Insight into the dynamics of a Newtonian fluid through a rectangular domain with an emphasis on heat transfer

Fluid flow coupled with temperature effects has attained prime importance due to its huge applications in different fields like casting and welding industries, geothermal extraction, and lubrication technologies. The present study is a novel numerical method for computations for fluid flow with temperature effects in a rectangular domain. A control volume method is employed as a numerical method for solving continuity, momentum, and energy equations. Owing to the difficulties associated with solving these governing equations, numerical computations are presented in the computational grid by using the control volume method. A modified algorithm is suggested for the current problem. The magnitude of the velocity, temperature, and pressure at different nodes in horizontal and vertical directions of the computational domain is investigated. Along the diagonal nodes, the pressure declines and then grows consistently. The temperature for mercury $\left(Pr=0.015\right)$ is higher than for water $\left(Pr=6.57\right)$ at a particular node.