer, the Beavers-Joseph slip condition was used and in the porous medium the Darcy law was employed to describe the flow. Predictions for the onset of convection were obtained from the analysis by the perturbation technique. The effect of surface deformation and depth ratio, z (which is equal to the depth of the fluid layer/depth of the porous layer) on the onset of fluid motion was studied in detail.
This scientific report investigates the heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate with constant wall temperature. The problem is modelled in terms of coupled partial differential equations with initial and boundary conditions. Some suitable non-dimensional variables are introduced in order to transform the governing problem into dimensionless form. The resulting problem is solved via Laplace transform method and exact solutions for velocity, shear stress and temperature are obtained. These solutions are greatly influenced with the variation of embedded parameters which include the Prandtl number and Grashof number for various times. In the absence of free convection, the corresponding solutions representing the mechanical part of velocity reduced to the well known solutions in the literature. The total velocity is presented as a sum of both cosine and sine velocities. The unsteady velocity in each case is arranged in the form of transient and post transient parts. It is found that the post transient parts are independent of time. The solutions corresponding to Newtonian fluids are recovered as a special case and comparison between Newtonian fluid and Maxwell fluid is shown graphically.
Baking temperature and time are among the conditions for producing good quality cakes. The aim of this study was to investigate the effects of baking temperature and time on the volume expansion, moisture content, and texture of moist cakes baked in either an air fryer or a convection oven. The cakes were baked under different conditions: (1) baking temperature of 150 °C, 160 °C, and 170 °C for both air fryer and convection oven and (2) baking time of 25, 30, 35 min for air fryer and 35, 40, 45 min for convection oven. Baking temperature and time were found to have a significant (p