Fundamentals Of Thermal Fluid Sciences 4th Edition Pdf 176 Fix

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Our analysis was based on solving relevant equations for heat transport and fluid flow in the various domains. Within all phases we solved the equation for change of temperature based on an assumption of constant thermal conductivity,

where T, t and v are the temperature, time and velocity vector respectively. The thermal diffusivity of each of the domains is represented by αi where i is an index identifying each of the domains (water, bottle, milk, etc.). It is important to note that the second term on the left hand side of this equation, representing thermal convection, was removed when applying the equation within the solid domains. Within the fluid phases we had to account for flow. This was achieved by solving for the Navier Stokes equation for Newtonian fluids, with the Boussinesq approximation for thermal compressibility, coupled with the continuity equation, which are respectively given by,

where ρi is the density of fluid "i", P is the deviatoric pressure, μ i is the viscosity of fluid "i", βi is the thermal expansion coefficient of fluid "i",g is the gravity vector and T0 is the characteristic (operating) temperature. 2b1af7f3a8