The conjugated temperature distributions of a microchannel fluid flow between two semi-infinite parallel plates are obtained analytically. The variables separation and transformation techniques are implemented to introduce the degenerate hypergeometric differential equation, the solution of which is given in terms of Kummer’s functions. The eigenvalues of the corresponding transcendental characteristic equation are obtained using a mathematical solver software package. Non-dimensional analysis of the governing equations introduced the parameter of “solid-fluid heat conduction ratio” \(k_k\). Values of this parameter are considered to present two limiting case solutions, namely, the adiabatic boundary solution, when \(k_k\approx 0\) and the isothermal boundary solution, when \(k_k> 100\). The Nusselt number \(Nu\) of the two limiting solutions is obtained and compared accurately with the corresponding values from the literature. The effect of the Knudsen number \(Kn\), the Biot number \(Bi\), and the conductivity ratio \(k_k\) on the temperature, temperature jump, and the Nusselt number is investigated. It is found that the temperature jump near the flow entrance becomes more significant with increase in \(Kn\), \(Bi\), or \(k_k\). On the other hand, the Nusselt number is found to increase with growing \(Kn\) and decrease with increasing \(Bi\) or \(k_k\).
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Al-shyyab, A.S., Darwish, F.H., Al-Nimr, M.A. et al. Title Analytical Study of Conjugated Heat Transfer of a Microchannel Fluid Flow between Two Parallel Plates. J. Engin. Thermophys. 29, 114–135 (2020). https://doi.org/10.1134/S1810232820010099