This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...

The aim of this paper is to enhance thermal performance of a microchannel heat sink by using nanoencapsulated phase change material (NEPCM) slurry as a cooling fluid instead of pure fluid. A threedimensional model of a circular channel using water slurry of NEPCM was developed. The results show a significant reduction in the mean fluid temperature along the channel and heat sink wall temperatu...

We sketch a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.

Surface heat flux estimation using temperature measurement data from the interior points is known as inverse heat conduction problem (IHCP). Several methods have been developed as solution techniques for IHCP’s including analytical and numerical approaches. Digital filter representation for IHCP solution (Woodbury and Beck, 2013; Beck et al., 1985) is one of the methods which can be used for ne...

We investigate the response of conductive and convective ice shells on Europa to variations of heat flux and interior tidal-heating rate. We present numerical simulations of convection in Europa’s ice shell with Newtonian, temperature-dependent viscosity and tidal heating. Modest variations in the heat flux supplied to the base of a convective ice shell, F , can cause large variations of the ic...

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...

Transient heat conduction in semi-infinite medium with a time dependent flux as boundary condition has been solved by semi-derivative integral-balance method. Two versions fluxes have considered: power-law and exponential.

This computational study investigates the nonlinear dynamics of unstable convection in a 2D thermal convection loop (i.e., thermosyphon) with heat flux boundary conditions. The lower half of the thermosyphon is subjected to a positive heat flux into the system while the upper half is cooled by an equal-butopposite heat flux out of the system. Water is employed as the working fluid with fully te...

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...