Applying properties of the Laplace transform, the transient heat diffusion equation can be transformed into a fractional (extraordinary) differential equation. This equation can then be modified, using the Fourier Law, into a unique expression relating the local value of the time-varying temperature (or heat flux) and the corresponding transient heat flux (or temperature). We demonstrate that t...

Numerical continuation is used to follow branches of steady solutions to the three-dimensional Marangoni–Bénard problem in a zero gravity environment. The upper surface of the fluid is heated by a constant heat flux while the bottom is maintained at a constant temperature. Instability arises due to temperature-dependent surface tension effects but surface deflection is ignored. Containers with ...

Computational and mathematical models provide an important compliment to experimental studies in the development of solar energy engineering in case of electro-conductive magnetic micropolar polymers. Inspired by further understanding the complex fluid dynamics of these processes, we examine herein the non-linear steady, hydromagnetic micropolar flow with radiation and heat source/sink effects ...

The continuous casting process of metals and alloys is nowadays frequently utilized in metallurgical industry, and more general in material engineering. Typically, the liquid material flows into the mould (crystallizer) having the walls cooled by flowing water. The solidifying ingot is pulled out by the withdrawal rolls. Below the mould the side surface of the ingot is very intensively cooled b...

A boundary element method is applied for the numerical solution of a boundary value problem for a two-dimensional steady-state bioheat transfer model of the human eye. The human eye is modeled as comprising four distinct homogeneous regions. The boundary condition on the outer surface of the cornea is non-linear due to heat radiation. An iterative approach is used to treat the non-linear heat r...

An immersed-boundary method, previously developed for flow-field simulation, is extended to study heat-transfer problems of flow over a circular cylinder. The Dirichlet-type isothermal temperature boundary conditions and the Neumann-type iso-heat-flux boundary conditions are both implemented. To verify the accuracy of the simulation method, L2-norm are computed to test the order of accuracy of ...

A thorough analysis of the stability of the uncoupled Rooth interhemispheric three-box model of thermohaline circulation (THC) is presented. The model consists of a northern high-latitude box, a tropical box, and a southern high-latitude box, which correspond to the northern, tropical, and southern Atlantic Ocean, respectively. Restoring boundary conditions are adopted for the temperature varia...

the heat and mass transfer analysis for mhd casson fluid boundary layer flow over a permeable stretching sheet through a porous medium is carried out. the effect of non-uniform heat generation/absorption and chemical reaction are considered in heat and mass transport equations correspondingly. the heat transfer analysis has been carried out for two different heating processes namely; the prescr...

It is found in many film-cooling experiments and computational analyses that a heated surface is employed to simulate the actual film-cooling condition with a cooling jet and a hot main flow. Considering that the dominant energy passage in turbine airfoil film cooling is always from the hot combustion gas flowing into the airfoil, employing a heated surface to simulate the actual film cooling c...

in the present work, study of the vibration of a functionally graded (fg) cylindrical shell made up of stainless steel, zirconia, and nickel is presented. free vibration analysis is presented for fg cylindrical shells with simply supported-simply supported and clamped–clamped boundary condition based on temperature independent material properties. the equations of motion are derived by hamilton...