## 1 Introduction  
Natural or mixed convection on a heated layer in a porous medium is a frequently discussed subject. Natural convection heat transfer and fluid flow have been widely investigated in various engineering applications such as solar collectors, drying processes, fire control, geophysics, formations in chemical industries, the storage of radioactive nuclear waste, cooling, and geothermal applications. Numerous investigations on the subject moreover have a wide presence in the literature [1; 2; 3; 4; 5; 6; 7].  
[PERSON] and [PERSON] [8] examined the effects of the Peclet number by studying mixed convection in a porous horizontal channel. They obtained analytical solution porous layers at low Rayleigh number conditions. [PERSON] et al. [9] analytically studied the effects of mixed convection on a flat horizontal layer. The horizontal surface has either been down-feed heated or up-feed cooled. The developing equations were solved using the finite difference method after they have been converted into dimensionless form. [PERSON] and [PERSON] [10] numerically studied the mixed convection within a down-feed heated horizontal channel filled with a porous medium. They had found that Rayleigh and/or the average Nusselt number had increased when the Peclet number was high. [PERSON] [11] investigated the heat characteristics of laminar mixed convection on a horizontal flat plate inserted into a porous medium. [PERSON] et al. [12] numerically and experimentally examined the laminar natural convection in a cavity heated from bottom due to an inclined fin. They had found that heat transfer can be controlled by attaching an inclined fin onto a wall. [PERSON] and [PERSON] [13] studied the effects of radiation on the mixed convection on a horizontal surface in a porous medium, whereby it was assumed that the wall temperature had varied with the distance measured from the edge of the layer. The developing parabolic differential equations were numerically solved using the finite difference method. It was pointed out that heat transfer is strongly influenced by the number of radioactive flow, the temperature change of the wall, the non-dimensional Darcy parameter, and the free flow rate. [PERSON] et al. [14] theoretically studied mixed convection in a narrow vertical pipe filled with a porous medium. Their numerical results had revealed that the analytical and asymptotic solutions were in very good accord. [PERSON] and [PERSON] [15] numerically studied laminar mixed convection in a two-dimensional parallel straight channel filled with porous blocks of varying shapes, and presented the parameters affecting that heat transfer through graphs. [PERSON] and [PERSON] [16] studied mixed convection in a horizontal circuit that produces porous heat, whereupon the external cylinder was cooled, whilst the internal cylinder was heated. What had resulted was the formation of forced convection due to the cool external cylinder at a fixed angle speed. The obtained results had shown that the Richardson number had had an effect upon such flows in the circuit. Similar studies have also been produced and published by [PERSON] and [PERSON] [17], [PERSON] [18], [PERSON] and [PERSON] [19], [PERSON] and [PERSON] [20] and [PERSON] [21].  
In this study, mixed convection heat transfer was studied in a channel filled with a porous medium. Streamlines, isotherms, local and mean Nusselt numbers will be presented in the following sections of the paper for different Rayleigh numbers, the Peclet number, and the location of the heat source. Unlike the literature, the heat transfer in the channel was studied by heating \(1/3\) of the bottom of the channel, as well as by sliding to the up-stream and down-stream equally. The channel's length has been chosen to meet these requirements, which is about 10 times greater than the channel's height. The equations used for the analysis of both the flow and the heat transfer along the channel were numerically solved via the finite difference method.