An investigation of the heat transfer of Newtonian fluid flow through coaxial two pipes with variable radius ratio has been conducted with the boundary conditions of forced convection on the inner pipe walls and a radius magnetic field. This paper presents an exact analytical solution to the momentum equation and a novel semi‐analytic collocation method for solving the full‐term energy equation that takes Joule heating into account as well as viscous dissipation. Based on the results of the numerical fourth‐order Runge–Kutta method, it was found that increasing the magnetic parameter decreased the amount of friction on the surface of the pipe walls and the rate of heat transfer. As the radius ratio of the two pipes increases, so does the skin friction and heat transfer rate on the internal pipe walls. As Eckert (Ec) and Prandtl (Pr) numbers increase, the mean temperature as well as the dimensionless temperature between the two pipes increases. The increase in Biot number (Bi) has the opposite impact on the mean temperature. As Ec, Pr, and Bi increase, so does the rate of heat transfer on the inner wall of the pipe.
In this study, the heat transfer of a laminar, steady, fully developed, and Newtonian fluid flow in a channel is investigated. The main goal of the present study is solving the hydromagnetic Newtonian fluid flow and heat transfer inside a channel with the angular magnetic field and convective boundary conditions on the walls. As a novelty, the effect of thermal diffusion and advection term the walls and Joule heating in the energy equation has been considered. The governing equations include the continuity, momentum, and energy are presented, and considering the assumptions are simplified. Afterward, employing the dimensionless parameters, the governing equations are transformed into dimensionless forms. The exact solution is provided for the momentum equation. For solving the full energy equation, the analytical collocation method (CM) is conducted. The results are validated using the 4th order Runge-Kutta method. The results demonstrated that the dimensionless velocity, the bulk temperature inside the channel, and the channel wall's heat transfer rate decline when the Hartmann number and the magnetic field angle increase. Since the Prandtl and Eckert numbers reduce, the dimensionless temperature becomes more uniform, and the heat transfer rate on the channel wall decreases. Since the Biot number augments, the dimensionless temperature inside the channel reduces, but the channel wall's heat transfer rate first increases and then reduces.
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