Analytical solution for the transient temperature distribution in a moving rod or plate of finite length with surface heat transfer

Convection-radiation from a continuously moving, variable thermal conductivity sheet or rod undergoing thermal processing

“…The choice of insulated boundary condition at x ¼ L or X ¼ L * may not reflect the physics in its entirety but such a choice has been made in the pioneering papers by Karwe and Jaluria [13], Choudhry and Jaluria [20] and Jaluria and Singh [21] and found to provide satisfactory approximations to the more realistic condition except when L * and Pe are small. However, we did carry out the computations where this condition was replaced by a condition qðL * Þ ¼ cq a where c is constant.…”

“…The resulting ordinary differential equation for the steady state or the partial differential equation for the transient state, is then solved analytically or numerically. For example, Choudhry and Jaluria [20] obtained a double series solution for the twodimensional, transient temperature distribution in a moving rod or a flat plate moving with a constant velocity and losing heat by convection to the ambient fluid through a constant heat transfer coefficient. The same problem was solved numerically in a then contemporary paper by Jaluria and Singh [21].…”

An Investigation of Optimized Length Scales of the Heat Treatment of Metallic Plates

“…Choudhaury and Jaluria [14] have obtained an analytical solution for the two-dimensiona l unsteady heat conduction equation, with the presence of the convective term in the axial direction and a uniform boundary condition, by employing the coordinate transformation. The nal solution is obtained by superpositio n of both "pseudo-steady " and "pseudo-transient " parts.…”

Convective-radiative fin with temperature dependent thermal conductivity, heat transfer coefficient and wavelength dependent surface emissivity

“…Karwe and Jaluriya [6] used Crank-Nicolson finite difference method to compute the temperature fields in the fluid and in the moving material. Choudhury and Jaluria [7] found a double series solution for the two dimensional, transient temperature distributions in a moving rod or a plate moving with a constant speed and losing heat by convection to the ambient fluid through a constant heat transfer coefficient. Aziz and Lopez [8] studied the heat transfer process in a continuously moving sheet or rod of variable thermal conductivity that releases heat by simultaneous convection and radiation.…”